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Microwave excited copper halide and strontium-ion recombination lasers

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Microwave excited Copper Halide and
Strontium-ion Recombination Lasers
0
O
Jason W. Bethel
A thesis submitted in application fo r the degree o f
D octor o f Philosophy
in the
School o f Physics and Astronomy
University o f St. Andrews
September 1994.
ProQuest Number: 10166264
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To my Mother and Father
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Declaration
I Jason William Bethel certify that this thesis has been composed by myself, that it is a
record of my own work and that it has not been accepted in partial or complete fulfilment of
any other degree or qualification.
I was admitted to the Faculty of the University of St. Andrews under
Ordinance General No. 12 on the 1st October 1990.
Date ^
Signed
I hereby certify that the candidate has fulfilled the conditions of the
Resolution and Regulations appropriate to the Degree of Ph.D.
Signature of Supervisor
Date
Copyright
In submitting this thesis to the University of St. Andrews, I understand that I am giving
permission for it to be made available for use in accordance with the regulations of the
University Library for the time being in force, subject to any copyright vested in the work
not being affected thereby. I also understand that the title and the abstract will be published,
and that a copy of the work may be made and supplied to any bona fide library or
researcher.
Abstract
Microwave excited Copper halide and Strontium-ion recombination lasers
J. W. Bethel
School of Physics and Astronomy, St. Andrews University
Submitted for the degree o f Doctor of Philosophy
September 1994
Microwave excitation of pulsed metal vapour lasers (copper halide and strontium-ion
recombination lasers) is investigated. Two waveguide coupling structures were designed
and built, one based on a ridge waveguide; and the other based on a rectangulai* waveguide
with a tapered narrow wall which was designed to produce a uniform, travelling
microwave field. These coupling structures were designed to produce a transverse electric
field at high pressure, with high electron densities, using pulsed microwaves with peak
powers of up to 2.5 MW, compatible with the necessary requirements for copper and
strontium based systems. The magnetron power supply was modified to produce double
pulses of variable spacing (between 15 and 500 jis).
Laser oscillation was observed on the cyclic transitions of neutral copper
(A=510.6 and 578.2 nm) and on the recombination transition of singly ionised strontium
(/l=430.5 nm) for the first time in microwave excited systems. The performance of the
tapered waveguide coupling structure was found to be superior to the ridge waveguide
coupling structure. The efficiency of coupling of microwave power into the discharge was
mainly dependent the buffer gas type and pressure and the electron density. At higher
pressures, higher coupling efficiencies aie observed (over 70 percent for pressures of over
500 mbai* of helium). The performance of the lasers using both the coupling stmctures was
poor when compared to conventional copper based lasers. This was attributed to the
interaction of the copper halide with the discharge and a nonuniform temperature
distribution along the axis of the quaitz tube. An average output power of 18 mW was
achieved for both lines in a copper bromide laser. The strontium-ion recombination laser
was operated at threshold average microwave input powers, no output powers were
measured. The electric field and the electron density of the discharges in both laser
systems were estimated and compared with those occurring in the respective conventional
laser systems.
PhD Thesis
J. W. Bethel
Acknowledgements
First of all I would like to thank my supervisor Dr. Chris Little for his help and
encouragement during my PhD. Also Professor Arthur Maitland whose boundless
enthusiasm and dedication will always be an inspiration. Peter and Dave for many useful
and enlightening discussions, especially in the early days (when I didn't have a scoobie).
Natalie for proof reading the substantial sections of this tiresome piece! All the boys in the
workshop, especially Jim Clarke and Dave Nielson; and not forgetting Miles Whyte for
having the insight to "Brass it out". Frits Akerboom for his invaluable glass blowing skills
and Sunday afternoon lunches (Frits and Kath) which substantially increased the average
level of nutrition in my diet.
I would particularly like to thank Tudor Bell and Paul Beecham, of EEV
Lincoln, for their constant willingness to answer what must have been interminable
questions about the power supply and microwave queries in general. The SERC for funding
three quarters of my time at St. Andrews and the DSS for sponsoring the other quarter!
Finally I would like to thank my friend; and all the members of Laser 1
(Smelly Trev, Exaggerated Col, Steve trains, Simon) along with my fellow inmates of
172 South Street (Gordon R, Jonny, Neil, Gordon K. and indeed anyone who graced us
with their presence there, Malcolm R., Finlay C.) and whoever it was who introduced me to
King's Head Sherry (at 15% alcohol by volume and only £1.89 a bottle, it should come as
no surprise that I can no longer recall who it was, or in fact who I am or why I did this PhD
in the first place!).
PhD Thesis
J. W. Bethel
Publications arising from this work
Journal Publications
"A microwave-excited strontium-ion (À-430.5 nm) recombination laser".
J. W. Bethel, A. Maitland, C. E, Little, P. M. Beecham, T. C. Bell and S. Webb,
Optics and Quantum Electronics. Volume 26, pp 1079-1087. 1994.
"A microwave-excited copper halide laser".
J. W. Bethel, A. Maitland, C. E. Little, P. M. Beecham, S. Webb, T. C. Bell.
Optical and Quantum Electi'onics. Volume 25, pp 483-488. 1993.
Conference Publications
"Microwave Excited Lasers".
Jason W. Bethel and Chris E. Little.
Proceedings of the 8 th International School on Quantum Electionics,
Laser Physics and Applications, Vaina, Bulgaiia. September 1994, in press.
"A Sr+(A,430.5nm) recombination laser with microwave excitation".
J. W. Bethel, A. Maitland, P. M. Beecham, T. C. Bell, S. Webb and C. E. Little.
Proceedings of CLEO, Anaheim. U. S. A., paper CFD6 , p 403. 8-13 May 1994.
"Copper halide laser with microwave pumping".
J. W. Bethel, A. Maitland, P. M. Beecham, T. C. Bell, C. E. Little.
Proceedings of CLEO, Baltimore, U. S. A., paper CWJ21, p 298. 2-7 May 1993.
PhD Thesis
7. W. Bethel
Glossary of Abbreviations
ac
Alternating current
AVLIS
Atomic Vapour Laser Isotope separation
BBO
Beta Barium Borate
CHL
Copper halide laser
CVL
Copper vapour laser
dc
Direct cuiTent
FWHM
Full width at half maximum
HDPE
High density polyethylene
LE
Longitudinally excited
Nd:YAG
Neodinium Yttrium Aluminium Garnate
PRF
Pulse recuiTence frequency
PTFE
Teflon
rf
Radio frequency
rms/RMS
Root mean squaie (value)
RWCS
Ridge waveguide coupling structure
SRL
Sti'ontium-ion recombination laser
TE
Transversely excited
TEmn
Transverse electric (modes indicated by m,n)
TEM
Transverse electromagnetic
TM
Transverse magnetic (modes)
TWCS
Tapered waveguide coupling structure
UV
Ulti’a-violet
PhD Thesis
7. W. Bethel
List of Symbols
A
Aik, 12,21
Cross-sectional area
Optical transition probabilities
a
Dimension of broad wall of rectangular waveguide
a'
ao
ccp
Radius of the sleeve ai ound quaitz tube exiting the RWCS
Initial attenuation constant of microwaves in the TWCS
Attenuation constant of plane electiomagnetic waves in a plasma
Cfr
Thiee-body electron ion recombination coefficient
<^He, Sr,..
ccrp
Thiee-body election ion recombination coefficient for species He, Sr,..
Attenuation constant of microwaves in a rectangulai’waveguide containing a
B
plasma tube
Magnetic field
b
bo
P
pc
Dimension of nairow wall of rectangular waveguide
Initial dimension of narrow wall in TWCS
Phase constant of microwaves in rectangulai’waveguide
Resonant frequency of modulator chaiging circuit
Pp
Apxp
Phase constant of plane electiomagnetic waves in a plasma
Change in the phase constant from rectangular waveguide to rectangular
waveguide containing plasma tube
C
Ci
Capacitance
Total probability of decay of the ith level
Cnp
Total capacitance of the PFN referred to the primaiy of the pulse tiansformer.
CpFN
D
d
Ô
Sq, ôsi. Si
Total capacitance of the PFN
Duty cycle of current pulses
Ridge sepaiation in a ridge waveguide
Skin depth
Fraction of energy lost by electrons with collisions with heavy body
V
E
Eo
Erp
PhD Thesis
pai’ticles, atoms, ions
Differential operator
Electiic field
Electric field in empty rectangular waveguide
Perturbed electiic field in rectangulai’waveguide containing a plasma tube
</. W. Bethel
List o f Symbols
Eq
■Erms
Et
Electiic field strength in the centie of a waveguide
Root means squaie electiic field stiength
Transverse component of electric field
e
e
50
Chai'ge on electron
Permittivity
Effective peimittivity of a plasma
Permittivity of free space
Sm
Energy of metastable helium atoms
51^2
Sp, £2 '
Peimittivity of material 1, material 2
Relative peimittivity of plasma, quaitz
AE 2 \, i,j
Ae
Asx
Energy level spacing between levels 2 and 1, i and j.
Dissociation energy
Energy released in recombination of helium atoms
E 12,21
Rate of election coUisional excitation, de-excitation
/ 12, 21
Oscillator strength for transition 1 to 2, 2 to 1
Potential in region i
g
Ratio of outside radius, R 2 , to inside, Ri, radius of quartz tube
gl, g2
%
Yxi
Statistical weights of levels 1 and 2
Propagation constant of microwaves in an empty waveguide
Propagation constant of plane, electi omagnetic waves in a plasma
Propagation constant of microwaves in a plasma filled waveguide
%'p
Propagation constant of microwaves in a rectangulai" waveguide containing a
plasma tube
H
Hrp
Magnetising field
Perturbed magnetising field in rectangular* waveguide containing plasma tube
Hq
Magnetising field in centr e of waveguide
7}
Transverse component of the magnetising field
Impedance of free space, 377 O.
I
Zrrns
7pk
Current
Root mean squaie cunent
Peak current
J
j
(pi ^2
Current density
^ |^
Potential in regions 1 and 2 of rectangular* waveguide containing plasma tube
k
kc
Boltzmann constant
Cut-off wavenumber
L
Inductance
PhD Thesis
J. W. Bethel
List o f Symbols________________________________________________
vi
La
Lp
Anode inductor
Primary winding inductance of the pulse ti ansformer
Lg
Secondaiy winding inductance of the pulse transformer
^L1,L2
L
/a
Primaiy, secondaiy leakage inductance
Length of ridge taper
Length of plasma tube in TWCS
k
/w
Distance between ridge and the waveguide wall, in the ridge waveguide
Length of resonant cavity
Ao
Wavelength of microwaves in free space
%
Ac
Wavelength of microwaves in waveguide
Cut-off wavelength of microwaves in waveguide
At
Wavelength of microwaves in tapered section of ridge waveguide
Arp
Wavelength of microwaves in RWCS
M, Mi
Mass of buffer gas atom, ith component
me
ji
Mass of electron
Permeability
N
%
Number density of atoms
Number density of atoms in level k.
Wm
Number density of metastable helium atoms
//He, Sr,...
n
Uq
vc
Number density of He, Sr,...
Turns ratio in the pulse transformer
Electron density
Total collision frequency of electrons and atoms
vea, ei
Election atom, election ion collision rates for momentum tiansfer
i^m
vtot
Collision frequency for momentum transfer
Total elastic collision frequency of electrons with atoms and ions
P
Power flow
p
Of
Pressure
Firing angle of the thyratron in ac resonantly chaiged modulator
R
Reflection of plane electiomagnetic waves at a dielectric interface
R\^ 2
Tel)
p
Quai’tz tube radius: inner, outer
Rate constant for transitions between levels i and j
Coulomb logarithm
Pr
Resistivity
S
Poynting vector
5 1,2,0
s
Area of plasma, quaitz tube, waveguide
Ridge width in ridge waveguide
PhD Thesis
J. W. Bethel
List of Symbols
______________________________________________________vii_
<7
Conductivity of a plasma
T
Tq
Transmission of plane electiomagnetic waves at a dielectiic interface
Electron temperatuie
Tg
t
Ui
Ü2
Me
Gas temperature
Time
Energy of microwave in the ridge waveguide
Energy contained in the fringing fields of the step in the ridge waveguide
Energy absorbed by a plasma per electron per collision
V
Voltage
V
V
Volume
Velocity
Wi^2
Pumping rates
Angulai' frequency of electromagnetic waves
CO
6%
cop
Angular frequency of alternator
Plasma frequency
Z
Zc
Zrp
Inti'insic impedance
Ionic chai’ge
Impedance of TWCS
X ,y, z
r, 6
Cartesian coordinates
Cylindrical coordinates
oo
Infinity
PhD Thesis
T W. Bethel
Contents
Acknowledgements
Publications aiising from this work
i
ü
Glossary of Abbreviations
iii
List of Symbols
Contents
iv
viii
Chapter 1: Introduction
1.1 Aim of this work................................................................................. 1
1.2 Copper vapour and copper halide lasers..................................... 1
1.3 Str ontium-ion recombination lasers.................................................... 4
1.4 Microwave excited gas lasers.............................................................. 6
1.5 Format of this thesis........................................................................... 9
References.................................................................................................10
Chapter 2: Propagation of microwaves
2.1 Introduction
............................................................................... 14
2.2 Propagation of microwaves in a rectangular waveguide............... 14
2.3 Propagation of microwaves in a ridge waveguide.......................14
2.3.1 Estimation of the electric field in a ridge waveguide................18
2.4 Propagation of microwaves in ionised gases.................................
2.4.1 Motion of electrons in an ionised gas
under the influence of an external field...........................
23
23
2.4.2 Electric field at a free-space/plasma interface..................... 26
2.4.3 Effect of the plasma on the phase and
attenuation of an electromagnetic wave................................... 27
2.4.3 Effect of a discontinuity on the
propagation of wave in a plasma.............................................31
2.4.4 Power absorbed in a plasma....................................................34
2.4.5 Summary of the effects of the ratios
Vin/^o and cop/œ on wave propagation................................ 34
2.5 Propagation of microwaves in a
rectangular' waveguide containing a plasma........................................38
2.5.1 Rectangular waveguide containing a plasma tube..................39
PhD Thesis
J. W. Bethel
Contents
_________________________________________________________
2.5.2 Electiic field in the rectangulai* waveguide
containing the plasma tube...................................................... 46
2.6 C onclusions................................................................................... 49
References................................................................................................ 51
Chapter 3: Strontium-ion Recombination Lasers: Excitation Mechanisms
3.1 Introduction.......................................................................................52
3.2 Energy level considerations for
population inversion by recombination.............................................53
3.3 Three-body election-ion recombination............................................60
3.4 Election temperatuie in the afterglow of a helium buffer gas........... 64
3.5 Effect of discharge pulse shape on the performance of SRLs
....... 68
3 .6 Operating characteristics of SRLs..................................................... 69
3.7 Scaling issues in SRLs..................................................................... 70
72
3.8 C onclusions..........................
References................................................................................................ 74
Chapter 4: Copper Halide Lasers: Excitation Mechanisms
4.1 Introduction............................
4.2 Cyclic lasers................
76
76
4.3 Kinetic processes in copper halide lasers..................................79
4.3.1 During the current pulse.......................................................... 80
4.3.2 During the interpulse period.............................................83
4.3.3 Buffer gas effects in copper halide lasers.......................... 85
4.4 Operating chaiacteristics of copper halide lasers.............................. 88
4.4.1 Double-pulsed lasers................................................................89
4.4.2 Continuously pulsed lasers.................
90
4.4.3 Addition of hydrogen.............................................................. 91
4.4.4 Lifetime studies of copper halide lasers............................ 92
4.4.5 Copper halide HyBrlD laser....................................................93
4.5 C onclusions......................................................................
93
References................................................................................................ 95
Chapter 5: Microwave Pumping Configurations
5.1 Inti'oduction.......................................................................................98
5.2 Pumping requirements for strontium-ion recombination lasers.....101
5.3 Pumping requirements for copper halide lasers..............................102
PhD Thesis
J. W. Bethel
Contents________________________________________________________________ ^
5.4 The ridged waveguide coupling stincture....................................... 104
5.4.1 Electric fields in the ridge waveguide.................................... 104
5.4.2 Impedance matching of the ridge waveguide....................107
5.4.3 Mechanical design of the RWCS........................................... 109
5.4.4 Performance of the RWCS.....................................................I l l
5.5 The tapered waveguide coupling stracture......................................112
5.5.1 Theoiy of tapered waveguide containing plasma tube...........112
5.5.2 Design of the TWCS.............................................................. 115
5.5.3 Electiic fields in the TW CS................................................... 119
5.5.4 The ratio of the electiic field to the neutral number density... 121
5.5.5 Impedance of the TW CS................................................... ...123
5 .6 Peifoimance of the TWCS.............................................................. 125
References.............................................................................................. 127
Chapter 6: Experimental results of the Microwave excited
Copper halide laser
6.1 Introduction..................................................................................... 130
6.2 Preliminary experiments with the CuCl using the RWCS........... 130
6.2.1 Experimental details............................................................... 130
6.2.2 Performance of the RWCS for pumping the CuCl laser........134
6.3 Measurements of the absorption of microwaves
in discharges occurring in helium and neon buffer gases................ 138
6.3.1 Experimental details............................................................... 138
6.3.2 Estimation of the electric field and
the electron density in the plasma.............................. ....145
6.3.3 Summary................................................................................150
6.4 Results of laser oscillation in CuCl and CuBr using the TWCS.... 150
6.4.1 Performance of the TWCS for CuBr
and CuCl with neon buffer gas..............................................152
6.4.2 Effects of the copper halide on the discharge........................ 160
6.4.3 Experiments to reduce the
temperature variation along the tube............................... 163
6.4.4 Performance of the TWCS as a coupling
structure for the copper halide laser.........................................165
6.5 C onclusions...........................
167
References...............................................................................................169
PhD Thesis
J. W. Bethel
Contents________________________________________________________________ ^
Chapter 7: Experimental results of the Microwave excited Strontium-ion
recombination laser
7.1 Inti'oduction.....................
171
7.2 Experiments using the TWCS for the strontium laser.................... 171
7.2.1 Experimental details................................................................171
7.2.2 Preparation of the laser tubes..............
172
7.3 Results of experiments with sti'ontium........................................... 174
7.4 Estimation of the election density from the
duration of the spontaneous emission
of the 430.5 nm transition...................................................... 178
7.4.1 Calculation of the recombination rate of Sr++........................179
7.5 C onclusions.................................................................................. 185
References...............................................................................................187
Chapter 8: Conclusions and future work
8 .1 Summai-y of the work in this thesis.................................................188
8 .2 Suggestions for future work............................................................190
8.2.1 Surface-wave coupling structuies.......................................... 190
8.2.2 All metal waveguide coupling structure...........................191
8.2.3 Transmission line coupling structure...............................192
8.2.4 Waveguide containing plasma tube,
operating close to cut-off....................................................... 194
8.2.5 Microwave pulse compression........................................ 195
8.4 C onclusions.................................................................................197
References............................................................................................... 198
Appendix A: Magnetron power supply
A1 Magtest modulator power supply for the magnetion...............199
A 1.1 Alternator char ging of the PFN .........................................199
A 1.2 Discharge of the PFN through the pulsetransformer
207
A2Modification of the charging circuit...........................................211
A2.1 Pulse Forming Network design........................................ 211
A2.2 Double-pulse circuit
................................................ 215
A3 Performance of the double-pulse circuit...................................220
References........................................................................................222
PhD Thesis
J. W. Bethel
CHAPTER
1
Introduction
1.1 Aim of the work
The aim of the experimental work described in this thesis was to investigate the feasibility of
microwave excitation of the metal vapour lasers based on the cyclic transitions of neutral
copper, and on the recombination transitions of doubly ionised strontium. This chapter
provides a short introduction to copper and strontium lasers, along with their applications
and current status of development. We also discuss the problems which arise in these laser
systems when conventional electrical excitation is used and give arguments as to why
microwave excitation is an attractive alternative. We also describe some of the more general
features of microwave excited lasers. Finally the chapter concludes with a brief outline of
this thesis.
1.2 Copper vapour and copper halide lasers
The elemental-metal copper vapour laser (CVL) has proved to be by far* the most successful
in the family of lasers which utilise self-terminating transitions in atomic or ionic
metal-vapours. Since the first report of laser oscillation on the so-called 'cyclic' transitions
(/l=510.6 and 578.2 nm) of atomic copper vapour in 1966, by Walter et al. [1, 2], CVLs
have now become available commercially with average output powers of up to 100 W [3]
from a single laser tube. However, using oscillator-amplifier systems with 12 chains,
reseai'chers at Lawrence Livermore National Laboratories have reported an average power of
over 8 kW; and in a single amplifier, average powers of 650 W at 1% electrical to optical
PhD Thesis
1
J. W. Bethel
Chapter 1_______________________________________________________Introduction
efficiency have been obtained [4]. Typically, CVLs operate at high pulse recurrence
frequencies (PRFs) of between 2 and 32 kHz, with output pulses of 10 to 50 ns full-width
half-maximum (FWHM), at high-peak powers of up to 500 kW and efficiencies of up to 1%
[3,5]. At present, copper based lasers aie the most efficient source of coherent, visible light
from a single tube. Their applications include large screen projection advertising and
simulators, underwater mapping and communications, high speed photography,
dermatology (port wine stain removal using the yellow 578.2 nm line, whilst the 510.6 nm
line is strongly absorbed by melanin, and can therefore be used for treating pigmented
lesions) and tuneable dye-laser pumping [6 ]. Industrial applications of CVLs include
materials processing, especially for metals such as copper and aluminium which are difficult
to machine using CO2 or Nd:YAG lasers due to their high reflectivity in the infrared. CVL
pumped dye-lasers have medical applications in cancer photodynamic therapy [7], atomic
vapour laser isotope séparation (AVLIS), and adaptive optics for astronomy [8 ]. CVL
pumped Ti: AI2O3 lasers provide tuneable radiation in the red and near* infrared with average
powers of up to 5.5 W (TEMqq) with a 38.5 per cent slope efficiency [9]. Additionally,
by pumping non linear* materials such as BBO (Beta-Barium Borate), CVLs have become a
promising source of ultra-violet (UV) light with average powers reported of 9 W at
255.3 nm from doubling the green line (other UV lines available are 289.1 nm from
doubling the yellow transition and 271.2 nm from sum frequency mixing [10, 11]). High
power UV radiation is useful for a variety of applications such as photolithography,
micromachining of polymeric materials and fluorescence mapping.
hi elemental CVLs, copper pieces placed along the floor of the discharge tube
are heated to around 1600 °C, in order to provide the optimum partial pressure of copper
vapour, by the waste heat produced in the discharge [12]. It is these high temperatures
which lead to problems in engineering the laser tube. In most high power CVLs,
contaminants released in the fibrous insulation which surrounds the alumina discharge tube
and from the alumina itself, must be removed by a constant slow flow of the neon buffer
PhD Thesis
2
J. W. Bethel
Chapter 1_______________________________________________________Introduction
gas. In addition, the high temperatures mean long warm up times for the laser to reach
optimum temperature, and can result in sagging of the alumina discharge tube with
prolonged operation. These problems led to the development of copper-halide lasers (CHLs)
using copper(I)chloride (CuCl), copper(I)bromide (CuBr) and copper(I)iodide (Cul). These
copper halides are more volatile than elemental copper and the lasers therefore have lower
operating temperatures of -370 °C, -420 ^C and 500 ®C for CuCl, CuBr and Cul
respectively [13]. Design considerations for these systems are much less stringent due to the
lower operating temperatures, and faster start-up times make them more convenient to
operate than conventional CVLs. The most successful of the CHLs has been the CuBr laser,
with its highest reported average output power of 112 W and an efficiency of 1.71% at
100 W [14]. However, commercial development of these lasers has been slow due to the
problems involved in producing a stable, high-power long-lived sealed-off device (see
chapter 4).
A recent development of CuBr lasers [15], in which the copper halide
mixture is formed in the dischai'ge, by a reaction between HBr gas and copper (now referred
to as Copper 'HyBrlD' lasers), has resulted in a revival of interest in copper-based lasers.
Operating temperatures of these lasers ar e in the range 500-800 °C and have stai t-up times
of around 20 minutes [15] and average output powers of up to 201 W at 1.9 percent
efficiency (or 120 W at 3.2 percent efficiency) [16]. The design considerations aie similar* to
CHLs, but one of the main advantages is the ability to precisely control the CuBr and
hydrogen par tial pressure in the dischar ge, independently of the input power (and hence the
tube wall temperature) to the dischat*ge. Hydrogen is a vital component in CHLs and CVLs,
the addition of a few percent leads to a doubling of the output power [17].
Commercialisation of copper lasers (either copper halide or elemental copper)
requires long term output stability, a long lifetime, low price and (ideally) a sealed-off
system for 'user friendly' operation. One of the lifetime limiting processes for sealed-off
copper lasers is the diffusion of the metal out of the discharge zone. This diffusion could be
PhD Thesis
3
J. W. Bethel
Chapter 1_______________________________________________________ Introduction
reduced by operating the laser at high buffer gas pressures. The output power of copper
based lasers may also be expected to increase with increasing buffer gas pressure because of
the higher number densities of copper atoms supportable in the discharge at these higher
pressures (see section 4.3.3). However, to maintain the current density at higher buffer gas,
the tube voltage (and hence the electric field) must be increased commensurately. At present,
the tube voltages are limited (to around 40 kV) by the currently available high voltage
switches (usually thyratrons). In addition, the risetime of the current pulse in a pulsed, gas
discharge becomes slower as the pressure and hence the impedance of the dischai'ge is
increased. However, in copper based lasers it is important to have rapidly rising current
pulses in order to efficiently populate the upper laser levels (see chapter 4). Another problem
which is particularly evident in CHLs is electrode erosion, which occurs due to the highly
reactive nature of the gas mixture and this can also lead to dischai'ge instabilities. Therefore,
it is highly desirable to have an electiodeless discharge. The improvement in output power,
stability and lifetime of a high-pressure, sealed-off, electiodeless dischai'ge would make
copper lasers significantly more attractive from a commercial point of view, These
characteristics are promised by the application of microwave excitation (see section 1.4)
whose feasibility is examined in this work.
1.3 Strontium-ion recombination lasers
Strontium-ion recombination lasers (SRLs) aie useful sources of violet (416.2 nm and
430.5 nm) radiation with average output powers usually in the range of a few watts [18]. At
present, stiontium (and also calcium) recombination lasers are the only pulsed lasers which
produce simultaneously such high peak and average output powers at these wavelengths.
Strontium lasers would make the ideal complement to copper (510.6 nm) and gold
(628.3 nm) vapour lasers for use in large screen projection advertising and simulators.
Their relatively long pulse lengths (up to 1 [is) make the SRL a valuable pump source for
PhD Thesis
4
W. Bethel
Chapter 1_______________________________________________________ Introduction
narrow line-width blue-green dye lasers. In addition, they have possible medical applications
in ophthalmology and fluorescence diagnostics.
Since the first reported observation of laser oscillation on the recombination
transitions of strontium ions [19, 20 ], considerable effort has gone into the development of
these lasers [21]. The highest average output power reported so far* is 3.9 W, from a water
cooled tube [22]. Despite their modest efficiencies (around 0.15 percent), SRLs have shown
great promise for scaling to higher output powers. Specific output pulse energies for low
recurrence rate devices rival those of copper vapour lasers (6 |xJ cm“^ for longitudinally
excited systems (LE) and 50 [iJ cm-^ for transversely excited systems (TE)) [23, 24, 25].
However, attempts thus far* to increase the recurrence rates of these systems (and hence the
average output powers) have been frustrated by the occurrence of strong radial thermal
gradients [26] (see chapter 3).
Although these lasers operate at a lower temperature than CVLs (around
600 °C), there are still some significant engineering problems which need to be overcome
before a commercial device can be produced. The strontium metal is relatively reactive even
at room temperature. At 600
it is extremely so. Therefore, reaction of the strontium
vapour with usual the electrode materials inevitably occurs. These reactions again result in
degradation of the electi’ode and lead to instabilities occurring in the dischai'ge.
SRLs, like copper based lasers, show improved operation at high buffer gas
pressures. For SRLs, the increase in power output is much more dramatic than in copper
based lasers (power output increases approximately linearly with increasing helium buffer
gas pressure [21], see chapter 3). However, as the pressure of the dischai'ge is increased
(and hence the impedance of the dischai'ge), the current pulse termination time is increased
and this leads to slower recombination and a reduction in output power. These lasers aie
subject to the same problems as copper lasers when operated at high pressures Le, discharge
PhD Thesis
5
J. W, Bethel
Chapter 1
Introduction
instabilities and limited tube voltages available with present switching technologies. Again
microwave excitation offers an attiactive alternative to conventional excitation techniques.
1.4 Microwave excited gas lasers
Microwave excited gas discharges are promising alternatives to electrically excited
dischai’ges. Plasmas can be created by microwave pumping in many different ways, ranging
from plasmas produced in guiding media such as conducting metal waveguides, confined in
dielectric tubes contained in waveguides, or in free space. Discharges created in this way
have no internal electrodes and hence impmities in a microwave pumped system can be kept
to a minimum. This is especially important for the development of strontium based lasers,
due to the highly reactive nature of strontium. In addition, there will be no electi'ode induced
dischai'ge instabilities and this is an important consideration for laser systems especially
when operating at higher buffer gas pressures. The absence of cataphoresis in the oscillating
field of the microwaves, will reduce the loss of metal ions from the dischai'ge zone. In
sealed-off lasers, cataphoresis is often a major contributing factor in limiting the lifetime of
the laser tube. From the commercial point of view, the possibility of producing sealed-off
laser tubes with much longer lifetimes than is possible in conventional electrically excited
systems is veiy attiactive.
In conventional electrically excited pulsed gas discharges, the impedance of
the dischai'ge can change significantly during the excitation pulse. Therefore it is difficult to
obtain good matching of the circuit components to the dischai'ge, to ensure efficient power
deposition in the plasma. Impedance mismatches between the circuit and the dischai'ge can
also result in ringing within the dischai'ge circuit. This ringing can result in recovery failure
of the thyratron (latching), which reduces the thyratron lifetime considerably. In a
microwave pumped system, the magnetron can be isolated from the dischai'ge by using a
circulator. Therefore, this means that the pulse shape delivered to the system {i.e. the
PhD Thesis
6
J. W. Bethel
Chapter 1_______________________________________________________Introduction
discharge) is independent of the discharge conditions. In both copper based lasers and
SRLs, the pulse shape is very important for efficient laser oscillation. For the case of SRLs,
the excitation pulse needs to be terminated as rapidly as possible with no ringing. In a
microwave pumped system this can be made possible because the magnetron stops
oscillating when the voltage pulse applied to it drops below about 80 percent of the peak
value. Therefore, the rise and fall times of the rf pulse can be made very short (10 or 20 ns,
or so) and these will be independent of the plasma conditions. In practice though, the fall
time is limited somewhat by the charging circuit of the magnetion (see appendix). In copper
vapour lasers, the thyratron lifetime is very often reduced as a result of prolonged operation
at excessive peak currents, à l/à t, and so on. On the other hand, the thyratron switch in the
circuit for the magnetron (see appendix) ‘sees’ a constant load, and the risetime requirements
of the magnetron are not nearly so stringent (see appendix). Hence, the lifetimes of
thyratrons driving magnetrons are very much higher than those driving metal vapour laser
tubes (and the thyratrons are usually the much cheaper glass tubes as opposed to ceramic
tubes used in most lasers).
One problem associated with microwave discharges is the coupling of
microwave power into a plasma with high electron densities (see chapter 2). However, the
coupling of microwave power into the dischai'ge tends to increase with increasing buffer gas
pressure and both copper and strontium based lasers perform better at elevated pressure, as
discussed above and in chapters 3 and 4. Provided there is sufficient microwave peak power
available, relatively high electric fields can be produced in microwave excited plasmas.
Therefore, it should be possible to produce the necessary electric field to number density
ratios required for optimum performance of these lasers at high pressures (see chapter 5).
Operation at high buffer gas pressures will also lead to a reduction in the diffusion of the
metal atoms out of the active zone of the discharge. This is another factor which should
favour long life operation. Magnetrons can operate at multi-kilohertz recurrence rates at
efficiencies of up to 70 percent, with average output powers of 6 kW and peak output
PhD Thesis
1
J, W. Bethel
Chapter 1_______________________________________________________ Introduction
powers of 6 MW [27]. Therefore, magnetrons should be able to provide the output
chai acteristics requked for the pumping of metal vapour lasers.
In view of the above properties of microwave excited discharges, it is not
suiprising that considerable reseai'ch effort has been put into microwave pumped gas lasers
in the past ten yeais, most notably for excimer lasers, carbon dioxide lasers and helium-neon
lasers. Other laser systems which have been pumped using microwaves include nitrogen
[28], neon-hydrogen [29], carbon monoxide [30], bromine [31], chlorine [31], caibon [31],
sulphur [31], silicon [31], argon-ion [32], helium krypton-ion [33], argon xenon [34],
xenon, HCN [35], atmospheric air [36], chemical lasers (HF and DF) [37] and finally the
metal vapour lasers strontium (on the cyclic, infra-red transitions) [38] and helium-cadmium
[39]. Of these systems, the most promising appeal's to be the microwave excited 00% laser.
Output powers of 116 W at 13 percent efficiency have been obtained with a very compact
device pumped by a standard commercially available magnetron [40]. The helium-neon
lasers show higher gain, higher efficiency, reduced noise levels and better beam quality than
their electrically excited counteipaits [41]. The availability of transistor oscillators allows the
possibility of producing a compact device. Although a small commercial microwave-excited
excimer laser is now available for use in micro-machining which gives average output
powers of up to 60 mW and peak powers of 400 W (using Ki'F, [42]), they are limited in
size due to the skin effect of the microwaves in these relatively dense plasmas (electron
densities of 10^^ to 10^^ cnr^ [43]). Additionally, the optimum pump power densities for
these lasers are vei'y high (aiound 2 MW cm"^ [44]) and this puts large volume devices out
of range for commercially available magnetrons operating at high PRFs.
PhD Thesis
8
7. W. Bethel
Chapter 1______________________________________________________ Introduction
1.5 Format of this thesis
We begin chapter 2 by discussing the propagation of microwaves in plasmas, waveguides
and rectangulai' waveguide containing a discharge tube. We also consider the effect of the
various plasma conditions {Le. buffer gas pressures, electron densities), corresponding to
those which occur in conventional CHLs and SRLs, on the propagation of the microwaves,
the power absorbed and the electric field strength in the dischai'ge.
In chapters 3 and 4 we examine the basic physics of strontium-ion
recombination and copper-halide lasers respectively, along with their operating
chaiacteristics. In chapter 5, the design and construction of the two waveguide coupling
structm'es used in this investigation are detailed.
In chapter 6 we present the experimental results of the Copper Halide (CuCl
and CuBr) laser developed using these two coupling structures and compaie their respective
performances. In addition, the effects of the buffer gases helium and neon, on the absolution
of microwave power in the discharge is examined and the electron density is estimated. The
possible reasons for the relatively low output powers obtained with the microwave excited
CHL compared with conventional electrical excitation are discussed, with reference to the
effects of the presence of copper halide vapour on the absorbed power and stability of the
dischai'ge.
In chapter 7 we present the results of microwave excitation of the
strontium-ion recombination laser and estimate the electron density from the time-resolved
spectroscopy of the spontaneous emission of the strontium vapour from the discharge. The
value of electron density obtained is compared with that obtained using the method described
in chapter 6 . Finally, in chapter 8 , concluding remarks about the performance of the
microwave excited metal vapour lasers aie made and possible future work is considered.
PhD Thesis
9
J. W. Bethel
Chapter 1_______________________________________________________Introduction
References
1.
Pulsed-laser action in atomic copper vapom\
W. T. Walter, M. Piltch, N. Solimene and G. Gould.
Bulletins of the American Physical Society, vol. 11, p 113, 1966.
2.
Efficient pulsed gas discharge lasers.
W. T. Walter, N. Solimene, M. Piltch and G. Gould.
IEEE Journal of Quantum Electronics, vol. 2, No. 9, pp 474-479, September 1966.
3.
The Advanced Copper Vapour Laser.
Technical report.
Oxford Lasers Ltd., Newtec Place, Magdalen Road, Oxford, England, 0X 4 IRD.
4.
Status of copper vapour laser technology at Lawrence Livermore National Laboratory.
B. E. Warner.
Proceedings of CLEO, CFH4, pp 516-517, May 1991.
5.
High-power dye lasers pumped by copper vapour lasers.
C. W. Webb, edited by F. J. Duaite.
pp 143-182, Springer-Verlag, Berlin, 1991.
6.
Copper-vapour lasers find specialised applications.
J. Hecht.
Laser Focus World, vol. 29, No. 10, pp 99-103, October 1993,
7.
CYLs serve in medical PDT systems.
H. W. Messenger.
Laser Focus World, vol. 27, No. 4,pp 129-132, April 1991.
8.
Artificial guide stars.
H. W. Friedmann.
Proceedings of CLEO, CFDl, pp 400-401, May 1994.
9.
Efficient high-power copper-vapour-laser pumped Ti:AI2O3 laser.
M. R. H. Knowles and C. Webb.
Optics Letters, vol. 18, No. 8, pp 607-609, April 15 1993.
10.
High average power second-harmonic generation using copper laser oscillator/amplifier source.
W. A. Molander.
Proceedings of CLEO, CThM2, p363, May 1994.
11.
Nonlinear frequency conversion of CuBr vapour laser emission by BBO crystal.
T. S. Petrov, N. V. Sabotinov, S. T. Trendafilov, Lin Fucheng and Zhang Guiyan.
Journal of Physics D; Applied Physics, vol. 25, pp 1169-1171, 1992.
12.
Copper vapour lasers operating at high pulse repetition frequencies.
N. V. Sabotinov, S. D. Kalchev and P. K. Telbizov.
Soviet Journal of Quantum Electronics, vol. 5, No. 8, pp 1003-1004, 1976.
13.
Comparison of CuCl, CuBr and Cul as lasants for copper vapour lasers.
S. Gabay, I. Smilanski, L. A. Lewis and G. Erez.
IEEE Journal of Quantum Electronics, vol. 13, No. 5, pp 364-365, May 1977.
14.
CuBr laser witli average lasing power exceeding 100 W.
V. F. Elaev, G. D. Lyakh and V. P. Pelenkov.
Atmospheric Optics, vol. 2, No. 11, pp 1045-1047, November 1989.
PhD Thesis
10
J. W. Bethel
Chapter 1_______________________________________________________Introduction
15.
Characteristics of a copper bromide laser with flowing Ne-HBr buffer gas.
E. S. Livingstone, D, R. Jones, A. Maitland and C. E. Little.
Optical and Quantum Electronics, vol. 24, pp 73-82,1992.
16.
A high-efficiency 200 W average power copper HyBrlD laser.
D. R. Jones, A. Maitland and C. E. Little.
IEEE Journal of Quantum Electronics, in press.
17.
Parametric study of the CuBr laser with hydrogen additives.
D. N. Astadjov, N. K. Vuchkov and N. V. Sabotinov.
IEEE Journal of Quantum Electi'onics, vol. 24, No. 9, pp 1927 1935, September 1988.
18.
Design of a 1.7 W stable, long-lived strontium vapour laser.
D. G. Loveland, D, A. Orchard, A. F. Zeirouk and C. E. Webb.
Measurement Science and Technology, vol. 2, pp 1083-1087,1991.
19.
Stimulated emission due to transitions in alkali-earth metal ions.
E. L. Latush and M. F. Sém.
Soviet Journal of Quantum Electronics, vol. 3, No. 3, pp 216-217 Nov.-Dee. 1973.
20.
Laser recombination transitions in Ca II and Sr II.
E. L. Latush and M. F. Sém.
Soviet Physics JETP, vol. 37, No. 6 pp 1017-1018, December 1973.
21.
Gas-discharge recombination lasers based on strontium and calcium vapours:
A review.
E. L. Latush, M. F. Sém, L. M. Bukshpun, Yu. V. Koptev and S. A. Atamas.
Optics and Spectroscopy, vol. 72, No. 5, pp 677-680, May 1992.
22.
Influence of the temperatiu*e of the active medium on the stimulated emission characteristics of an
Sr-He recombination laser.
L. M. Bukshpun, E. L. Latush and M. F. Sém.
Soviet Journal of Quantum Electronics, vol. 18, No, 9, pp 1098-1100, September 1988.
23.
High-pressure high current transversely excited Sr'*' recombination laser.
M. S. Butler and J. A. Piper.
Applied Physics Letters, vol. 42, No. 12, pp 1008-1010, October 1984.
24.
Optimisation of excitation channels in the dischai'ge-excited Sr"** recombination laser.
M. S. Butler and J, A. Piper.
Applied Physics Letters, vol. 45, No. 7, pp 707-709, October 1984.
25.
Transverse-dischai'ge copper-vapour laser at 5 kHz.
J. J. Kim and N. Sung.
IEEE Journal of Quantum Electronics, vol. 25, No. 5, pp 818-819, May 1990.
26.
Average-power scaling of self-heated Sr'*' afterglow recombination laser.
C. E. Little and J. A. Piper,
IEEE Journal o f Quantiun Electronics, vol. 26, No. 5, pp 903-910, May 1990.
27.
Magnetrons for Linear Accelerators,
Product Data, September 1992.
EEV Carholme Road, Lincoln, LN l ISF.
28.
Nitrogen laser pumped by a freely localised microwave discharge.
A. A. Babin, A. L. Vikharev, V. A, Gintsburg, O. A. Ivanov, N. G. Kolganov, M. I. Fuks.
Soviet Technical Physics Letters, vol. 15, No. 3, pp 176-177, March 1989.
PhD Thesis
11
T W. Bethel
Chapter 1_______________________________________________________ Introduction
29.
Neon-hydrogen plasma laser pumped by a microwave discharge.
V. A. Vaulin, V. I. Derzhiev, V. M. Lapin, V. N. Slinko, S. S. Sulakshin, S. I.
Yakovlenko and A. M. Yanchaiina.
Soviet Journal of Quantum Electronics, vol. 19, No. 3, pp 323-324, March 1989.
30.
CW carbon monoxide laser with microwave excitation in the supersonic flow.
P Hofftnann, H. Hugel, W, Schall and W. Schook.
Applied Physics Letters, vol. 37, No. 7, pp 673-674, October 1980.
31.
Br, C, Cl, S and Si laser action using a pulsed microwave discharge.
J. E. Brandelik and G. A. Smith.
IEEE Journal of Quantum Electronics, vol. 16, No. 1, pp 7-8, January 1980.
3 2.
Microwave-excited ionised argon laser.
S. F. Paik.
Proceedings of the IEEE, vol. 56, No. 11, pp 2086-2087, 1968.
33.
Microwave excitation of Argon ion and Helium-Krypton ion lasers.
P. J. Dobie.
PhD thesis, St. Andrews University, Scotland 1988.
34.
Microwave dischar ge excitation of an Ar-Xe laser.
C. L. Gordon III, and B. Feldman and C. P. Christensen.
Optics Letters, vol. 13, No. 2, pp 114-116, February 1988.
35.
An explanation of the direction of the relaxation in the HCN gas microwave laser, and a new
assignment of further laser lines along the path of internal vibrational energy redistribution.
W. Quapp.
Applied Physics B, vol. 48, pp 257-260, 1989,
36.
Air ultraviolet laser excited by high power microwave pulses.
V. A. Vaulin, V. N. Slinko and S. S. Sulakshin.
Soviet Journal of Quantum Electronics, vol. 18, No. 11, pp 1457-1458, November 1988.
37.
HE and DF Laser action by a pulsed microwave discharge,
J. E. Brandelik, W. K. Schuebel and R. F. Paulson.
IEEE Journal of Quantum Electronics, vol. 14, No. 6, pp 411-413, June 1978.
38.
Ion laser utilising microwave-excited strontium vapour.
V. F. Kravchenko, V. S. Mikhalevskii, S. P. Chubar and A. P. Shelepo.
Soviet Journal of Quantum Electronics, vol. 14, No. 6, p 725, June 1984.
39.
Use of microwave gas discharge in optical quantum generators (review).
Ya. N. Muller.
Radio Electronics and Communications systems, vol. 22, No. 10, pp 55-68, 1979.
40.
Development of CO2 laser excited by 2.45 GHz microwave discharge.
J. Nishimae and K. Yoshizawa.
Proceedings of SPIE, vol. 1225, High-Power Gas Lasers, pp 340-348, January 1990.
41.
Use of transverse microwave discharge in a compact efficient He-Ne laser.
Ya. N. Muller, V. M. Geller and V. A. Khrustalev.
Soviet Journal of Quantum Electronics, vol. 9, No. 10, pp 1302-1303, October 1980.
42.
UV waveguide lasers.
Data sheet for models SGX-1000 and SGX-500.
Potomac Photonics Inc., 4445 Nicole Drive, Lantham, MD 20706.
PhD Thesis
12
/. W. Bethel
Chapter 1_______________________________________________________ Introduction
43.
Time-resolved election density measurements in rare-gas-halide laser discharges.
R. C. Hollins, D. L. Jordan and J. Coutts.
J. Phys. D: Applied Physics, vol. 19, No. 1, pp 37-42, January 1986.
44.
Krypton fluoride laser excited by high-power nanosecond microwave radiation.
V. A. Vaulin, V. N. Slinko and S. S. Sulakshin.
Soviet Journal of Quantum Electionics, vol. 18, No. 11, pp 1459-1461, November 1988.
PhD Thesis
13
J. W. Bethel
CHAPTER
Propagation of Microwaves
2,1 Introduction
In this chapter we discuss the propagation of microwaves in rectangular and ridge
waveguides, and compare the electric field distributions that can be obtained in them. The
char acteristics of a plane wave that propagates from free space into a plasma ar e described,
with emphasis on the influence of the plasma parameters on the coupling of microwave
power to the plasma. We use the theory of wave propagation in plasmas and in waveguides
to estimate the perturbing effect of a plasma column in a rectangular waveguide on the
electric field and propagation constant.
2.2 Propagation of microwaves in a rectangular waveguide
The electric field E and the magnetic field B of an electromagnetic wave at any frequency are
described by Maxwell's equations:
V .E = - ,
(2.1)
V .B = 0,
(2.2)
9B
V xE = - ^ ,
(2.3)
dt ’
PhD Thesis
14
/. VT. Bethel
Chapter 2 __________________________________________ Propagation o f Microwaves
and
V XB = ^
(2.4)
where J is the total electric current density, p is the total chaige density, e is the permittivity
and fi is the permeability of the medium in which the waves aie propagating thiough. These
equations aie fully generalised and can be applied to any inhomogeneous, non-isotropic
medium. The general form of Maxwell's equations for a sinusoidally varying field in a
non-conducting (p = 0 medium is [ 1]
E + œ ^ l i e E = 0,
(2.5)
H + 0}^^£H = 0,
(2.6)
H=-,
/i
(2.7)
where H is the magnetising field. These are the wave equations for the electromagnetic
fields, and they can be solved to give the components of electiic and magnetic fields subject
to the boundary conditions of the particular system under examination. For the case of a
rectangulai* waveguide, the boundary condition is the existence of a perfectly conducting
surface. Therefore, the electric field components parallel to the waveguide walls must vanish
at the walls. Solving equations 2.5 and 2.6 under these conditions and then substituting the
resultant solution into equations 2.3 and 2.4 leads to two independent sets of field
components called Transverse Electric (TE) and Transverse Magnetic (TM) modes [1].
For TE modes, the component of the electric field par allel to the direction of propagation is
zero and for TM modes the corresponding magnetic field component is zero. The energy
flow and propagation direction for all electromagnetic waves is defined by the Poynting
vector given by [2 ]
S = EXH.
PhD Thesis
15
(2.8)
J. W. Bethel
Propagation of Microwaves
Chapter 2
The TE modes in a rectangulai- waveguide of width a and height b are given
below for the case where the wave is tiavelling in the z direction, and therefore Ez=0.
£x =
jCùjlHQ nit
mKx . riTcy
cos
sin
exp j [ ù ) t - pz).
b
a
b
(2.9)
(2 .11)
£ z = 0.
(2 . 12)
^
^
^
b
=^ H c o s ^ s in ^ e x p ;( « - ^ z ) ,
k
b
- H q cos
kc =
a
mnx
b
nTvy
cos
mTi:
a J
./
_ \
exp j{(Dt- pz).
I
n
2
k
Xq
1
(2.14)
(2.15)
K '
-
P =
XcT =
k
(2.13)
(2.16)
(2.17)
-
v^c y
where kc is the cut-off wavenumber, Ac is the corresponding wavelength of microwaves at
cut-off, p is the propagation constant and Ag is the wavelength of the microwaves in the
waveguide. These TE modes are classified as TEmn modes, where the integers m and n
correspond to the paiticular mode of propagation in the waveguide, and the fundamental
(lowest order) mode is TEio- Figure 2.1 shows the electric field distribution for the lowest
PhD Thesis
16
J. W. gefAeZ
Chapter 2
Propagation of Microwaves
Waveguide
“ Wall
Figure 2.1.
The electric field lines of the T E io
rectangular waveguide.
mode in a
order mode and it can be seen from this that the field is highest in the centre of the
waveguide and is constant for constant x values. For sinusoidally time-varying fields the
power flowing through the waveguide is given by [ 1]
ba
1 _ / _
$\ . _
(2.18)
00
Therefore, for a TEio mode, we get the following relationship between the input power and
the electric field in the waveguide [3]:
1
^0 ^
-
(2.19)
^c J
where E’m is is the time-averaged value of the electric field, for a field which varies
sinusoidally with time, at the centre of the waveguide (where the field is maximum for the
TEio mode).
The impedance of a travelling electr omagnetic wave is given by
PhD Thesis
17
/. W. Bethel
Chapter 2
Propagation of Microwaves
A
(2 .20)
where the subscript t is used to denote the transverse components of the field. It can be
shown for TE modes in a rectangulai* waveguide that [1]
Ac
Z=77
A0
( 2 .21 )
where rj is the impedance of free space (377 H). This expression is independent of the shape
of the waveguide and is therefore valid for TE modes in any hollow metal waveguide.
2.3 Propagation of microwaves in a ridge waveguide
The ridge waveguide is a vaiiation on the rectangulai* waveguide and is sometimes referred
to as an H-shaped waveguide (see figure 2.2 showing the cross section of the waveguide).
The metallic ridges in the waveguide essentially act as a shunt capacitance and this has the
effect of increasing the cut-off wavelength relative to the normal rectangulai* waveguide of
the same size. In addition, the higher order modes in the ridge waveguide have an increased
cut-off frequency. Therefore these waveguides are important because they have the
advantage of a wide monomode range [4].
A
b
V
a
Figure 2.2.
The cross-section of the ridge waveguide.
PhD Thesis
18
J. W. Bethel
Chapter 2
Propagation of Microwaves
Figure 2.3.
The volume element A dz, of the ridge waveguide, where A is the shaded
region
2.3.1 Estimation of the electric fields in a ridge waveguide
Although is not possible to solve Maxwell's equations exactly for a ridge waveguide, the
electric fields in such a waveguide can be calculated numerically using computer codes.
Alternatively, they can be estimated from transmission line theory by considering the effect
of the shunt capacitance of the ridges [5]. Hopfer [5] used transmission line theory to
estimate the electric fields in a ridge waveguide. By assuming that the voltage distribution
between the ridge and the unridged region is continuous, Hopfer showed that the electric
field disti'ibution is given by [5]
2 TZ
E( x ) = Eg c o s- — X
Ac
0 <X (
(2 .2 2 a)
between the ridges and
cos
in the unridged region where 5, d, 6 , and
KS
0 jrv ^
sin —
0 ( x ' { Ij,
A,
(2.22b)
aie indicated in figure 2.2 and Ac is the cut-off
wavelength in the waveguide. The maximum electrical energy, dC/i, contained in the TEio
PhD Thesis
19
/. W. Bethel
Chapter 2
Propagation of Microwaves
mode in a volume element Adz (see figure 2.3) is assumed to be the same as for a
rectangular waveguide, Le.
dA dz.
àU i =
(2.23)
LA
The energy which is contained in the fringing fields is obtained by considering the
capacitance of the step,
dUo = - c v ^ ,
(2.24)
where the capacitance of the step is approximated by
/
C -^ lo g ,
%
Kd
cosec
X Ü )
V
(2.25)
Therefore, the total power tiavelling in the z-direction becomes
d f/]
d^
jj
(2.26)
d?
where àz/dt is the group velocity of the microwaves. Hence, by evaluating this integral over
the cross section of the ridge waveguide, we obtain the relation between the power
transmitted in the waveguide and the rms electiic field at the centie of the ridge.
m
P=
^0 ^0 d
Xg 2n a
k
2d
2 ( 7ÏS
cos
] l o g ,[ c o s e c ( |) ^
Ka
\Ka.
ns
-j----------12 kü
(2.27)
I s in fa n ) +
4
KKa)
b
{2n \i/! k )\X ^ J
4
k
)
where K^Xc/a and i//=( 1-Vn)/2 and m=l for a double ridge waveguide. The cut-off
frequency Xq can be estimated from figure 2.4, and /ig can be calculated using equation
2.17. Figure 2.5 shows the electric field distribution plotted for the fundamental mode for
various ridge dimensions (ignoring the effect of the edge of the ridge on the field
PhD Thesis
20
J. W. Bethel
Chapter 2
Propagation of Microwaves
disti'ibution). These figures show that the effect of the ridge is to concenti'ate the electiic field
in the centre of the waveguide. The effect is increased with decreasing values of d/b and s/a.
In addition, the magnitude of the electric field increases as d/b and s/a decrease, and is higher
than that found in rectangular waveguides. These features of the electric field in the
ridge waveguide make it attractive for use as a coupling structure for pumping
gas discharge lasers (see chapter 5 and 6 ).
i
ao
4-5
d/b=0.5
0.4
0.6
Ratio, s/a.
0.8
1
Figure 2.4.
The variation in the cut-off wavelength for the ridge
waveguide against the ratio s/a for the T E io mode,
from reference [5].
PhD Thesis
21
J. W. Bethel
Propagation o f Microwaves
Chaptei' 2
1
r
1-------------
d/b ratio=0.2
j/a=0.1
j/a=0.3
1
I
s/a=0.65
4
I
i
I
d/b ratio=0.3
3
2
1
0
5/fl=0.1
d/b ratio=0.65
I
0.5
Distance from centre of ridge waveguide, cm.
Figure 2.5.
The electric field distribution in a ridge waveguide for
various ridge dimensions.
PhD Thesis
22
J. W. Bethel
Chapter 2___________________________________________Propagation of Microwaves
2.4 Propagation of microwaves in ionised gases
In order to understand the effect of a plasma in a waveguide on its propagation
characteristics, we must first look at the propagation of a plane Transverse Electro Magnetic
(TEM) wave in an ionised gas. The plasmas with which we are concerned aie expected to be
macroscopically neutral (equal numbers of electrons and ions) and of low density (electron
to neutral gas atom ratios of less than 1:1000). In addition, due to the mass difference
between electrons and ions, the motion of ions in the electromagnetic field can be neglected
and only the electrons aie considered to be mobile. However, the motion of the electrons is
affected strongly by collisions with neutial gas atoms. These election-atom collisions aie the
mechanism for power transfer from an oscillating field to the plasma. The total loss of
energy from the field due to these collisions is accounted for in the effective collision
frequency for momentum transfer Vm. The total collision frequency Vc and the effective
collision frequency for momentum ti ansfer Vm, from MacDonald [6 ], for helium and neon,
are plotted in figures 2.6 and 2.7. These show that the values of Vc and Vm are
approximately equal for the typical electron energies found in metal-vapour laser
discharges (2-10 eV). The total collision frequency for helium is almost independent of
electron energy for energies of above 6 eV, however this is not the case for neon, as can be
seen in figure 2.7. The collision frequencies Vc and Vm» for both helium and neon at fixed
electron energies, increase lineaily with pressure.
2.4.1 Motion of electrons in an ionised gas under the influence of external fields.
The plasma we will initially deal with is considered to be uniform, isotropic and linear. We
can therefore write the equation of motion of an electron in a plasma undergoing collisions
with neutr al gas atoms as [7]
dV
ytIq —— =
—
V—6 ( E + v x B ) ,
(2.28)
where v is the velocity, mq is the mass and e is the electronic charge of the electrons. This
PhD Thesis
23
J. W. Bethel
Propagation of Microwaves
Chapter 2
c T l.5
o
Collision frequency for
momentum transfer, Vm
Total collision frequency, v
g 0.5
Electron energy, eV.
Figure 2.6.
Ratios o f the total collision frequency and collision frequency for
momentum transfer to pressure p for helium.
rQ
Total collision frequency, v
cr
Collision frequency for
momentum transfer, Vm
Electron energy, eV.
Figure 2.7.
Ratios of the total collision frequency and collision frequency for
momentum transfer to pressure p for neon.
PhD Thesis
24
J. W. Bethel
Propagation of Microwaves
Chapter 2
equation is known as the Langevin equation. The first term on the right hand side of the
Langevin equation is the impeding force due to collisions with atoms. For the case where Vm
is zero, no energy will be transferred from electrons to the heavy body pai ticles (atoms and
ions) because these heavy body pai'ticles only gain energy from the field via collisions with
electrons. When the external magnetic field B is zero, the solution of equation 2.28 for an
electric field with a time dependence of expy
becomes
—^ E
v=
(2.29)
m (V m + ; ® ) '
Therefore, the current density J becomes
J
E
(2.30)
= —n ^ e V = g E =
« e ( Vm + j(o )
’
where uq is the electi on density and the conductivity of the plasma <7is defined as
n ^e
(J
2
^ e ( ^m
(2.31)
7^)
Therefore, using equation 2.5 we can define an effective peimittivity £eff as
(o:
^eff = ^0 1
m
(o:
(2.32)
-
(D
A)
1 + I'm
G)
1 + I'm
where cüp is known as the plasma frequency. It is the natural fiequency of oscillation of the
electrons (when Vm=0) without the influence of external fields and is given by
dip =
(2.33)
where £q is the peimittivity of free space.
PhD Thesis
25
J, W. Bethel
Chapter 2
Propagation of Microwaves
2.4.2 Electric field at afree-space/plasma interface
The boundaiy condition for the normal component of the electric field at the interface
between two dielectric media with relative permittivities of e\ and £2 , for the case of no
surface chai*ges, can be obtained from equation 2.1 and is given by
1^11^1 - 1^2 1^2-
(2.34)
Therefore, for a wave propagating from free space (where ei=l) into a plasma, the electric
field will change by the ratio eo/l^eff I, if we assume no reflection occurs at the boundary.
There will in fact be a significant reflection at this boundary and this is dependent upon the
plasma conditions (see section 2.4.4). The ratio eo/l^eff I is plotted below in figure 2.8.
Ip
O
Electron density, cm“^
Figure 2.8.
The ratio of the perm ittivity of free space to the plasma
permittivity plotted against the û)p/û) ratio for various values of
the ratio Vm/d>« Also shown are the corresponding electron
densities for microwaves of 3 GHz.
PhD Thesis
26
7. W. BgfAeZ
Propagation o f Microwaves
Chapter 2
We can see that when the collision frequency is small (Vm/û!)less than about 0.1), there is a
significant increase in the electric field which occurs at the resonance condition, where the
plasma frequency and the angular frequency of the field aie equal, i.e. C0p/m=l. Under these
conditions, the electric field in the plasma is significantly enhanced compared with the field
outside the plasma. This field enhancement is reduced as the pressure of the gas (and hence
the collisional frequency) increases. At plasma frequencies corresponding to cop/oxl, the
electric field inside the plasma is equal to the field outside the plasma, and the wave travels
unattenuated through the plasma.
For higher plasma frequencies (mp/m>l), the electric field in the plasma
will be significantly reduced compared to the free space field. For a microwave frequency
of 3 GHz and an electron density found in typical metal vapour lasers of around
10^^ cm“3, the plasma field is reduced by a factor of over 500 when Vm/G) is less than 1.
However when Vm/œ is greater than about 10, the ratio of go/l6eff I is approximately unity up
to a 'critical' plasma frequency. When the plasma frequency exceeds this value, the electric
field in the plasma becomes approximately inversely proportional to the squaie of the cop/co
ratio. The critical plasma frequency is approximately proportional to the squaie of the Vm/G>
ratio.
2.4.3 Effect of the plasma on the phase and attenuation of an electromagnetic wave
For a plasma which is infinite, isotropic and linear, we obtain the same expression as
equation 2.5 for the propagation of waves in a plasma, but the permittivity is now given by
equation 2.32 and hence we can write
O).
Vm®;
1
PhD Thesis
- ]
27
E = 0.
(2.35)
J. W. Bethel
Propagation of Microwaves
Chapter 2
For a plane wave in an infinite medium travelling in the z-direction, the solution of
equation 2.35 is
= ^O zG xp(;'0( - Ypz),
(2.36)
where the propagation constant ^ is given by
r;
(o:
1
(xP^IIS q
Vm®;
(2.37)
-
This expression can be separated into its real and imaginary parts to give
j. >1
CDl
ry2
P“
2
<o^ + v l
+
1-
+
m
CO,
2
,
(2.38a)
J
1A
P
2
œ^psQ
CO'
a>^ + v l
co:
+
1
Vm
Û)
-
2
(2.38b)
(2.39)
where
Hence equation 2.36 becomes
Ez = £ ‘0zexp(-O !pz)exp(7(fflr-)3pz)).
(2.40)
Therefore the terms Op and jSp represent the attenuation constant and the phase constant of
the plane wave in a plasma medium. When mis greater than mp, the propagation constant jg
becomes totally imaginary and microwaves can travel freely thr ough the plasma without any
attenuation. However, for the case where Vm is much less than the angular* frequency of the
waves m, (for instance, at very low buffer gas pressures), and m is less than the
plasma frequency mp, then the phase constant Pg tends to zero and the waves are attenuated
exponentially, as is evident from equations 2.39 and 2.40. We can define a parameter J,
PhD Thesis
28
J. W. Bethel
Chapter 2
Propagation of Microwaves
6
I
§
Figure 2.9.
The variation of the attenuation index, ccp, against the Vm/co ratio
for various cop/o) ratios. The electron densities corresponding to a
microwave frequency of 3 GHz for these cOp/co ratios are shown in
brackets.
called the skin-depth, which coixesponds to the distance at which the electric field is reduced
by a factor of l/e of its initial value on entering the plasma.
0 =
1
a.
(2.41)
The parameters Op, jSp and S aie plotted against the ratio Vx^/O) in figures 2.9 to
2.11 for various values of plasma frequency. For the discharge conditions typical of copper
and strontium vapour lasers (a few hundred mbar and electron densities of around 10^^ cm“^)
the skin depths are approximately 5 mm. However for fixed electron densities, as Vm/d)
PhD Thesis
29
J. W. Bethel
Chapter 2
Propagation of Microwaves
I
I
Figure 2.10.
The variation of the phase constant, /?p, against the Vm/co ratio for
various û)p/co ratios. The electron densities corresponding to a
microwave frequency of 3 GHz for these û)p/û) ratios are shown in
brackets.
PhD Thesis
30
J. W. Bethel
Chapter 2
Propagation of Microwaves
Figure 2.11.
The variation of the skin depth, 8, against the Vm/co ratio for
various û)p/û) ratios. The electron densities corresponding to a
microwave frequency of 3 GHz for these C0p/<y ratios are shown in
brackets.
becomes greater than 1, the skin depth increases in approximately linear fashion with the
square root of Vm/û>for electron densities above 10^^ cm~3. At values of Vm/û) below 1, the
skin depth remains almost constant as Vm/û) decreases. This occurs because the plasma is
then dominated by the influence of the ratio tUp/m, rather than the effect of electron-atom
collisions {yro/co).
2.4.4 Ejfect of a discontinuity on the propagation of waves in a plasma
So far we have only considered the case of a propagating wave in a uniform, homogeneous
and infinite plasma medium. We now need to examine the effect of microwave propagation
across the boundaiy of two media with different permittivities. For simplicity, we will only
PhD Thesis
31
J. W. Bethel
Chapter 2
Propagation of Microwaves
Transmission
§
I
I
1
'B
0.6
i
0.4
1
^
Reflection
0.
Ratio of permittivités £ ^/ e .
Figure 2.12.
The variation in reflection and transmission of microwaves at a
dielectric interface, for various ratios of the dielectric constants of
the two media.
consider the case of a plane wave crossing an infinite interface between two dielectric media,
where the permittivity changes from £i to £2 at an angle which is normal to the interface. The
well known coefficients of reflection R and transmission T, of incident electromagnetic
waves are given by [2]
-i2
R=
%
'- 1
(2.43)
T=
PhD Thesis
(2.42)
32
J. W, Bethel
Propagation of Microwaves
Chapter 2
1.0
H
§
I
I
I
0.6
0.4
= 9.5
cm
0.2
Figure 2.13.
The fractional transmission of microwaves, at a quartz/plasma boundary, against
the Vm/û) ratio, for various cOp/0} ratios. The electron densities corresponding to
a microwave frequency of 3 GHz for these oup/o ratios are shown in brackets.
for the case where both media aie non-conducting. We can see from the figure 2.12 that the
more than three quarters of the incident power will be transmitted across the interface for a
wide range of 61/62 values. However this is not the case when medium 2 is a plasma, and
hence 62 is complex. In this situation, equations 2.42 and 2.43 become
-|2
^1
Re( 6 2 )
£l
and
PhD Thesis
T=
Re(s2)
33
1
(2.44)
(2.45)
J. W. Bethel
Chapter 2__________________________________________ Propagation of Microwaves
The transmission coefficient T is plotted in figure 2.13 against Vro/co for various cop/m ratios
and £1=3.8 for quartz. Here we can see a very complex dependence on the plasma
parameters, and in some cases, for example Vm/<5>=1 and an electron density of 10^^ cm"^,
a high proportion of the incident microwave power is reflected. For the discharge conditions
appropriate to cyclic and recombination lasers, the transmission coefficient varies widely
from about 0.3 to over 0.9 with the latter value corresponding to buffer gas pressures of the
order of 1 atmosphere i.e. Vm/ü)~100, (see figure 2.13).
2.4.4 Power absorbed in a plasma
So far we have discussed the propagation of plane electromagnetic waves from a
non-absorbing medium to a plasma across an infinite interface, and the subsequent effects of
the plasma on the wavelength and attenuation of the waves. In order to achieve the necessary
operating conditions {e.g. temperature, pressure and electric field) in the laser discharge, we
need to examine how the properties of the plasma will affect the absorption of microwave
power. For the lasers used in this investigation, the operating temperatures are
around 350-450
for the copper halide laser, and 600 °C for the strontium vapour laser.
We need to consider the heating effect of the microwaves for different plasma par ameters. In
addition, we also need to know qualitatively how the electron density and the buffer gas
pressure affect the electron energy in the plasma.
The power flowing into a volume, V, of plasma is given by the
time averaged Poynting vector integrated over the volume of the plasma. Applying Gauss's
theorem, we obtain the following expression for a sinusoidally varying field in an isotropic,
linear plasma
- I j R e ( E x H * ) d A = | - j f l £ £ ' 2 + - / i f f ^ \ i y + I j R e ( E , J * ) d y , (2.46)
S
PhD Thesis
V
V
34
J. W. Bethel
Chapter 2__________________________________________ Propagation o f Microwaves
where the values of E and H are the peak values of the fields [2]. The first tenn on the right
hand side represents power in the electiic and magnetic fields and the second term on the
right is the power deposited in the plasma in the form of Joule heating. This Joule heating
term can be rewritten as
I
dV ,
rms
(2.47)
and represents the total power absorbed due to elastic collisions of the electrons and atoms in
the plasma. Thus, the power absorbed increases lineaiiy with election density when all other
parameters are held constant. Moreover, by differentiating equation 2.47 we find that the
energy transferred to the plasma per election, by elastic collisions with atoms, is a maximum
when the ratio Vm/û) =1. This value corresponds to a neon buffer gas pressure of
around 25 mbar (for the electron temperatures between 5 and 7 eV found in copper halide
lasers with neon buffer gas [8]) and a helium buffer gas pressure of 10 mbar. However, at
these pressures, the skin depth of microwaves at a frequency of 3 GHz is only around
1 mm for an electron density of lO^^m'^. Also, whilst conventional copper halide lasers
operate well at these pressures, strontium-ion recombination lasers require much higher
buffer gas pressures of several hundred millibai' to support sti'ong laser oscillation.
i.e. for high buffer-gas pressures, as is
In the limiting case of
the case in copper and strontium vapour lasers, the energy absorbed by the plasma per
election, per collision, uc, becomes
Mc = —
«e
(2. 48)
v l
(It is noted in section 2.4 that Vm is independent of electron energy for helium, and is a
slowly increasing function of electron energy for neon.) In this situation an electron will
undergo many collisions with atoms during one half cycle of the field, therefore above
PhD Thesis
35
J. W. Bethel
Chapter!__________________________________________ Propagation of Microwaves
equation also corresponds to the case for a direct current dischai'ge. If we ignore the effects
of inelastic collisions» the equation shows that the electron energy decreases lineaiiy with
increasing collision frequency (buffer-gas pressure), when the electric field is held constant.
For both copper halide lasers (neon buffer gas) and strontium-ion recombination lasers
(helium buffer gas), the optimum average electron temperatures during the excitation pulse
are between 5 and 9 eV [8, 9]. Therefore in order to operate these lasers at high buffer gas
pressures (ai'ound 1 atmosphere) the electric field values must be increased commensurately
with the pressure in order to maintain the election energy.
On the other hand, when Vm/û>«l> which corresponds to low buffer-gas
pressures, the energy absorbed per election is given by
:
e 2 e rms
= -----------------------------------------------(2.49)
(O^
and is therefore independent of the buffer-gas pressure. However, at these lower Vm values,
the overall power absorbed by the plasma is reduced because even though the electron
energy is high, the electrons do not transfer this energy to the plasma and hence the heating
of the atoms and molecules is inefficient. This situation leads to highly excited species in the
discharge, but a low average gas temperature. In a copper halide laser this would lead to
ionisation of the copper atoms and hence a reduction in stimulated emission from the laser
transitions in the neutral copper (see chapter 4). For the stiontium-ion recombination laser,
low buffer gas pressures will not provide sufficiently rapid cooling of the electrons in the
afterglow and therefore laser oscillation will not be possible (see chapter 3).
2.4.5 Summary o f the
e ffe c ts o f th e r a tio s V jx/coan d cop/coon w a v e p ro p a g a tio n
So far we have looked at the effects of the values of Vm/O) and cop/co on the electric field,
transmission at an interface and the power absorption individually; however, they are all
inter-related phenomena. Therefore, in order to gain a cleaier picture of the effects of these
plasma parameters on the propagation of microwaves, we must look at the combined
PhD Thesis
36
J. W. Bethel
Chapter 2
Propagation of Microwaves
0.01
1000 -
%
I
I
10
“'
-9 _
rlO
-11
(Dp/û), ratio.
l(f
10
TIT
TT
10
nr
10' -
10'J3
10 14
10
15
Electron density, cin'^.
Figure 2.14.
Fractional power absorbed in a plasma for a plane TEM wave crossing an
infinite free-space plasma boundary, for a propagation depth of 1 cm, for
various values of the ratios, Vfa/co, and, a>p/o), with the electron density
corresponding to 3 GHz.
influences of the plasma permittivity, the transmission and the power absorbed in the ionised
gas for the various plasma conditions. Equation 2.51 below takes all of these effects into
account and represents the fractional absorbed power, fabs, in n plasma, for a plane wave
crossing an infinite free space-dielectric boundary for the case when the propagation
depth z « l m. The dependence of Pahs on the ratios cOp/co and Vm/ft), is plotted in
figure 2.14 as a function of electron density, for a propagation depth of 1 cm.
P ^s= T
,
PhD Thesis
37
2
]
I
JO
exp(-az)
I^effI
dz.
(2.50)
J. W. Bethel
Chapter!__________________________________________ Propagation o f Microwaves
For Vm/® « 1 the absorption of power is very low except when cop/m-l. As Vm/® is
increased, the fraction of absorbed power, fabs, for 0)p/m ~1 decreases when compared
with the Vm/® « 1 case.
For Vm/® » 1 , the peak of Pabs becomes constant for various Vm/® values.
These peaks in the absorbed power occur at lai'ger (O^lm values as Vm/® is increased.
Therefore, there is an optimum cù^lcù value for each pressure at which the fractional power
absorbed is a maximum and these values occur at larger 0)p/m values as Vm/® is increased.
2 .5 Propagation of microwaves in a rectangular waveguide containing a
plasma
The preceding sections of this chapter have covered the basic concepts of microwave
propagation in rectangular waveguides and in plasmas separately. However, in order to
effectively couple microwaves into a discharge we need to consider the effects of the
presence of a plasma in a waveguide. The solution of Maxwell's equations given for an
infinite plasma can apphed to a plasma-filled rectangular waveguide. In this case, the cut-off
wavenumber remains the same as in the case of an empty rectangular* waveguide, however,
the propagation constant
becomes [1]
2
2
f mn
a y
~b
(2.51)
where ^ f f is given by equation 2.32. The first two terms on the right are much smaller than
the third term for electron densities in the plasma corresponding to cop/cù near to unity
(because the wavelength in the plasma under these conditions is very much less than that in
free space-see figure 2.10). Hence, the propagation characteristics are the same as for the
case of a plane wave in an ionised gas described in section 2.4 (this is also the case for any
hollow metal, plasma-filled waveguide). This means that the waves will be attenuated for
PhD Thesis
38
/. W. Bethel
Chapter 2__________________________________________ Propagation of Microwaves
plasma frequencies greater than the angular frequency of the waves, Le. for electron
densities greater than 1 x 10^^ cm~3 using a microwave frequency of 3 GHz. Therefore, it
will not be possible to excite the required active length of plasma at the high electron
densities (-10^^ cm‘^) required of copper and strontium based systems. However it can be
shown that by applying a magnetic field to the waveguide [10], the cut-off for TM modes in
the waveguide occurs at higher electron densities. The magnetic field strengths required for
propagation of microwaves depend upon the electr on densities and the ratio of Vm/œ. For the
discharge conditions which occur in copper and strontium based systems, these magnetic
fields would need to be of the order of a few hundred millitesla. Such a discharge would
have many advantages over a conventional electrical discharge because the plasma could be
created in a metalhc container.
2.5.1 Rectangular waveguide containing a plasma tube
Although the plasma filled waveguide (in the absence of a magnetic field) is limited to
producing discharges with plasma frequencies less than the angular* frequency of the exciting
wave, this is not the case for waveguides which are only partially filled with plasma. For
example, it has been shown in circular* waveguides that electron densities over a factor of 11
higher than the critical electron density can be produced in a quar tz tube situated axially in
the waveguide [11]. The phase and attenuation characteristics of the various modes in these
circular* waveguides can be calculated for different plasma par ameters and tube dimensions
by solving equations 2.4 and 2.5 subject to the necessary boundary conditions. However,
for* a rectangular* waveguide containing a discharge tube, it is not possible to solve equations
2.4 and 2.5 analytically. Nevertheless, an approximation for the effect on the propagation
constant of the microwaves in a rectangular waveguide containing a plasma in a circular
quartz tube has been developed by Ponomarev and Solntsev [12]. The method they used
was based on obtaining an estimate for* the perturbation of the electric fields of
the TE 10 mode by the plasma tube, and using it to calculate the change in the propagation
PhD Thesis
39
J. W. Bethel
Chapter 2
Propagation of Microwaves
constant in the waveguide. The propagation constant %-p for a waveguide containing a
plasma tube is given by [12]
I (^1 -
^o)(Erp*EQ )d5
7rp = 770 +
Eq X
H jp
j + (E fp
(2.52)
^ H q jjd5
where X) is the propagation constant for the empty waveguide and is equivalent to p in
equation 2.16. The values of Erp and Hrp represent the perturbed fields in the waveguide,
and Eq and Hq are the unperturbed fields in an empty waveguide. Hence, the second term
on the right represents the perturbation due to the plasma and the dielectric tube. Ponomarev
and Solntsev assumed an infinitely narrow discharge tube, i.e.
1 k R2
« 1,
0
Region 1
(Plasma)
Region 0
Region 2
Figure 2.15.
The cross section of the rectangular waveguide containing the plasma tube.
where R 2 is the outside radius of the discharge tube (see figure 2.15) and Aq is the
wavelength of the microwaves in free space. The denominator in equation 2.51 can be
expressed as the power flowing through the waveguide for the fundamental mode, provided
that the perturbation due to the plasma is small. Hence the fractional change in the
propagation constant in the waveguide containing the plasma tube becomes
I ( E i -E q )(^i -
+ J ( ^ 2 - E q )(^2 “ ^0
7rp - J 7 0 _ .llQ(0
—J
7o
2 /0
PhD Thesis
•52
40
, (2.53)
J. W. Bethel
Propagation of Microwaves
Chapter 2
where 5q, Si and S 2 refer to the cross sectional areas of the rectangular waveguide, the
dielectric tube and the plasma respectively and similarly
ei and % and Eq, E j and E 2 ,
refer to the permittivities and the electric fields in the corresponding regions respectively.
The permittivity of the plasma £1 is equal to feff (from equation 2.32).
The electiic field in the plasma tube and in the vicinity of the tube/free-space
boundaiy can be expressed in teims of the scalar potential, (p.
(2.54)
There is no electrical charge present in the regions 0 and 2 in the figure 2.14, and hence the
electric field in these regions can be described by equation 2.1 with p=0. In addition, the
field in the plasma can also be expressed in this way because the plasma is assumed to be
neutral (equal numbers of electrons and ions). Therefore, we can express the electric fields
in the waveguide as follows:
V .(e ,-E ,) = 0,
(2.55)
where the subscript i refers to the areas 0, 1 or 2 in figure 2.14. It follows from the relation
2 tüR 2 /^0 « ^ that the potential in all the regions of the waveguide must satisfy Laplace's
equation:
(2.56)
W (p = 0.
Application of equation 2.55 and Laplace's equation to the plasma-dielectric tube and
dielectiic tube-air interfaces, results in the following boundaiy conditions for the system:
9 i \ ri = 9 i \ Ri
(2.57)
/Î1
and
9o \r2 = 9 2 \ R2
£0
PhD Thesis
R1
d(po
dr
CL58)
d(p2
dr
41
2 J
J. W. Bethel
Chapter 2
Propagation o f Microwaves
In addition, Ponomarev and Solntsev assumed that the electric field at a distance from the
discharge tube {e.g. at the broadwall of the waveguide) must coincide with the electric field
of the fundamental mode in an unperturbed waveguide, Le.
(2.59)
E q --V (p o -
The final boundary conditions result from conservation of energy which dictates that the
field at the centre of the plasma be finite. Le.
(2.60)
Laplace's equation for the thiee regions of the waveguide in cylindrical polai' co-ordinates is
+
r dr V
where d(p/dl~Q, and the subscript,
1 d^(Pi
C2.61)
dr
again refers to the regions in figure 2.15. The potential
in the waveguide is taken to be of the form
(2.62)
<Pi = ® j( r )c o s 0 .
Introducing the dimensionless variable, C=r/R\, equation 2.61 becomes
d^4>,-
1 d 0 ;'
dC "
C dC
0;
= 0,
(2.63)
whose solution is of the form
4*/ = A i +
B,
(2.64)
C’
and Ai and Bi are the constants which are determined by applying the boundary conditions
from equations 2.57 to 2.60 to the equations 2.63 and 2.64. These constants are given by
A\ =
, B i= 0,
^2
PhD Thesis
+ l) +
(2.65)
- 1 (/c + £p )
42
J. W. Bethel
Chapter!
Propagation of Microwaves
f
Â2 =
_fp_^
f i A l , B 2 = 2 1^2 )
«2 y
l
(2 .66)
2gI
(2.67)
2
2gwhere
^eff
^0
) ^2
+
^2
-----
^0
(2.68)
+1)
f = S2
e ^ ( g ^ + l ) + (g^ - 1 )
Therefore, by substituting equations 2.65-2.68 into equation 2.52, the fractional change in
propagation constant Ay^/'Yd becomes
Sïrp
_
J
( 4 1
70
*1
.
%
^2
(2.69)
+ l ) + g ^ - 1 (e p + / )
The real and imaginaiy paits of this equation represent, respectively, the attenuation constant
and the change in the phase constant as a fraction of the original propagation constant ^ of
the microwaves. In addition, the attenuation constant can also be written as [12]
a ip
7o
Si Vm
D
m
2 ’
Sq (0
/ +1
(2.70)
cot
where
m =
1+ /
PhD Thesis
2 ’
4 ê 2«-
D=
(2.71)
£2{g^ + i] + g^ +1
43
J. W. Bethel
Propagation of Microwaves
Chapter 2
0.2
R 1 = 0.2 cm.
g
1
^
0.05-
0.8
— I------------
T
R. = 0.4 cm.
Ro = 0.5 cm.
>
I
I
0.4
Vn/m = 100
5
R^ = 1.0 cm.
Rn= 1.1 cm.
>
100
10
"
1010
10^^
10 ^^
10l3
Election density, cm'^.
10^4
10^5
Figure 2.16.
The variation in the attenuation of microwaves in a rectangular
waveguide containing a discharge tube against the ratio 0)p/co, for
various values of the Vm/co ratio and tube radii. The electron
density corresponding to microwaves at 3 GHz is also shown.
PhD Thesis
44
J. W. Bethel
Propagation of Microwaves
Chapter 2
0,15
v ^ û )-1 0
1000
00
g -0.05
8
0.1
0.6
^
^
0.4
8 )'^.
0.2
=0.4 cm.
/?2 = 0.5 cm.
Vjx{co=^ 10
00
g M-0.2
-0 .4
3
1.0 cm.
Vm/G) =0.1
2
.9 ^
a '=3
1
•s
0
l§
li
—
/?2 = 1*1 cm
Vu/®=10
vn/® =1000
Vjj/(CO= 100
1
-2
-3
V n#= 1
I_____
1
0.1
(Dp/CD
ratio.
I________ I
10
"
1010
1011
12
100
10
10l3
10
Election density, cm‘^.
iq U
I
iq 15
Figure 2.17.
The variation in the phase constant of microwaves in a rectangular
waveguide containing a discharge tube against the ratio oip/o), for
various values of the Vm/® ratio and tube radii. The electron density
corresponding to microwaves at 3 GHz is also shown.
PhD Thesis
45
J. W. Bethel
Chapter 2___________________________________________Propagation o f Microwaves
The real and imaginaiy paits of equation 2.69 are plotted against coplco for various values of
VmM for various sizes of quartz tubes (£ 2= 3 .8 ) in figures 2.16 and 2.17. These figures
show significant resonance features at the point where (ûçlcù - 1.6. The shift from ûJp/û)=l
of this resonance feature decreases as the area of the plasma is increased, hence would tend
towai'ds Cûçtoy'l as the waveguide becomes filled with plasma.
For low
values, the attenuation constant increases dramatically when
the plasma is 'on resonance', as in the case of the plane wave in an ionised gas discussed in
section 2.4. Similaiiy, the effect is reduced at higher
values (higher gas pressures) and
the value of coptCDat which the resonance occurs increases which is analogous to increasing
the damping in a harmonic oscillator. Therefore, for the dischaige conditions we require for
copper and strontium metal vapour lasers, the maximum attenuation occurs for an electron
density of around 5 x 10^^ cm"^.
The phase constant exhibits normal dispersion, i.e. the wavelength in the
waveguide is increased by the presence of the plasma tube for ct)p/to values lower than those
corresponding to resonance. Conversely, when top/tois higher than that occurring at
resonance the waveguide exhibits anomalous dispersion where the wavelength is reduced by
the effects of the plasma tube. In this case, a slow wave can result, where the wavelength of
the microwaves in the waveguide is shorter than the wavelength in free space provided the
electi'on-atom collision rates are low enough (Vni/^o<0 . 1).
2.5.1 Electric fields in the rectangular waveguide containing the plasma tube.
The electiic fields in each of the regions i of the waveguide aie given by [12]
Eq = E qoo^Qy - Eg sin ^ 0
1 ( dO;
0;
^
COS0T---- —sin0 0
V dC
(
(2.72)
yj
where r and 0 aie the unit vectors in cylindiical polai' co-ordinates. Note that the above
PhD Thesis
46
J. W. Bethel
Chapter 2
Propagation of Microwaves
10
r....
AVni/ft)=0.1
<±>
fti
II
f
10'
1000
10 -1
\vm/0)= 100
10
'
\
B
>
10
1
10-4 -
1
I
\ y ’n/O)=10
-
\^/m=l
10'^
10
1
1
I
10 "
10 '
10
10
COJ (0 ratio.
10 '
10‘°
_i_____ I___ L j_____ I_____ L.
10*'
lo'^ lo'^
1 0 lo'^
io‘®
Electron density, cm"^.
Figure 2.18.
Electric field in the plasma relative to the empty waveguide, for
various values of the cop/co and Vm/w ratios, with the electron density
shown corresponding to a microwave frequency of 3 GHz.
theory does not take the effects of the skin depth into account because the electric field is
assumed to be uniform in the plasma. The skin effect can be estimated by making reference
to figure 2.11. This will become important for electron densities greater than around
10^^ cnr^ and pressures less than about 100 millibar of neon or 50 millibar of helium. The
consequence of the skin effect will be a reduction in the estimated electric field on the axis of
the plasma tube, when the discharge tube radius is greater than the skin depth.
If we substitute equations 2.65-2.67 into equations 2.72 for the various
regions of the waveguide, we can calculate the electric field relative to that in an empty
waveguide. The electric fields in the plasma are plotted in figure 2.18, and this shows a
PhD Thesis
47
7. W. Bethel
Chapter 2
Propagation of Microwaves
IQl
Vjjyto= 0.1
10®
tti
1
i
- ^ = 0 .9 5
10r l-
cm^}
- ^ = 9 . 5 {id^ cm^}
10“2
10-3
- ^ = 9 5 {lO^^ cm^}
I
10 -^
101
- ^ = 0 .9 5 t o
^
'v W ffl= 1 0
'
1
10®
bq
—
I
i
10
1
1
/
1
1
1
10-2 —
" - ^ = 9 . 5 {lO '^
- ^ - 9 5
cm ^}
{ l 0 '5 c m ^ }
t
10
I
1
101
- ^ = 0 .9 5
^
cm“^}
V^(D~ 100
10® - Y
- ^ = 9 . 5 io^^ c n f }
- ^ = 9 5 {lOl^ cm4
10-41.
0
0.5
1
1.5
Distance from the centie of plasma tube, cm.
2
Figure 2.19.
Electric field distribution in the cross section of the rectangular
waveguide containing a discharge tube where iîi= 0 .4 cm and
R 2-^-5 cm, for various values of the Vm/co and cOp/co ratios with
the electron densities corresponding to microwaves at 3 GHz
shown in brackets.
PhD Thesis
48
J. W. Bethel
Chapter 2___________________________________________Propagation o f Microwaves
similar relationship to figure 2.8 where the electric field for high Vm/û) values is almost the
same as in free space for plasma frequencies up to some critical value. Thereafter, the electiic
fields decrease with increasing cop/co ratio, as the conductivity of the plasma begins to
increase.
The fields in the cross section of the waveguide and the plasma tube are
plotted, along the y space coordinate of the waveguide, thiough the centre of the plasma tube
(which would be constant for the TEio mode in an empty waveguide), for various plasma
parameters and tube dimensions in figure 2.19. These show that as the plasma conditions
approach resonance, i.e. U)p/m=l, the electric field is concentrated in the plasma and is
reduced outside the plasma tube. For high plasma frequencies, the electric field is driven out
of the plasma and is higher outside the plasma tube than would be the case for an empty
waveguide. The fields in the plasma at these high plasma frequencies are considerably less
than in the empty waveguide, especially at the lower v^lcù values. However, as has been
shown earlier, this reduction in the electric field is offset by increasing the collision
frequency.
2.6 Conclusions
In the preceding sections we have discussed the propagation of microwaves in bounded and
unbounded media, and in ionised gases. In a plasma-filled waveguide in the absence of an
external magnetic field, the electron density in the plasma is limited to that corresponding to
the plasma resonance. This electron density is far* too low to support laser oscillation in metal
vapour lasers. However, in a partially filled waveguide, electron densities many times higher
than the plasma frequency can be generated. The equations for the propagation of
microwaves in an empty waveguide are modified if a plasma tube is present.
PhD Thesis
49
J. W. Bethel
Chapter 2__________________________________________ Propagation of Microwaves
We have shown that the electric field and the power absorbed in the plasma
are strongly dependent on the parameters of the plasma. In general, for bounded or
unbounded plasmas, at low buffer gas pressures there is strong absorption of microwave
power and correspondingly high electric fields in the plasma when the electron density
corresponds to the resonance condition. However, the absorbed power and electric fields in
the plasma are very low for plasma frequencies greater than the angular frequency of the
microwaves. At higher gas pressures, the power absorbed and the electric fields in the
plasma are greater than those prevailing at low pressures. Under such conditions, the electric
field to number density ratios {E/N, see chapter 5) and the electron densities appropriate to
strong laser oscillation in copper halide and strontium vapour lasers can be obtained using
microwaves. In the subsequent chapters, the excitation conditions for these lasers are
examined.
PhD Thesis
50
J. W. Bethel
Chapter!__________________________________________ Propagation of Microwaves
References
1.
Microwaves: An intioduction to microwave theory and techniques.
A. J. Baden Fuller.
Second edition, Pergamon Press, 1988.
2.
Electromagnetic fields and waves.
P. Lorrain and D. Corson.
Second edition. W. H. Freeman and Company, New York, 1970.
3.
Waveguide Handbook.
N. Marcuvitz.
First edition, McGraw-Hill Book Company, Inc., 1951.
4.
Higher order modes on usual waveguides.
D. Kother.
International Journal of Inffaied and Millimeter Waves vol. 8, No. 11, pp 1367-1389, 1987.
5.
The design of ridged waveguides.
S. Hopfer.
IRE Transactions of Microwave Theory and Techniques vol. 3, pp 143-151, October 1955.
6.
Microwave Breakdown in Gases.
A. D. MacDonald.
John Wiley and Sons, 1966.
7.
Gaseous Electionics and Gas Lasers.
B. E. Cherrington.
Pergamon Press Ltd, 1979.
8.
Electron temperature measurements in a copper chloride laser using a microwave radiometer.
E. Sovero, C. J. Chen and F. E. C. Culick.
Journal o f Applied Physics vol. 47, No. 10, pp 4538-4542, October 1976.
9.
A self-consistent model for a longitudinal dischai ge excited He-Sr recombination laser.
R. J. Carman.
IEEE Journal of Quantum Electronics vol. 26, No. 9, pp 1588-1608, September 1990.
10.
Slow-Wave Propagation in Plasma Waveguides.
A. W. Trivelpiece.
San Francisco Press, Inc.
11.
High-density resonantly sustained plasma in a variable-length cylindrical cavity.
R. M. Fredericks and J. Asmussen.
Applied Physics Letters, vol. 19, No. 12, pp 508-510, December 1971.
12.
Propagation constant in a rectangular waveguide containing a plasma in a dielectric tube.
V. N. Ponomarev and G. S. Solntsev.
Soviet Physics-Technical Physics vol. 11, No. 8, pp 1027-1031, February 1967.
PhD Thesis
51
J. W. Bethel
CHAPTER
Strontium-ion Recombination Lasers:
Excitation Mechanisms.
3.1 Introduction
For both direct cuirent (dc) and microwave excitation, nonequilibrium conditions in a plasma
are necessary for the production of a population inversion and stimulated emission in
pulsed gas discharge lasers. These discharge excited lasers can be divided into two groups,
"recombination" non-equilibrium and "ionisation" non-equilibrium lasers. These terms
describe the type of nonequilibrium conditions in the plasma which occur in the dischar ge
during stimulated emission. During ionisation nonequilibrium, the ion temperatures
(determined from the degree of ionisation using the Saha equation) are much lower than the
electron temperatures and the system is characterised by a strong pumping of excited states
from lower levels, primarily by electron collisions. These conditions occur during the
dischar ge pulse and ar e typical of the majority of pulsed gas lasers, especially cyclic metal
vapour lasers e.g. copper vapour lasers (see chapter 4). In contrast, recombination
nonequilibrium refers to the situation where the ion temperatures specified by the Saha
equation are higher than the electron temperatures. These conditions occur in the immediate
afterglow of a pulsed discharge. Recombination non-equilibrium is characterised by the
relaxation of the plasma, i.e. recombination of electrons and ions and by the population of
excited states from above. This is the opposite to ionisation non-equilibrium. The strontium
recombination laser operates in this second regime.
PhD Thesis
52
J. W, Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
In this chapter we will discuss the requirements for recombination pumping,
outlining the energy level structure and discharge conditions necessary for maximum
efficiency. The effect of the electron temperature and the pulse shape on the kinetics and
chaiacteristics of the laser is discussed. Finally we address the problem of scaling strontium
vapour lasers to large volumes and examine the possible advantages using a microwave
pumping system.
3.2 Energy level considerations for population inversion by recombination
The principle behind achieving stimulated emission under the conditions of recombination is
discussed by Zhukov et al. [1]. In the recombination regime, the upper laser levels are
pumped via a downwaid flux of de-excited atoms or ions whereas in the ionisation regime
the pumping takes place mainly in an upwaid direction. This means that there is relatively
weaker pumping of the lower laser levels during recombination than for the ionisation
regime. Hence, in some respects, it is easier to create a population inversion for
recombination conditions than for ionisation conditions. Additionally, tlie potential energy of
ions built up during the current pulse can be 'stored' and 'released' at the end of the
excitation pulse. This allows more efficient use of the dischaige pulse energy than that which
occurs in cyclic lasers.
In a strontium-ion recombination laser, laser oscillation occurs on transitions
in the excited Sr^ ion (figure 3.1 shows the energy level diagram for the
ion). The
upper laser level, 6 ^Sy 2»is pumped via electron de-excitation of the high lying levels, which
aie populated by the recombination of the 5'/*++ ions (see section 3.3). Zhukov et al. [1],
derived qualitatively the conditions necessary for recombination pumping in a system
consisting of two groups of energy levels, 2 i and Ij, where the energy levels, i and j within
PhD Thesis
53
J. W. Bethel
Chapter 3
Strontium-ion Recombination lasers
1/2
12
1/2
3/2
3/2
5/2
5/2
7/2
Ionisation
limit 11.03 eV
10
8
6
4
2
Metastable
“ levels
Sr+
0
Figure 3.1.
Energy level diagram of the Sr+
transitions in bold [2].
PhD Thesis
ion
54
showing
the
recom bination
laser
/. W. Bethel
Chapter 3
Strontium-ion Recombination lasers
Pumping,
2i
I
Laser transition
Pumping, W
y
Level population Ny/gy^
Figure 3.2.
Population inversion between two widely separated groups,
where the population of energy levels within the each group is
determined by electron impact processes and therefore follows a
Boltzmann distribution.
the respective groups 2 and 1, are closely spaced (see figure 3.2). The energy level
distribution for the Sr^ ion approximates very closely to this simple example. In this case,
the upper laser level, 6 ^Sy 2 is the lowest in the group of higher lying levels, and the lower
laser level,
(for the 430.5 nm transition), is the highest in the lower lying group of
levels. Following the analysis in [1], the rate of electron de-excitation from the upper level,
2 , to the lower level, 1, is given by
^21
1
2
^ .
&1 ^
7 1 2 ----
(3.1)
3
^2
J
The rate for the reverse process, F 12, is obtained from the principle of detailed balance and is
PhD Thesis
55
J. W. Bethel
Chapter 3
Strontium-ion Recombination lasers
-1
exp
Fn “ /i2
V
^ 2 1
(3.2)
/cr,e J
where AE%i is the energy difference between the two levels, k is the Boltzmann constant,
7e is the electron temperature, gi and g%are the statistical weights of the levels and/12 is the
oscillator sti'ength for the transition. These two equations show that in a super-cooled plasma
where the electron temperature is low, i.e. AE2 i>&:Te, the rate of electron de-excitation
exceeds the rate of electron excitation. Additionally, under these conditions, Zhukov et al.
[ 1] showed that for the case of singly charged ions if àE 2 \>kTç,, as is the case for the
ion, then
F 21 ( 0
AE 21
+ 1
(3.3)
^ 2 1 (^ )
Therefore, de-excitation of levels occurs much more rapidly for ions than for atoms when
the electron temperature is low.
Figure 3.1 shows that for a Si"^ ion, the spacing between the energy levels in
each of the groups is small compaied with the spacing between the upper and lower laser
levels. Therefore, when the electron density is sufficiently high, the probability of collisional
transitions between the levels i and j within their respective groups exceeds the probability of
optical transitions. Hence, this results in a Boltzmann distribution of the populations of the
levels within the group. (Note, however, that the population distribution between groups 1
and 2 will not follow a Boltzmann distribution, unless the election density is very high). For
these conditions, the criterion for establishing a population inversion becomes [ 1]
7 exp
j^ i
W2
giN j
Wi
8
PhD Thesis
kT.e J
f AEf - A E i
exp
kT.
>1,
(3.4)
% Q & exp
56
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
where W\ and W2 are the pumping rates of the levels in groups 1 and 2 respectively
(see figure 3.2), AEfj is the energy difference between the i J th level and the lowest level
in the respective group and the total probability of optical and collisional (impact) transitions,
Q , is given by
^ i ~~ ^ ik
where
tiq
^ik^& ’
(3.5)
is the electron density, A ik is the probability of optical transition. For the
simplified case where the energy spacing of these levels, AEi and AEj, aie so small that each
group of levels may be considered to be a single level, equation 3.4 becomes
g l ( A i 2 + ^ 12 « e ) \
•
7------------------- r /
^ 2 ( ^ 2 1 + ^ 21^ e ) ^ 2
(3.6)
When the electron density is low, we can neglect the transitions due to collisions and the
above equation can be written
(3.7)
^ 2^21
W2
At these low electron densities, it is unlikely that a population inversion would occur in
Sr'*' ions because the energy difference between the upper and lower groups of levels
(AE21) is greater than that between the lower group and the ground state (AEio). Therefore,
the probability for optical ti ansitions from the upper group to the lower group (A21) will be
greater than the corresponding transitions from the lower group to the ground state (A10).
A population inversion due to optical transitions could be established if AE21 was less than
AEio, as is the case for the levels depicted in figure 3(a). However, this inversion would be
destroyed by collisional excitation between the levels as the electron density increases, the
effects of which are increased for decreasing energy level separation (depicted by
equation 3.2).
PhD Thesis
51
J, W. Bethel
Chapter 3
Strontium-ion Recombination lasers
Recombination pumping
W2
Laser emission
Laser emission
Radiative decay
I
0
(a)
Election
de-excitation
i_
_
_
_
(b )
Figures 3.3 (a) and (b).
At higher election densities, a population inversion can be created in Sr^ ions
if
(3.8)
The energy level configuration most suitable in this case is shown in figure 3.3(b), which is
very similar to the distribution of the groups in Sr'^ ions. In this situation, a population
inversion cannot be created by optical transitions because A£'2 i>A£'io a n d
therefore A 21 >A 10 . However, when the electron density is high and AE 2 i>AEio,
collisional de-excitation from the lower level to the ground state (jFio«e) will exceed the
corresponding rate from the upper level to the lower level (i^2 P^e)- By considering only the
upper and lower laser levels, the metastable level and the ground state of the
PhD Thesis
58
ion,
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
Zhukov et a l showed that a population inversion will occur only for electron densities
exceeding 5 x lO^^cm"^ [3].
The ratio between the collisional de-excitation of the lower laser level to the
ground state and the reverse process ie. paiasitic population of the lower laser level from the
ground state (Foi^e), is given by
^
=^exp
^10
&0
(3.9)
Therefore, provided that the electron temperature is low (A£‘io>A:7’e), a population inversion
will be established between groups 2 and 1 in figure 3.3(b). In the
ion, this to the 6 ^Sj/2
and the 5 ^Py 2 3/2 levels (see figure 3.1). However, laser oscillation usually only occurs on
the 6^Sj/2"5^P3/2 transition (430.5 nm), because the inversion is higher (about a factor of
two) than for the 6^Sy2~5^Pi/2 (416.2 nm) transition. This is due to the state of local
thermodynamic equilibrium imposed by inelastic election collisions between the two 5^P
levels at low electron temperatures [4]. Additionally, the probability of radiative transitions
from 6 ^Sj/2 to ^^^ 3/2
about twice that for 6 ^Sy 2 to 5^Py2- Therefore laser oscillation on
the 416.2 nm transition is only observed when a dispersive element is introduced into the
cavity to prevent oscillation at 430.5 nm.
In the above discussion, we have seen that the population inversion is very
strongly dependent upon the election temperature and one of the main processes which can
destroy this inversion is parasitic pumping of the lower laser level. For strontium-ion
recombination lasers, the electron temperature is especially important because metastable
levels, 4^Di/2,3/2’ be between the lower laser level and the ground state. These provide an
efficient channel for depopulating the lower laser level as long as the electron temperature is
low (AEio»kTQ), A detailed computer model, [4], showed that approximately 50 per cent
of the population of the lower laser level is de-excited by electron collisions via these
metastable levels (see figure 3.4). However, if the electron temperature is increased, the
PhD Thesis
59
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
inversion will be destroyed by parasitic pumping from these metastable levels, as suggested
by equation 3.9. The remaining strontium ions in the lower laser level are depopulated by
electron collisions directly to the ground state. The processes which act to reduce the electron
temperature in the discharge afterglow of a helium buffer gas are discussed in section 3.4.
We can now summarise the general requirements for the creation of a
population inversion using electron-ion recombination. The upper laser level should be the
lowest in the upper lying group of closely spaced levels and the lower laser level should be
the highest in the lower lying group of closely spaced levels. The electron density should be
high enough (greater than around 5 x 10^^ cm"^ [3]) so that optical transitions can be
neglected and the election temperature ought to be as low as possible. Electron de-excitation
occurs more rapidly in ions than atoms, hence the transition should occur close to the ground
state (where the energy levels are more widely spaced) of an ion rather than an atom. Ideally
levels between the lower laser level and the ground state should not be metastable, and
finally, the radiative transition linking these two states should be allowed. As we have seen,
the specti'Lim of singly ionised stiontium fulfils all but one of these criteria.
3,3 Three-body electron-ion recombination
In the previous section we saw how recombination pumping can lead to a population
inversion in
ions. The process of recombination in a strontium-ion recombination laser
is achieved via the three-body recombination of the doubly ionised strontium. The
production of these iS'r++ ions can be accomplished by two entirely different processes. In
SRLs operating at high pulse recurrence frequency (PRF), electron collisional ionisation
predominates and can occur in a stepwise manner or directly during the current pulse.
Sr + e - ^
+ 2e
(3.10)
+ e -> Sr++ + 2e
PhD Thesis
60
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
S r 6—
or
+3ë.
(3.11)
The mean energy of the discharge electrons is aionnd 10 eV [4]. This mechanism leads to
the production of what is generally termed the 'short pulse mode' of stimulated emission,
which generally begins within 100 ns of cessation of the current pulse. The duration, full
width at half maximum (FWHM) of the laser pulse produced in this mode is generally
around 250 ns [5].
An alternative process for the production of
ions is via Penning
collisions with helium ions and ionised moleculai’helium [6]
Sr + & +
+He + e
(3.12)
Sr +
^
+ 2 He + e
This mechanism leads to the production of the 'long pulse mode', which occurs about a
microsecond after the cessation of the dischai'ge pulse and has a duration of about 2 jxs [5].
However this mode has not been observed in high-PRF SRLs and in this investigation we
are only concerned with the short pulse mode.
The number density of str ontium atoms in a typical SRL discharge is between
1 and 3 x lO^^cnr^ [7], the majority (about 98 per cent [4]) of which is doubly ionised to
form
ions during the current pulse. After the formation of the
population, the
subsequent reaction for their recombination with electrons is given by
Sr^~^ + g + g —> S r ^
+ e.
(3.13)
Highly-excited, singly-ionised strontium ions are produced in this reaction (see figure 3.1).
Subsequent electron de-excitation occurs to the upper laser level,
6^Sy2>
laser
oscillation at /W416.2 nm (under suitable conditions, see section 3.2) and 430.5 nm occurs
on the transition between this level and the lower laser levels, 5^Pi/2^3/2» respectively.
However, Caiman's model [4] indicates that at the peak of the laser pulse, about 50 per cent
PhD Thesis
61
J. W. Bethel
Chapter 3
Strontium-ion Recombination lasers
12
10
Electron de-excitation
Radiative de-excitation
8
8
I
4
VO
2
o
s
0
Figure 3.4.
Percentage particle flow rates through the Sr+* energy levels at the
peak of the laser pulse [4].
PhD Thesis
62
/. W, Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
of the total downward recombination flux of
ions bypasses the upper laser level
completely (see figure 3.4). Only about 7.5 per cent of the total flux eventually leads to
stimulated emission at 430.5 nm. The rate limiting process for the three-body recombination
of
ions (equation 3.12) is
dt
n l,
= —« f fiSr
(3.14)
where Uq is the election density and % is the recombination coefficient given by [8]
« r = 1.8 X 10“ ^°
sec-1
®
'
(3.15)
p = zl\n (l + z l)
where Tq is the election temperature and Zc is the (integer) ionic chaige. Here we see that the
recombination rate is about 18 times faster for doubly ionised species than singly ionised
species. Moreover, there is a very strong dependence on the electron temperature, as is the
case for the formation of a population inversion in
ions. Therefore, following the initial
ionisation of the strontium atoms, the electrons must be cooled to below about 5000 K
before recombination can take place [4]. In the next section we will discuss the processes
which lead to the decay of the electron temperature in the dischaige afterglow of a helium
buffer gas.
Following laser oscillation and subsequent electron de-excitation to the
ground state of the 5'r+ ion, the 5r+ ions then recombine with electrons to form neutral
strontium atoms. However, there is a remnant density of
ions (3-4 x 10^^ cm"^ [7] just
before the onset of the next current pulse. These Sr~^ ions, together with the corresponding
helium ions, account for the residual electron density at the beginning of the next discharge
pulse. Figure 3.5 summaiises the pump scheme for the strontium-ion recombination laser.
PhD Thesis
63
/. W. Bethel
Chapter 3
Strontium-ion Recombination lasers
12
e + e—
10
8
Sr+* + e
Electron de-excitation
and radiative decay
6
Electron
excitation
1/2
430.5 nm
416.2 nm
4
1/2,3/2
Electron de-excitation and
radiative decay
2
Metastable levels
3/2,5/2
Sr+
0
4
Electron
excitation
Electron de-excitation
2
0
Figure 3.5.
Pump scheme for the strontium-ion recombination laser.
PhD Thesis
64
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
3.4 Electron temperature in the afterglow of a helium buffer gas
The two previous sections have shown the importance of a low electron temperature in both
the process of recombination of
ions and the subsequent stimulated emission on the
430.5 and 416.2 nm transitions in & + ions. We will now investigate the rate of decay of the
electron temperature in the afterglow. For efficient recombination pumping, the election
temperature must decay very rapidly after the cessation of the discharge pulse. The electrons
lose the majority of their energy via elastic collisions with the buffer gas atoms. The fraction
of energy lost during each of these collisions, Jg, is given by
o
2 mg
5 ^ = —^ ,
M
(3.16)
where me is the electron mass and M is the mass of the buffer gas atoms. Therefore, for the
most efficient transfer of energy, the buffer gas atoms must be as light as possible.
Additionally, in order to ensure that the strontium atoms are ionised in preference to the
buffer gas atoms, the ionisation potential of the buffer gas atoms should be as high as
possible. Hence, helium is used as a buffer gas in recombination lasers due to its low mass
and high ionisation energy (24.5 eV [9]). In addition, helium has a relatively large
cross-section for elastic collisions (~5 x 10“^^ cm"^ [9]), which results in a large collision
frequency for momentum transfer (see figure 2.6). By neglecting minor reactions,
Zhukov et al showed that the energy balance of the electrons in the afterglow of a helium
discharge is given by [1]
—
/cTgWg
=—
—Tg
)^ m ^ e
^ ^ r^ r^ e’
where Sm and N m are the energy and the number of the metastable helium atoms,
respectively,
< 0 V q>
is the quenching rate of these metastable helium atoms, Acr is the
energy released in recombination of the helium ions,
is the recombination coefficient (of
singly ionised helium) given by equation (3.15) and 7g is the gas temperature. The term Vtot
PhD Thesis
65
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
represents the total collision frequency and includes electron-ion, Vei, and electron-atom,
Vea, collisions:
=
Vea = (l-76 X 10“ ^®
Vei = 3.64
X
^
a
V
e
a
(3-18)
® - 9.18 x 10“^^
ICr® r;'-®
Ze (In A -1 .3 7 )
(3.19)
A = 1 .2 4 x l0 '^ (7 ’;'-®n;°-®)
where A^He+ and A^Heai'e the number densities of helium ions and atoms respectively.
Therefore, the first term on the right hand side of equation 3.16 represents the energy lost by
the electrons during collisions with atom and ions. This term dominates in the early
afterglow of the dischai'ge. The second and third terms represent heating of the electrons due
to collisional de-excitation of the metastable helium atoms and recombination of the helium
ions, respectively. These two terms are important later in the afterglow and the effect of both
is to slow the rate of cooling of the electrons at these later times. Hence we can see that by
increasing the rate of collisions, we can increase the rate of cooling of the electrons in the
afterglow. Therefore, as the recombination rate of the
ions is strongly dependent on the
electron temperature (see equations 3.14 and 3.15), this will result in a laige increase in the
pumping of the upper laser levels. In addition, the production of a population inversion in
ions is also very sensitive to the electron temperature (see section 3.2). Therefore, it
should be expected that SRLs will perform significantly better at increased buffer gas
pressures because the collision rate for electrons and helium atoms is directly proportional to
the helium pressure. This has been observed experimentally by Latush et al [10] who
observed a five-fold increase in output power for an increase in buffer gas pressure from 1
to 4 atmospheres.
In a typical SRL laser discharge, the mean electron temperature during the
current pulse reaches values of around 10 eV (-77,000 K) [4]. This electron temperature
begins to fall as the cuiTent pulse peaks and rapid cooling of the electrons occurs via inelastic
PhD Thesis
66
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
collisions with other species, along with election-atom collisions with helium neutrals. As
the electron temperature falls below 20,000 K, the electrons are cooled predominantly via
collisions with helium atoms. After a period of aiound 300 ns the electron temperature has
fallen to 5000 K and the
lying levels of
ions begin to recombine with electrons and populate the high
ions. During this period the fraction of energy transferred from electrons
to the gas via electron-atom and electron-ion collisions is approximately equal (see
equations 3.19). (Note that the fraction of energy transferred during collisions of
and
Sr^ ions with electrons is negligible because their atomic mass is much higher than that of
helium).
Following this initial period of rapid cooling (about 2 p,s after the current
pulse has terminated), the rate of decrease of the election temperature slows down markedly
even though Tq (-3500 K) is still much higher than the average gas temperature. This is due
to the effects of reheating of the electrons, via recombination of the helium ions and
de-excitation of the helium metastable levels, represented by the second and third terms in
equation 3.16. Later in the afterglow (about 7 ps) the effects of recombination reheating due
to super-elastic collisions of electrons with
states act to slow the decay of the electron
temperature further. Subsequently, the electron temperature decreases monotonically to the
gas temperatuie during the inteipulse period.
Equation 3.16 ignores the effect of the
and Sr^ ions and the strontium
atoms. However, as the strontium vapour pressure increases, the effect on the cooling rate
of the electrons becomes important. This is because the strontium atoms become ionised
preferentially to the helium atoms, due to the lower ionisation energy of the stiontium atoms.
There is thus a reduction in the number of helium ions (hence a reduction in Vei) and
therefore the rate of cooling of the electrons in the afterglow is reduced. Therefore, in a
typical SRL, the output power drops as the vapour pressure of strontium exceeds the
optimum value (around 0.03 mbar [7]), even though the electron density is increased
(denoted by an increase in the current pulse), as well as the peak and duration of the
PhD Thesis
67
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
spontaneous emission of the 430.5 nm transition [3]. The drop in output power is due to
collisional electron impact excitation from the metastable levels to the lower laser levels at
these increased election temperatures (see equation 3.9).
3.5 Effect of discharge pulse shape on the performance of SRLs
Another factor which affects the electron temperature in the afterglow of these discharges is
the rate of fall of the excitation pulse. A slowly terminating current pulse has a detrimental
effect on the laser output because the electron temperature in the plasma will remain high
during the current pulse. In addition, any ringing in the current pulse (produced as a result of
less than optimum matching of the power supply to the discharge), will result in reheating of
the discharge. The effects of reheating by a small excitation pulse in the afterglow were
investigated in [6]. The results obtained showed a significant dip in the both the spontaneous
and stimulated emission of the 430.5 nm line, corresponding to the application of the pulse.
This was attributed to an increased concentration of the metastable levels, 4^Dg/2,5/2, which
will lead to par asitic population of the lower laser levels by stepwise excitation.
The FWHM of the current pulse in a longitudinally-excited (LE) excited dc
discharge is generally between 100 and 200 ns. This is usually accompanied by some
ringing at the end of the pulse, due to less than perfect impedance matching between the
power supply and the discharge. However, in a microwave excited discharge, there is no
residual microwave power present once the rf pulse has terminated, provided the magnetron
is correctly matched to the power supply (see appendix). In addition, the termination time of
the rf pulse is dependent upon the parameters of the power supply which drives the
magnetron, and is independent of the discharge parameters. Therefore, the termination time
of the excitation pulse in the laser tube will be influenced to a much lesser degree by the
buffer gas pressure in the discharge. This is in contrast to dc discharges in which the
FWHM of the current pulse is increased with increasing buffer gas pressure, because of the
PhD Thesis
68
J. W. Bethel
Chapter 3
Strontium-ion Recombination lasers
increase in the impedance of the plasma at these higher pressures. Hence the potential of
producing a rapidly terminating microwave pulse at high buffer gas pressures could have a
significant advantage over dc excited systems.
3.6 Operating characteristics of SRLs
Strontium-ion recombination lasers are operated in the self-heated regime whereby the waste
heat from the electrical discharge (Joule heating) is used to raise the wall temperature of the
discharge tube to about 600 °C, in order to provide the necessary vapour pressure of
strontium (0.03 mbar [7]). A typical LE strontium vapour laser is shown below. The
current pulse in these lasers is usually of the order of 200 A cm'^ with FWHM of between
150 and 200 ns [1, 4], at voltages of around 15 kV and PRFs of a few kilohertz. The
electron densities at the peak of the laser pulse are about 5 x 1044 cm"^ [3, H ]. A
discharge is struck in a helium buffer gas at pressures of between 300 mbar and 1
atmosphere [12]. The laser tube is usually passively air-cooled, with average output powers
(at /W430.5 nm) typically in the range 1-2 W, at efficiencies of around 0.1 percent [2, 13].
However, enhanced output powers (3.9 W) have been obtained by using water-cooled
tubes [14]. Although quaitz and alumina dischai'ge tubes have been used [4, 15], SRLs
Brewster-angled
silica end windows
Gas outlet
Gas inlet
Quartz tube
Stiontium pieces
O-rings
Water-cooled flange Beryllia or alumina tube
Electrode
Figure 3.6.
Typical conventional strontium vapour laser.
PhD Thesis
69
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
using beiyllia tubes have proved to be superior due to the higher thermal conductivity and
their chemical inertness (low reactivity) with the noiinally highly-reactive stiontium metal at
these elevated temperatures.
Transversely-excited (TE) dc SRLs have been successfully operated and
these lasers produce specific peak output energies of around an order of magnitude higher
(50 |xJ cm"3 [16]) than their LE excited alternatives (6 fiJ cm“^ [5]). These higher specific
output powers are due to the higher electric fields (4-10 kV cm"^) and current densities
(1000 A cm‘2) available in TE excited systems [16]. However, they have so far been
limited to low recurrence rates, due to discharge instabilities which occur at higher
recurrence rates at the high buffer gas pressures necessary for efficient laser oscillation [17].
For a more comprehensive review of strontium-ion recombination lasers, see
reference [10].
3.7 Scaling issues in SRLs
The average output powers of passively air-cooled SRLs are currently limited to 2-3 W
[10,12]. Higher output powers have been achieved by enhancing the heat removal from the
tube by water-cooling. Under these conditions, it is possible to operate SRLs at higher
repetition rates (29 kHz) and therefore with higher specific input powers than in passively
air-cooled SRLs and output powers of 3.9 W have been reported [14].
The above mentioned LE excited systems all consist of relatively narrow bore
discharge tubes (internal diameter of around 1 cm). Volume scaling of SRLs has
been undertaken by Butler and Piper [5] for LE excited lasers. A specific output energy
of 6 pJ cni"3 was obtained using a laser with a volume of 1000 cm^ (at low PRFs of
between 1-100 Hz), which is compaiable to the specific output energies of copper vapour
lasers (8 pJ cnr^ [18]). However, when the PRF is increased, then the effects of radial
PhD Thesis
70
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
theimal gradients (where the gas temperature on axis is liigher than that at the wall) and slow
interpulse thermal relaxation of the dischai'ge medium begin to adversely affect the output
power of these lasers. This results in a depletion of the inter-pulse neutral strontium
and helium number densities on axis [4]. Therefore there will be a lower number density
of
ions available on axis after the application of the current pulse as the PRF is raised.
Additionally, the rate of cooling of the afterglow electrons on axis will be reduced due to the
depletion of helium atoms in this region. This results in a higher axial electron temperature
and hence an increase in the population of the lower laser levels. As a consequence of this,
the laser beam profile becomes annular. By using rectangular bore discharge tubes, the
surface-area to volume ratio of the discharge is increased and this reduces the radial
temperature gradients. Enhanced output powers have been obtained, using rectangular bore
tubes, at higher repetition rates than is usual in chcular bore tubes (1.82 W at 6.7 kHz in a
volume of 114 cm^ [19]).
Another alternative to increasing the bore of the discharge is to increase the
length of the discharge. However, as the length increases, the impedance of the discharge
increases for the same buffer gas pressure and tube diameter. Therefore the FWHM of the
current pulse increases, hence it becomes increasingly difficult to maintain a rapidly
terminating high current density discharge at the high buffer gas pressure required for
optimum SRL operation. In addition, due to the limitations in current thyratrons, it is
difficult to obtain high PRFs (tens of kilohertz, at kilowatt average powers) at voltages
greater than about 40 kV (for which an LC inverter circuit should be used [10]). Therefore
the electric field in the dischai'ge is reduced, hence the ionisation of the strontium will be
reduced, resulting in a reduction of the recombination pumping and hence the population
inversion. However, by using a two section discharge tube, a tube length of 90 cm has been
used to obtain 3W of average power (see reference [10]) at pressure of 720 mbai'.
PhD Thesis
71
7. W. Bethel
Chapter' 3____________________________________ Strontium-ion Recombination lasers
3.8 Conclusion
SRLs aie promising sources of high peak and average power blue (430.5 nm) radiation.
However, as we have seen, the population inversion in SRLs is highly sensitive to the
election temperature in the discharge afterglow of the helium buffer gas. In addition, the
output powers in SRLs aie very sensitive to the strontium vapour pressure. This is because
of the adverse effect that a high strontium number density has on the rate of cooling of the
electron temperature in the afterglow of a He-Sr dischai'ge.
The output powers in conventional SRLs are currently limited by the heat
removal from the discharge tube, restrictions imposed by the present generation of
thyratrons on the tube voltages and recurrence rates, and the shape of the current pulse at
high pressures. The length of LE excited lasers is also limited by the tube voltages attainable
using present switching technologies [10].
The reliability of conventional LE SRLs is affected by the highly reactive
nature of the hot strontium vapour. Impurities introduced as a result of electrode sputtering
and even outgassing of electrodes themselves, leads to the production of strontium
compounds and hence requiring the laser to be reloaded with strontium metal. The
recurrence rates of SRLs can also be limited by electrode instabilities, resulting in an
unstable current pulse and hence leading to erratic laser output powers. Finally, the
redistribution of the strontium in the discharge tube due to diffusion and axial cataphoresis
(the latter affects all ion lasers) will eventually lead to a reduction in tube lifetime for a
sealed-off system.
Microwave-excited tiansverse-discharges, on the other hand, could offer a
promising alternative to electrically excited LE and TE SRLs. Magnetrons can produce
pulses shapes which are independent of the discharge conditions. Microwave discharges can
be operated at high pressures (multi-atmosphere [20]) with high coupling efficiencies
(approaching 100 per cent after ignition of the discharge). Operation at high pressures has
PhD Thesis
72
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
been shown to be advantageous for SRL performance (see section 3.3) and the effects of
diffusion are also reduced at high buffer gas pressures. A microwave excited SRL will have
no electrodes and therefore will be free from both the impurities introduced by electrode
sputtering and instabilities induced by the electrodes. Finally, the oscillating nature of
microwave dischaiges rule out any cataphoretic effects and will result in longer lifetimes for
sealed-off tubes.
PhD Thesis
73
J.W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
References
1.
Recombination lasers utilising vapours of chemical elements.
1. Principles of achieving stimulated emission under recombination conditions.
V. V. Zhukov, E. L. Latush, V. S, Mikhalevskii and M. F. Sem.
Soviet Journal of Quantum Electronics, vol. 7, No. 6, pp 704-708, June 1977.
2.
Atomic energy levels.
C. E. Moore.
United States Department of Commerce, August 1952.
3.
Recombination lasers utilising vapours of chemical elements.
2. Laser action due to transitions in metal ions.
V. V. Zhukov, V. S. Kucherov, E. L. Latush and M. F. Sem.
Soviet Journal of Quantum Electionics, vol. 7, No. 6, pp 708-714, June 1977.
4.
A self-consistent model for a longitudinal discharge excited He-Sr recombination laser.
R. J. Carman.
IEEE Journal of Quantum Electronics, vol. 26, No. 9, pp 1588-1608, September 1990.
5.
Optimisation of excitation channels in tlie discharge-excited Sr"^ laser recombination.
M. S. Butler and J, A. Piper.
Applied Physics Letters, vol. 45, No. 7, pp 707-709, October 1984.
6.
Role of multistage collisions of the second kind in the mechanism of pumping of a
helium-strontium recombination laser.
E. L. Latush, Yu. V. Koptev, M. F. Sem, G. D. Chebotarev and D. A. Korogodin.
Soviet Journal o f Quantum Electionics, vol. 21, No. 12, pp 1314-1320, December 1991.
7.
Time resolved measurements of population state densities in a Sr"^ recombination laser.
R. Kunnemeyer, C. W. McLucas, D. J. W. Brown and A. I. McIntosh.
IEEE Journal o f Quantum Electronics, vol. 23, No. 11, pp 2028-2032, November 1987.
8.
Election recombination coefficient with three-body collisions in a plasma
I. S. Veselovskii.
Soviet Physics-Technical Physics, vol. 14, No. 2, pp 193-197, August 1969.
9.
Microwave breakdown in gases.
A. D. MacDonald.
John Wiley and Sons, 1966.
10.
Gas-discharge recombination lasers based on stiontium and calcium vapours:
A review.
E. L. Latush, M. F. Sem, L. M. Bukshpun, Yu. V. Koptev and S. N. Atamas.
Optics and Spectioscopy, vol. 72, No. 5, pp 672-680, May 1992.
11.
Electron density measurements in a stiontium vapour laser.
D. G. Loveland and C. E. Webb.
J. Phys. D; Applied Physics, vol. 25, pp 597-604, 1992.
12.
Pumping of strontium-ion recombination laser in a system with a cut-off thyration.
P. A. Bokhan and D. E. Zakievskii.
Soviet Journal of Quantum Electronics, vol. 21, No. 8, pp 838-839, August 1991.
13.
Design of a 1.7 W stable long-lived strontium vapour laser.
D. G. Loveland, D. A. Orchard, A. F. Zerrouk and C. E. Webb.
Measurement Science and Technology, vol. 2, pp 1083-1087, 1991.
PhD Thesis
74
J. W. Bethel
Chapter 3____________________________________ Strontium-ion Recombination lasers
14.
Influence of the temperature of the active medium on the stimulated emission characteristics of an
Sr-He recombination laser.
L. M. Bukshpun, E. L. Latush and M. F. Sem.
Soviet Journal of Quantum Electronics, vol. 18, No. 9, pp 1098-1100, September 1988.
15.
Forced-air cooled strontium-ion recombination laser.
J. W. Bethel and C. E. Little.
Optics Communications, vol. 84, No. 5,6, pp 317-322, August 1991.
16.
High-pressure high-current transversely excited Sr'*' recombination laser.
M. S. Butler and J. A. Piper.
Applied Physics Letters, vol. 42, No. 12, pp 1008-1010, June 1983.
17.
Repetitively pulsed transversely excited Sr"*"recombination laser.
M. Brandt.
IEEE Journal of Quantum Electionics, vol. 20, No. 9, pp 1006-1007, September 1984.
18.
Scaling of tlie discharge heated copper vapour laser.
I. Smilanski, A. Kerman, L. A. Levin and G. Erez.
Optics and Communications, vol. 25, No. 1, pp 79-83, April 1978.
19.
Investigation of a high average power rectangular bore Sr+ recombination laser.
R. M Heiitschel, R. J. Carman and J, A. Piper.
Proceedings of CLEG, Anaheim, paper CThR2, pp 545-546, May 1992.
20.
Improved perfoimance of the microwave-pumped XeCl laser.
P. J. K. Wisoff, A. J. Mendelsohn, S. E. Harris and J. F. Young.
IEEE Journal of Quantum Electronics, vol. 18, No. 11, pp 1893-1840, November 1982.
PhD Thesis
75
/. W. Bethel
CHAPTER
Copper Halide Lasers:
Excitation Mechanisms.
4.1 Introduction
In the previous chapter, we saw how a population inversion in a vapour consisting of singly
ionised strontium in a buffer gas of helium could be created under recombination
nonequilibrium conditions. In this chapter we discuss the requirements for creating a
population inversion in a copper-based system using ionisation nonequilibrium conditions.
For this case, laser oscillation occurs on the cyclic transitions of neutral copper atoms during
the rising edge of the current pulse, when the ion temperatures are much lower than the
electron temperatures. We will also discuss the dominant kinetic processes which occur in a
copper halide laser and their effect on determining the operating characteristics of the laser.
4.2 Cyclic lasers
The term 'cyclic laser’ refers to the sequential (rather than simultaneous) collisional
excitation and then relaxation of the energy levels in the active species, usually neutral
atoms. They are generally three level systems (see figure 4.1) which are usually
characterised by the following properties [1]. The upper laser level is a resonance level
which is strongly connected to the ground state by a radiative transition and the lower laser
level should be long lived, i.e. a metastable level. The population inversion is transient
PhD Thesis
76
J.W . Bethel
Copper Halide lasers
Chapter 4
Upper laser level
3
CO
Lower laser levels
(Metastable)
Ground state
1
Figure 4.1.
The cyclic energy level system.
because the lower laser levels become populated via stimulated emission during the laser
pulse and must be deactivated before another excitation pulse can be applied. Hence, cyclic
lasers are inherently pulsed.
9.6 ns (615 ns)
Upper laser
level
00
a
r-
cn
cn (S
Lower laser
level
~w
\D
r,o\
a :
a
<N cn rH
cn cn
A
0
cn
s
0
0^
0
cc
a
4p P 3 /2
4p Pj/2
00
CN
cn
IT)
Ground state
Figure 4.2.
Radiative lifetimes of the energy levels in neutral copper, the extended lifetimes
for the trapped states are shown in brackets, [2].
The radiative lifetimes of the upper laser levels are very short (9.6 ns for
neutral copper, see figure 4.2 [2]) and the radiative transition probability of the resonance
PhD Thesis
77
J. W. Bethel
Chapter 4_______________________________________________ Copper Halide lasers
transition, A31, in an isolated atom is much greater than that for the laser transition A32 .
Therefore, in order to obtain laser oscillation on the transition from level 3 to level 2, the
radiative lifetime of the upper laser level must be significantly increased, without reducing
the transition cross section from level 3 to level 2. For the cyclic system described, a photon
winch is emitted from the upper laser level (resonant) in an isolated neutral atom will be lost
to the discharge. However, if a photon emitted from such an excited atom interacts with
ground state atom of the same species, it will excite an electron into the upper laser level of
this atom and therefore the photon is not lost. If there aie sufficient numbers of these atoms
in the discharge, then the effective lifetime of the upper level will be greatly increased. For
the case of copper, the lifetime of the upper level is extended to 615 ns for copper atom
densities in excess of 10^^ cm"^ (see figure 4.2) [2], This mechanism is known as radiative
trapping and allows transitions from the upper laser level to the lower laser level to occur
under these conditions because A32(laser transition) becomes greater than A 31 (trapped
resonance transition). Stimulated emission on the laser transition eventually terminates
because the inversion is destroyed as a result of the increasing metastable, lower laser level
populations. These metastable levels must be cleaied before laser oscillation can begin again.
The energy difference between the metastable level and the ground state should be small.
This is because the energy released during de-excitation of this level is lost as heat.
However, if the spacing is too small then collisional excitation by electrons will occur,
reducing the population inversion (as indicated by equation 3.2). Therefore, the optimum
spacing should ideally be between 0.75 and 2.2 eV [1]. To minimise population of the
metastable level during excitation of the upper levels, the risetime of the dischar ge current
pulse must be fast enough that the upper level is populated preferentially by virtue of a high
electron temperature during that time. Finally, if the laser transition is to be efficient, the
energy level spacing between the upper and lower laser levels should be a significant fraction
of the spacing between the lower laser level and the ground state. That is to say, that the
quantum efficiency of the laser transition should be as high as possible.
PhD Thesis
78
J. W, Bethel
Copper Halide lasers
Chapter 4
3d levels
levels
10
1/2
1/2
3/2
-<
3/2
5/2
>*
3/2
5/2
lonis^ion limit
7.72 eV
8
6
I
4
2
Cu
0
Figure 4.3.
Energy level diagram for neutral copper showing the laser transitions investigated in
this work in bold [3].
4.3 Kinetic processes in copper halide lasers
It can be seen from figure 4.3 that the energy level scheme in neutral copper atoms fulfils all
the conditions required for an efficient cyclic laser. The quantum efficiency of the laser
transition (^Pi/2 3/2 to ^ ^ 312,512) ts high (about 60 per cent) and therefore a high proportion
of the excitation energy will result in laser output. However, in elemental copper vapour
lasers (CVLs), the operating temperature necessary to produce the optimum vapour pressure
of copper vapour (0.2 to 0.4 mbar [3]) is so high (about 1500 °C), that the time required for
PhD Thesis
79
/. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
the laser to reach a stable average output power can be up to 2 hours. Engineering difficulties
such as alumina sagging and outgassing of alumina tubes and insulation, mean that the
buffer gas must be flowed thiough the dischai'ge tube to purge the system. Additionally, the
recurrence rates of discharge excited (dc) CVLs are limited to 5-10 kHz for maximum
average output power because of the reduced dealing of the metastable levels on axis at high
on-axis gas temperatures (see section 4.2.2) [4]. It was for these reasons that copper halide
lasers (CHLs) were developed because the volatile nature of copper halides allows operation
at much lower tube wall temperatures (around 500 °C) than elemental copper based lasers
[5].
Comprehensive computer modelhng of elemental copper [6,7, 8] and copper
halide lasers [9], has been already been carried out, so in this section we will only outline
some of the more important processes which take place. The mechanisms which occur in a
copper halide laser can be divided into two, the processes which take place during the
current pulse and those which occur in the inteipulse period. The principle of excitation of
CHLs is the same as for elemental copper lasers, except that the copper halide molecule must
first be dissociated to provide free copper atoms in the discharge.
4.3.1 During the current pulse
Copper halide lasers are operated in a pulsed electrical dischai'ge, usually in a buffer gas of
either neon or helium. At the optimum operating temperature for CHLs, there is a number
density of copper halide molecules of between 10^^ and 10^^ cm"^. Eaily devices relied on
double-pulsed excitation. During the first current pulse, electron collisions dissociate the
copper halide molecules to provide free copper and halogen, X, atoms. The following
reactions have been proposed by Kushner and Culick [9] and Haistad [10]
PhD Thesis
CuX + 6 —^ Cu + X + (? —Aê,
(4.1)
CuX + € —^ Cu + X
(4.2)
80
—Afi,
J. W. Bethel
Copper Halide lasers
Chapter 4
Ground state
Metastable level
I
I
Laser window
0
300
100
200
Time after dissociation pulse, |xs.
400
Figure 4.4.
The number densities of the ground and metastable levels
in copper in the afterglow of a Cul-Ar mixture, showing
the laser window*. Data from reference [10]
where Ae is the dissociation energy. In both cases, the majority of the free copper atoms
produced will be in the metastable state and therefore no laser action is observed during this
current pulse. If the second discharge pulse is applied immediately following the dissociation
pulse, then radiative trapping will not be possible because there will be too few atoms in the
ground state. On the other hand, if the time period between the dissociation pulse and the
second discharge pulse is too long, then the copper atoms will recombine with the halide
atoms and this will also result in a low ground state population of atoms. Therefore there is a
limited time period, after the application of the dissociation pulse, within which an excitation
pulse must be applied in order to achieve laser oscillation. The population inversion between
the ^Pi/2 3/2
the ^Dg/2 5/2 states (see figure 4.3) is created by direct electron collisional
excitation, during the application of this second discharge pulse. Figure 4.4 shows the
'laser window' along with measured number densities of ground and metastable level states
of copper in the discharge afterglow of a Cul-Ar mixture [11]. The optimum sepaiations of
PhD Thesis
81
J, W. Bethel
Chapter 4
Copper Halide lasers
the dissociation and the excitation pulses are dependent upon the metastable deactivation
processes, the recombination of copper and halogen atoms, buffer gas type and pressure
(see figures 4.5 and 4.6).
Ground state
-o
Metastable
level '5/2
.
Ü
I
i
Neon pressureNq
— e— 26mbai'
— X— 2.6 mbai'
Laser emission
0
100
200
300
Time after dissociation pulse, jis.
400
Figure 4.5.
M easured densities of ground and m etastable levels of neutral
copper, in a double-pulsed CuCl laser for two values of neon buffer
gas pressure, illustrating the effect on the stimulated emission of
the 510.6 nm transition. Data from reference [14].
In addition to the electron collisional dissociation of the copper halide
molecules and excitation of the copper atoms, the formation of electrons and ions during the
current pulse also plays an important role in the mechanisms for creating a population
inversion in copper atoms. Although the majority of the electrons in the discharge are
produced as a result of ionisation of the buffer gas (helium or neon), there is a significant
fraction of copper ionised during the current pulse (aiound 50 percent of the prepulse copper
atom density [6]). This is because the ionisation potential of copper atoms (7.73 eV) [12] is
close to the excitation energy of the upper laser level (see figure 4.3). These copper ions can
take no part in laser oscillation, hence their production leads to a reduction in laser
efficiency. The electron temperature in the discharge during the current pulse reaches values
PhD Thesis
82
J. W. Bethel
Chapter 4
Copper Halide lasers
1016
Ground state
Tube diameter
40 mm
4 mm
I
Metastable level
J
D5/2
-©
Laser emission
0
100
200
300
Time after dissociation pulse, (is.
400
Figure 4.6.
Measured densities of ground and metastable levels of neutral copper, in
a double-pulsed CuCl laser for two values of neon buffer gas pressure,
illustrating the effect on the stim ulated em ission of the 510.6 nm
transition. Data from reference [14].
of between 5 and 8 eV [8 , 13]. The electron densities during the current pulse are of the
order of lO^'^ cm“^.
4.3.2 During the interpulse period
The kinetic processes which occur in the period between the discharge pulses are very
important in determining the operating characteristics of the copper halide laser. The three
key processes which occur in the interpulse period are the recombination of copper and
halogen atoms, relaxation of the copper metastable states, and repopulation of the ground
state densities of the neutral copper atoms. In addition, we have the decay in the electron
PhD Thesis
83
y. W, Bethel
Chapter 4________________________________________________ Copper Halide lasers
temperature and the recombination of electrons and ions, the latter of which affects the
breakdown voltage in a conventional dc dischaige laser.
The recombination of the copper and halogen atoms is the main loss process
for the ground state copper atoms. It has been suggested that formation of copper halide
molecules could take place via volume recombination:
{CujCUj^ j + X + M —> CuX + M ,
(4.3a)
where M could be any third body (most likely a buffer gas atom) [8] and also
( ^ C u / X
—^CuX-\~e,
(4.3b)
could be important. Alternatively, recombination of the copper and halide molecules could
take place at the wall, following diffusion there [10]:
Cu + X —>
^ CuX.
Cu" + X ~ -^Cu" + X
and
»
Cu + X - ^ D i j f - ^ C u X
(4.4)
(4.5)
It would be expected that in diffusion-controlled recombination, increasing
the pressure of the buffer gas and diameter of the dischai'ge tube, would lead to a reduction
in the rate of decay of the ground state of the copper atoms [10]. This was confirmed
experimentally by Nerheim [14] in double-pulsed systems (see figure 4.5 and 4.6). The
population of copper atoms in the metastable state following dissociation is high, therefore in
a double-pulsed system these excited species must relax to the ground state before the
application of the second discharge pulse. Many mechanisms for the deactivation of the
metastable levels have been proposed, such as diffusion to the walls, collisions with neon
atoms and collisions with electrons. At low buffer gas pressures, the dominant mechanism
appeal's to be diffusion to the wall [15]. However, when the pressure, p and the diameter, d,
of the discharge tube fulfil the following condition, p(P'>l?>0 mbar cm^ [16] the rate of
PhD Thesis
84
J. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
decay of the metastable atoms can only be explained, without contiadiction, by collisional
de-excitation by cool electrons [17]. This is also the mechanism for deactivation of the
metastable levels in 5r+ions (see equation 3.9). The rate of relaxation of the metastable
atoms is almost always exponential, and follows the decay of the electron temperature in the
late afterglow very closely [14, 17]. The rate of fall of the electron temperature is very
similai' to that described for an SRL in section 3.4 and tends towards the gas temperature in
the late afterglow.
The formation of negative halide ions by electron attachment,
X + 6 + M —> X
+ M,
(4.6)
becomes important later in the afterglow and during this time they become the dominant
negative charge carrier in the discharge [9]. The electron density drops by almost three
orders of magnitude (over a period of around 150 jits), primarily as a result of the formation
of these negative ions. The corresponding reduction in electron density in an elemental
copper vapour laser is only about a factor of two [18]. This significant drop in preionisation
can lead to the formation of unstable and constricted dischar ges and hence inefficient laser
oscillation, in systems where the PRF is too low, or the copper halide vapour pressure is too
high (as a result of a high wall temperature). Another consequence of this lower prepulse
electron density in copper halide lasers is a higher breakdown voltage of the discharge than
in elemental copper lasers. Figure 4.7 shows a simplified pump scheme for a copper halide
laser.
4.3.3 Buffer gas effects in copper halide lasers
Copper halide (and elemental copper vapour) lasers can be operated in buffer gases of
helium, neon or argon [19, 20]. However, for continuously pulsed lasers, neon has proved
to give consistently higher output powers than either helium or argon and in turn helium
gives higher output powers than argon. The reason for the enhanced output power in neon is
PhD Thesis
85
J. W. Bethel
Chapter 4
Copper Halide lasers
Ionisation potential (7.72 eV)
8
6
I
4
election
impact^
2
4s D 3/2
/
4s^D 5/2
de-excitation by election
impact plus wall collisions.
0
1/2
--------------Copper atom
•3.8 eV CuCl
•2.5 eV CuBr
Copper halide
molecule
0
Figure 4.7.
Simplified pump scheme for a copper halide laser. Laser transitions shown in bold.
PhD Thesis
86
J. W. Bethel
Chapter 4________________________________________________Copper Halide lasers
not fully understood, although the decay rate of the metastable copper atoms in a neon buffer
gas (7.2 X lO'^ s'l and 5.4 x 10^ s'i for the ^0^/2 and ^Dg/2lGvels respectively) is faster
than in a helium buffer gas (3.7 x 10^ s“l and 3.6 x 10"^ s’l for the ^Dg/2 and ^Dg/2 levels
respectively) [17].
If we consider the energy balance equation,
where
is the rate constant for the transition between the i and the j th levels, Eij is the
energy difference in the two levels, M'l is the mass of the ith component and Vm^ is the
corresponding collision frequency of momentum transfer. The remaining terms are as
defined in chapter 3 section 3.4. This equation shows that the collision frequency for
momentum ti'ansfer, Vm, plays an important role in the mechanisms which affect the electron
temperature, as it appear s twice. As Vm increases, the cross-section for inelastic processes
increases and this lowers the electron temperature during the discharge pulse. In addition,
the rate of cooling in the afterglow discharge increases. The value of Vm in helium is about
twice that in neon (see figure 2.6 and 2.7) and therefore CHLs can operate at higher
pressures in a neon buffer gas than in a helium buffer gas. This results in reduced
reassociation rates for the copper and halogen atoms and hence an increase in the lifetime of
the ground state copper atom, as a result of lower diffusion rates following Harstad's [10]
argument. Furthermore, the diffusion of all the species out of the active medium will be
reduced, resulting in potentially longer lifetimes in a sealed-off system.
The copper halide vapour has a complex effect on the characteristics of an
inert gas discharge. For low halide vapour pressures, the effect is small and the discharge
remains stable for PRFs corresponding to maximum output power. However, as the vapour
pressure increases (for example at elevated tube temperatures), there is a dramatic increase in
the number of inelastic collisions with the copper halide molecules and the products of their
PhD Thesis
87
/. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
dissociation (copper and halide atoms and ions). Therefore, there will be an increase in the
production of negative halogen ions (see equation 4.4) and a corresponding decrease in the
election density, towards the end of the interpulse period. This leads to a reduction in both
the metastable deactivation and the ground state density of the copper atoms. Additionally,
due to lower preionisation, the discharge becomes less stable and can be ineffective in
pumping the upper laser levels. Hence, a lai'ger than optimum vapour pressure of the copper
halide is detrimental to laser output. However, an increased number density of copper halide
molecules in the dischai'ge can be accommodated if the buffer gas pressure is also increased
commensurately. In this case, due to the greater number of elastic collisions at these higher
pressures (see equation 4.7) the electric field must be increased approximately lineaiiy with
the pressure, in order to maintain the required optimum election energy during the discharge
pulse. The increase in copper halide numbers should result in a lai'ger number of ground
state copper atoms available for laser oscillation. Therefore, it should be possible to increase
the output power of these lasers by operating at higher pressuies.
4.4 Operating characteristics of copper halide lasers.
Laser oscillation has been observed in the three copper halides, CuCl, CuBr and Cul. The
operating chaiacteristics of these lasers are very similar, with the optimum temperatures of
the three halides increasing from CuCl to CuBr to Cul (370°C, 420®C, SOO^C,
respectively), as their volatility falls [21]. The number densities of the molecules at their
respective optimum operating temperatures is almost identical (between 2.5-4x10^^ cm"3
[22]). Due to their relatively low operating temperatures with halides, the dischai'ge tubes
can be fabricated from quartz and quite complex tube designs can be created by a skilled
glass blower. Usually these quai’tz tubes contain apertures to maintain the straightness of the
discharge, which can be difficult at high copper halide vapour pressures, high buffer gas
pressure and low recurrence rates. The lasant is normally placed in heated sideai'ms in the
PhD Thesis
88
/. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
quartz discharge tube to allow more precise control of the halide vapour pressure [17]. The
relative output powers of each of the copper halides is around 6:3:2, for CuCl:CuBr:Cul
respectively [21].
4.4.1 Double-pulsed lasers
Laser oscillation in the vapour of copper halides was first observed using double-pulsed
systems [5]. In double-pulsed copper halide lasers, the first pulse acts as the dissociation
pulse and the second pulse excites the neutral copper atoms to the upper laser level.
However, these types of laser aie no longer used except in diagnostic experiments. In the
present study, the microwave excited copper halide laser was operated in the double pulsed
regime, due to the limitations of the magnetron power supply (see appendix).
Typically, double-pulsed lasers are longitudinally excited (LE), the
recurrence frequency of the pulse pairs is usually low (a few Hz) and the system is
externally heated. Double-pulsed lasers are characterised by high output pulse
energies (38
|LiJ
cm"^) at operating voltages of ai'ound 20 kV (for tube lengths of 30 cm)
and current pulse densities of between 50 and 100 A cm~^ at pressures around 10 mbar of
helium and 25 mbar of neon [23, 24]. However, the efficiency of these systems is low,
ai'ound 0.3 percent (ignoring the dissociation pulse) [11]. This because the dissociation of
the halide molecules, during the first discharge pulse, into copper and halogen is only
around 3 percent and falls to around 1 percent at the onset of laser oscillation. At the
optimum operating temperatures for these lasers, the copper halide molecule is likely to
occur in the trimer state, CugXg, and subsequent dissociation of this molecule into copper
and halogen occurs during the dissociation pulse. The optimum pulse separations for the
dissociation pulse and the excitation pulse increases from CuCl, CuBr to Cul in accordance
with the electron affinities of the corresponding halogen atoms (chlorine=3.61 eV,
bromine=3.36 eV, iodine=3.06 eV) [17]. The actual sepaiations are dependent upon the tube
diameter and the buffer gas pressure (see figures 4.5 and 4.6)
PhD Thesis
89
/. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
Transversely excited (TE) double pulsed copper halide lasers have also been
operated in a similar manner to LE excited systems {i.e. externally heated and low PRFs)
[25, 26]. Output powers of up to 50 [iJ cm"^, at efficiencies of 0.3 per cent (for the
excitation pulse), have been obtained for similar pressures as those found in their LE
counteipai'ts, although the electric fields aie considerably higher in TE systems (around 5
kV cm"l) [25, 26]. However, tube designs in TE lasers are considerably more complicated
and difficult to construct than those of LE lasers and they are therefore not as common.
4.4.2 Continuously pulsed lasers
With the advent of more advanced thyratrons capable of switching high voltages (up to
25 kV) at high average powers (tens of kilowatts), the majority of high power copper halide
lasers are now LE systems and continuously pulsed (due to the problems in developing TE
systems at high PRFs, pulsed TE copper halide lasers are rai'e). The kinetic processes
involved in continuously pulsed CVLs aie slightly different from those in double pulsed
systems. The recurrence rates of these systems are generally between 15-25 kHz depending
on the tube diameter and the buffer gas pressure [27, 28, 29]. In continuously pulsed CHLs,
the dissociation of copper halide molecules can build up over a period of successive
discharge pulses to reach high levels (between 50 and 100 percent [11, 17]). This results in
higher efficiencies than in double pulsed systems because the free copper atoms aie recycled
through excitation, laser oscillation and deactivation, up to four times before finally
recombining with a halogen atom [11]. Therefore, there is less energy lost via recombination
of the copper halide molecules (see figme 4.7). The copper halide molecules in the discharge
of high recurrence rate systems aie more likely to be in the monomer state (CuX) because the
recombination rate of the tiimer (CU3X3) is much slower than the monomer [17].
Efficiencies of 1.6 percent and output powers of 19 W have been obtained
for small bore tubes {i.d. = 20 mm) with the addition of hydrogen [27]. The maximum
average output power so far obtained from a copper halide laser is 112 W in a 6 cm bore
PhD Thesis
90
J. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
tube with an active length of 1.5 m (with the addition of hydrogen) [29]. However the
specific pulse energies obtained from continuously pulsed lasers (between 2 and 8 p,J cm~^
[30]) are much less than those in double pulsed systems. This is due to the lower
dissociation and excitation energies used in continuously pulsed lasers (using the same input
pulse energies at high recurrence rates would result in over-heating of the dischai'ge tube). In
combination with the incomplete relaxation of the dischai'ge species (election and ions) in the
interpulse period, lai'ger radial gradients in number densities occur in continuously pulsed
systems than in externally heated double pulsed systems [10], which act to reduce the
specific output pulse energy.
4.4 3 Addition of hydrogen
Although in the present investigation, the effects of the addition of hydrogen to the
microwave excited laser aie not examined, it is worth mentioning the effects that the addition
of small amounts of hydrogen has on the output chaiacteristics of a copper halide laser. In
pure neon buffer gas, the output beam profile of the copper halide laser operating at
maximum output power, under ultra clean conditions, is annular [31]. On the addition
of -0.4 mbar of hydrogen, the beam becomes 'Gaussian-like', Le, brighter in the centre,
and the output power of the laser is increased by up to 100 percent. The effects on the
discharge are an increase in the breakdown voltage of the tube and a reduction in the peak
current, due to the resultant increase in the impedance of the tube.
Astadjov et a l [32] proposed that these effects are due to the formation
of H“ ions, which results in a decrease in the prepulse electron density. The electron
detachment rate of these H“ ions is over an order of magnitude higher than the ionisation rate
of copper atoms. Therefore the ionisation of copper is reduced, resulting in a greater
population of the upper laser levels and hence enhanced stimulated emission. However, this
explanation still needs to be verified. However, results of the addition of hydrogen to
elemental CVLs suggests that the decrease in prepulse election density is due to the increased
PhD Thesis
91
J,W. Bethel
Chapter 4
Copper Halide lasers
collision rate of the electrons (and hence increased cooling and electron-ion recombination)
afforded by the addition of hydi’ogen.
4.4.4 Lifetime studies copper halide lasers
Nowadays, the most commonly used lasant in copper halide lasers is copper bromide, due to
the higher output powers it permits. Extensive longevity studies using a sealed-off laser with
the copper bromide placed in heated external ovens have been undertaken by Sabotinov et al
[30]. The main problems associated with long lived sealed off copper bromide lasers are
related to discharge instabilities and contamination of the laser windows with pure copper.
Dischai'ge instabilities aie generally solved by using apertures to confine the discharge.
However, instabilities can still eventually arise in a sealed-off system due to the production
of free bromine in the discharge zone [30]. Porous copper electrodes and copper bromide
can absorb the liberated bromine and reduce this tendency towai'ds instability. Using such
electrodes and apertures as described, laser output powers of between 5 and 7 W have been
obtained in a system sealed off for 1000 hours, with a completely heated tube where
reservoir temperatures are lower than the rest of the tube (see figure 4.8) [30].
Apeiture
Heaters
y
Insulation
Quartz tube
I
I
rC
I
Discharge volume
.EX3
E33I,
y
I'
-Copper pieces
Electrode
Electi'ode
Oven heater
Copper halide
Figure 4,8,
Whole-heated sealed-off copper halide laser.
PhD Thesis
92
J. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
4.4.5 Copper HyBrlD Lasers
A new, important class of metal vapour laser is currently being developed in which the metal
donor (in this case, copper bromide) is created by the reaction of HBr gas with copper pieces
in the discharge zone [33]. The copper 'HyBrlD' (Hydrogen Bromide In Discharge) laser
has the advantage that the hydrogen is added to the discharge in a controlled manner in the
form of HBr gas and allows rapid waim-up times for these systems (about 20 minutes to
reach 100 W) [34]. Output powers and efficiencies exceed those of present copper halide
lasers (200 W at an efficiency of 1.9 percent and over 100 W at an efficiency of 3.2 percent
[34]) and they can operate over a wider temperature range (500-700°C). However, these
systems operate with a flowing gas and the HBr used is highly toxic and requires caieful
handling. Efforts are underway to develop a sealed-off system.
4.4 Conclusion
Copper-based lasers currently produce the highest average output powers, at
the highest efficiencies, in the visible region for a single element laser. Elemental copper
lasers have long start-up times and usually require flowing gas in the system. However
using a copper halide as the copper donor, these lasers can achieve much faster start up times
and have been operated for extended periods of time with sealed-off tubes. The output
powers of these lasers is expected to increase with increasing buffer gas pressures and the
reduced diffusion of the lasant from the active medium will extend the lifetime of these
lasers. However, increasing the buffer gas pressure can lead to unstable discharges and
erratic laser output in LE lasers. Transverse discharges on the other hand can be operated at
high pressures, electric fields and current densities, but they are difficult to construct and
become unstable at high PRFs. Transverse microwave dischaiges can be operated at high
pressures, high PRFs and produce high electric fields. The rise-time of the microwave pulse
is independent of the discharge conditions, unlike conventional dc discharges. Another
PhD Thesis
93
J. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
important point to consider is that there are no electrodes in a microwave discharge and
therefore no electrode induced dischai'ge instabilities can occur as result of degradation from
reactions with the copper halide.
PhD Thesis
94
J. W. Bethel
Chapter 4________________________________________________ Copper Halide lasei's
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PhD Thesis
95
J. W. Bethel
Chapter 4________________________________________________ Copper Halide lasers
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Buffer gas effects on ground and metastable populations in a pulsed CuBr laser.
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Stimulated emission due to transitions in copper atoms formed in tiansverse discharges in copper
halide vapours.
G. V. Abrosimov and V. V. Vasil'tov.
Soviet Journal of Quantum Electronics, vol. 7, No. 4, pp 512-513 April 1977.
26.
Operating chai acteristics of TE Copper Bromide Lasers.
M. Brandt and J. A. Piper.
IEEE Journal of Quantum Electronics, vol. 17, No. 6, pp 1107-1115.
27.
A new circuit for CuBr laser excitation.
N. K, Vuchkov, D. N. Astadjov and N. V. Sabotinov.
Optical and Quantum Electronics, vol. 23. pp S549-S553 1991
PhD Thesis
96
J. W, Bethel
Chapter 4________________________________________________ Copper Halide lasers
28.
High-efficiency CuBr laser with interacting peaking circuits.
N. K. Vuchkov, N. V. Sabotinov and D. N. Astadjov.
Optical and Quantum Electionics, vol. 20, pp 433-438, 1988.
29.
CuBr laser with output power exceeding 100 W.
V. F. Elaev, G. D. Lyakh and V. P. Pelenkov.
Atmospheric Optics, vol. 2, No. 11, pp 1045-1047, November 1989.
30.
Copper bromide lasers - discharge tube and lifetime problems.
N. V. Sabotinov, N. K. Vuchkov and D. N. Astadjov.
Proceedings of SPIE High Power Gas Lasers, vol. 1225, pp 289-298, 1990.
31.
Effect o f hydrogen on CuBr laser power and efficiency.
D. N. Astadjov. N. V. Sabotinov and N. K. Vuchkov.
Optics and Communications, vol. 56, No. 4, pp 279-282, December 1985.
32.
Parametric study of tlie CuBr laser with hydrogen additives.
D. N. Astadjov, N. K. Vuchkov and N. S. Sabotinov.
IEEE Journal of Quantum Electronics, vol. 24, No. 9, pp 1927-1935, September 1988.
33.
Characteristics of a copper bromide laser with flowing Ne-HBr buffer gas.
E. S. Livingstone, D. R. Jones, A. Maitland and C. E. Little.
Optical and Quantum Electronics, vol. 24, pp 73-82, 1992.
34.
A high-efficiency 200 W average power copper HyBrlD laser.
D. R. Jones, A. Maitland and C. E. Little.
IEEE Journal of Quantum Electr onics, in press.
PhD Thesis
97
J. W. Bethel
CHAPTER
Microwave Pumping Configurations
5.1 Introduction
In this chapter we describe the design of the two waveguide coupling strictures used in this
investigation. The Ridged Waveguide Coupling Structure (RWCS), and the Tapered
Waveguide Coupling Structure (TWCS) are used to couple microwave power into a gas
discharge with the aim of producing laser oscillation on cyclic tiansitions of neutral copper
atoms and the recombination ti'ansitions of stiontium ions.
Many coupling structures have been used in the past to pump lasers or excite
gas discharges. For instance, laser oscillation has been observed in systems where the
dischai'ge tube is situated paiallel to either of the thiee axes of a rectangulai* waveguide, (see
figure 5.1). More elaborate designs involving rectangular waveguides consist of two
waveguides, a primary and a secondai-y, which shaie a common wall. The discharge tube is
situated in the secondary guide and microwave power is coupled from the primary to the
secondary via a series of apertures in the shaied wall. Ideally, the apertures are designed so
that an equal proportion of power is coupled from each in order to produce a unifoim electric
field along the length of the dischai'ge tube.
Circulai' waveguide coupling stiuctures, such as the Asmussen cavity [1] (see
figure 5.2) have been used in the attempt to pump copper chloride lasers [2]. The
electromagnetic field components can be solved quite readily for these symmetrical cavities
and therefore they can also function as a useful plasma diagnostic tool. This can be
PhD Thesis
98
J. W. Bethel
Chapter 5
a
Microwave Pumping Configurations
A
Electiic field
direction
Quaitz tube
rectangulai' waveguide
-----------
Figure 5.1.
Various coupling geometries that have been used for rectangular waveguides.
Coupling
antenna
Quartz tube
Sliding short
Figure 5.2.
An Asmussen cavity.
PhD Thesis
99
7. W. Bethel
Chapter 5
Microwave Pumping Configurations
accomplished by measuring the wavelength of the microwaves in the cavity and the power
absorbed by the plasma on resonance. Then, by solving the electromagnetic fields, subject to
the boundary conditions in the system, the electric field, the electron density and
electron-helium collision frequency in the plasma can be calculated [3].
In the past decade or so, the method of coupling microwaves into dischar ges
by using so called ‘surface-waves’ has received much attention [4]. These surface-wave
produced plasmas, in which the microwaves propagate along the dielectric interface between
the tube wall and the plasma, have been used to pump helium-neon, argon-ion and excimer
lasers as well as being employed for plasma diagnostic studies. There are numerous methods
of producing these surface-wave dischai'ges, but probably the most basic method is by
simply placing the discharge tube through holes in both broad walls of a rectangular
waveguide (a surfaguide, see figure 5.3). A movable short is placed after the plasma tube in
order to maximise the electric field in the vicinity of the dischai'ge tube, and hence maximise
the coupling of power to the tube. Often the dimension of the naiTow wall of the waveguide
is reduced by between 1/2 and 1/4 of the original height [5]. In a surfaguide, the electiic field
set up in the plasma is paiallel to the discharge tube and the microwaves propagate along the
tube until the electron density in the plasma becomes too low to support the surface wave.
Dischai’ge tube
Rectangulai* waveguide
A
Sliding short
Microwaves
Electric field lines
V
Figure 5.3.
A Surfaguide for producing surfacewave discharges, using a rectangular waveguide.
PhD Thesis
100
J. W, Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
This electron density at cut-off is, to a first approximation, a function the permittivity of the
tube and frequency of the microwaves [4].
In addition to the above mentioned systems, many other novel coupling
stmctures have been used to pump gas lasers, however there is insufficient space to mention
them all here. In general though, plasma-filled waveguides, as opposed to waveguides
partially filled with plasma, are not commonly used because the plasma frequency of the
discharge produced in such a system is limited to less than the angular frequency of the
microwave field (see section 2.5). Therefore if a plasma were to be excited in such a scheme
using a microwave frequency of 3 GHz, the maximum possible electron density would be
about 1.1x10^^ cm“3, in a collisionless plasma {i.e. low buffer gas pressure) without the
use of an external magnetic field [6],
5.2 Pumping requirements for strontium-ion recombination lasers
The operating conditions required for pumping strontium-ion recombination lasers (SRLs)
using conventional electrical dischai'ges aie given in section 3.6. In a typical longitudinallyexcited (LE) SRL, laser oscillation occurs in the discharge afterglow of a high current
density (-200 A cm"^), high pressure (several hundred mbar) helium buffer gas, in the
presence of about 0.03 mbar of strontium vapour at pulse recurrence frequencies (PRFs) of
several kHz [7]. The election densities in these dischai'ges aie of the order of 10^®-10^^ nT^
[8]. From equations 2.38a and 2.41, the corresponding microwave skin depths for the
electron densities are between 2.4 and 0.73 mm at 100 mbar, and 7.4 mm and 2.4 mm
at 1000 bar, in helium buffer-gas. This limits the radius of a plasma tube in the waveguide
because in order to produce a uniform electric field across the bore of the dischar ge tube, the
diameter of the discharge must not significantly exceed the skin depth.
PhD Thesis
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J. W. Bethel
Chapter 5___________________________________Microwave Pumping Configurations
In order to estimate the volume of the dischai'ge that can be pumped using the
existing microwave arrangement, we begin by considering the pump power densities used
for conventional SRLs. For pulsed metal vapour lasers in general, the input pump power
density for maximum laser output power increases as the discharge radius is reduced.
Experiments carried out by Butler and Piper [9], showed that for a LE SRL, with a tube
radius of 1.3 cm and discharge volume of 30 cm^, the optimum pump power-density was
48 kW cm"3, giving a total pump power of 1.4 MW. Therefore, with a peak output power
of 2.6 MW available from the magnetron (EEV type M5193), it should be possible to pump
an SRL with a discharge volume of about 50 cm^ for a similar' diameter dischar ge tube if the
all the microwave power is coupled into the dischai'ge.
5.3 Pumping requirements for copper halide lasers
The requirements for electrical excitation of copper halide lasers (CHLs) are detailed in
section 4.3. In contrast to SRLs, laser oscillation in conventional longitudinally, electricallyexcited CHLs occurs on the leading edge of the current pulse (-75 A cm'^) in a neon
buffer gas of between 20 and 100 mbar, in the presence of the copper halide vapour at a
par tial pressure of between 0.1 to 0.15 mbar [10, 11]. Copper halide lasers can also operate
using helium buffer gas in the place of neon, although the laser output power is lower.
Another important difference in the excitation mechanism of SRLs and CHLs is the need to
provide a dissociation pulse and an excitation pulse, if the PRF is not sufficiently high (see
section 4.2). The spacing between the two pulses is determined by the characteristic
recombination time of the copper and halogen atoms, and the rate of decay of the metastable,
lower laser levels (4 ^D^/2 ,5/2)' The second excitation pulse must be applied before a
significant number of copper halide molecules have reformed, but after the metastable copper
atoms have decayed in sufficient numbers. Therefore these lasers must be pumped either by
high PRF pulses (5-16 kHz) or by double-pulse methods (as is the case in this work). The
PhD Thesis
102
J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
electron densities during the current pulse are of the same magnitude (lO^^-lO^^ m“^) as
those found in conventional SRLs [12]; the corresponding skin depths for neon with an
electron temperature of about 5 eV are 0.4-1.7 mm at 100 mbar and 1.6-5.4 mm
at 1000 mbar. Although these values are slightly lower than those found in helium
dischai'ges due to the lower collision frequencies of electrons with neon, it should be
possible to use the same diameter tube as used for the stiontium laser.
The pump power densities in CHLs can vary widely from one system to
another. For example, in transversely excited (TE) systems operating at low PRFs, the
pump-power densities can be as high as 0.9 MW cm‘^ for a pump volume of 16 cm^ and
tube radius of 2 cm [13], although in [14] a lower power density of only 170 kW cm-3 was
used to excite a lai'ger volume of 150 cmr^ and a radius of 30 nun. On the other hand, self­
heated LE CHLs operating at high recurrence-rates have much lower pump-power densities.
For example, a LE CuBr laser with a dischai'ge diameter of 20 mm with an optimum pump
power-density of around 5.8 kW cm"^ was reported in [10]. This is because in LE systems
operating at high PRFs, practically all the moleculai' species are dissociated in the discharge.
Therefore lower excitation and dissociation energies are required, compared with low PRF
systems.
The magnetron available to us has a maximum average output power of
around 2.8 kW, which is more than enough to generate the wall temperature required
(-600 ®C for SRLs, and from 370-500 ®C for CHLs [11]) to provide the necessary partial
pressure of strontium or copper-halide vapour for optimum operating conditions. This is
done without any additional sources of heating. In addition, the width of the microwave
pulses can be vai'ied, from about 700 ns to 4 |is (see appendix), thus allowing the peak
powers and hence electric fields in the plasma to be adjusted whilst maintaining the optimum
input power (hence stiontium or copper halide vapour pressure) for operation.
PhD Thesis
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J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
5.4
The ridged waveguide coupling structure
This section describes a ridge waveguide coupling structure (RWCS), which is designed to
produce a transverse electric field across a quartz discharge tube, which is situated axially
along the waveguide. It has already been shown in section 2.3 that the electric field produced
in a ridge waveguide is higher than that produced in a rectangular waveguide for the same
transmitted power. This is because the ridges in the waveguide concentrate the electric field
in the vicinity of the dischar ge tube which is placed between the ridges.
Ridge waveguide coupling structures of this type have been successfully
used to pump a XeCl excimer laser using a commercially available magnetron, [15].
Conventional excimer lasers are usually pumped by a high-voltage high-current electrical
discharge, resulting in electron densities of over lO^^m-3. Similar* plasma conditions are also
found in SRL and CHL discharges. It was for this reason that a ridge waveguide coupling
structure was chosen initially for the present work.
The use of the RWCS was investigated as a possible pump source for the
copper(l)chloride laser, and allowed us to demonstr ate, for the first time, of laser oscillation
in a microwave excited copper laser (see chapter 6 ).
5.4.1 Electric fields in the ridge waveguide
The electric field along the axis of a ridge waveguide given by equation 2.27, (rewritten
below) is related to the dimensions of the ridges, wavelength of the microwaves and the
dimensions of the waveguide itself. Therefore, in order to produce the required electric field
across the dischar ge tube, suitable dimensions must be chosen for the ridges.
m
2 d
Ka
cos
2 (
Ka r
PhD Thesis
(
( 7 ü d\) ,
TVS
,
— loge cosec —- + - — +
\ 2 b j j iKa
\m j
\
b s m ^ { 2 7 v y r / K ) [ y k: J
104
(5.1)
4^""
J. W. Bethel
Chapter 5
Microwave Pumping Configurations
Curve 1 : (#=0.2
Curve 2 : d/b=^03
Curve 3 : dÂ>=OA
Curve 4 : d/tf=0.5
Curve 5 : d/b=0.6
Curve 6 : (#=0.65
0.2
0,4
0.6
0.8
Ratio of ridge to waveguide width, s/a.
Figure 5.4.
The electric field on the axis of the ridge against the ratio s/a for various
d/b values, with a peak microwave power of 1 MW in the ridge waveguide.
Electric fields along the axis of a ridge waveguide are plotted in figure 5.4, as
functions of the ratio s/a for various d/b values, where s is the width of the ridge, d is the
distance between the two ridges and a and b are the dimensions of the broad and narrow
walls of the waveguide, respectively (see figure 5.7). The graph shows that the electric
fields are higher for lower values of s/a and d/b. In fact, as the electric fields along the centre
of the ridge increase for lower s/a and d/b values, the fields outwith the ridge region are
reduced simultaneously, see figure 2.5. However, the above calculations are for an empty
ridge waveguide, and do not take into account the effect of the plasma and the quartz tube. It
has been shown in section 2.5.1, that the combined effect of the plasma and quartz tube on
the electric field in a rectangular’ waveguide can produce a significant perturbation in the
electric field distribution in the waveguide.
In experiments carried out on TE SRLs, by Butler and Piper [16], typical
values of the electric field used were between 4 and 10 kV cnr^. Similarly, in experiments
PhD Thesis
105
J. W. Bethel
Chapter 5
Microwave Pumping Configurations
12
Curve 1 :d/b=0.2
Curve 2 :d/b=0.3
Curve 3 : d/b=OA
Curve 4 : d/b=0.5
Ciu-ve 5 : d/b=Q.6
Cui-ve 6 : d/b=0.65
10
«4-1
8
6
4
2
0
0
2
6
4
8
10
Radius of sphere, mm.
Figure 5.5,
Field enhancement factor for a sphere above a grounded
plane against the sphere’s radius for various separation
corresponding to d/b values shown,
carried out by Brandt and Piper on a TE CuBr laser [14], electric fields of between 4.7 and
6.7 kV cm 'l were used. Figure 5.4 shows that for a d/b ratio of 0.3, corresponding to a
distance of 10 mm, the rms electric fields are between 20-13 kV cm~l, for s/a values of
between 0.1-0.8. However, because of the finite radius of the edge of the ridge, the field in
this vicinity will be enhanced and could lead to arcing at these points. This enhancement of
the field can be approximated by the case of a charged sphere above a grounded plane and is
given below in equation 5.2 [17]
^0
\2d~
\2d
-f 1 + — + 1
_ r _
_ r
—
2
+8
(5,2)
where d is the distance between the sphere and the plane, r is the radius of the edge of the
ridge, E q is the electric field in the centre of the ridge. This field enhancement as a function
of sphere radius is plotted in figure 5.5, for vaiious values of d/b. For the ridges used in the
PhD Thesis
106
J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
RWCS, a value of r=4 nini was chosen, which provides a field enhancement of ai'ound 1.6
for d=10 mm. The high electric fields which will be present in the ridge waveguide could
lead to problems with electrical breakdown (ai'cing) in the air within the coupling structure.
Electrical breakdown in a waveguide results in the reflection of most of the microwave
power at the arc, and in addition, can result in damage to the waveguide wall and the
discharge tube. In order to prevent arcing between the quartz tube and the ridges, the
waveguide was pressurised with up to 3 atmospheres of dry air. According to MacDonald
[18], at values of pb/n, of above about 13 cm-mbar where b is the waveguide height,
breakdown is independent of microwave frequency and is given by equation 5.3.
— ~ 22.8 kVcm“ ^bar“ ^
(5,3)
P
Therefore by equation 5.1, which relates the power flowing through the ridge waveguide to
the electric field in the centre of the ridge, an increase in pressure from 1 atmosphere to
3 atmospheres should increase the power handling capacity of the ridge waveguide by a
factor of 9. However surface-roughness, imperfections or particles in the waveguide will
drastically reduce the power handling capability of any waveguide.
5.4.2 Impedance matching of the ridge waveguide
In order to maximise the efficiency of coupling of the microwave power into the discharge,
the impedance of the ridge waveguide should be matched to that of the rectangular
waveguide. The impedance Zq, of any hollow metal waveguide operating in the TEio mode,
for microwaves with a free space wavelength Aq is given by [19]
X
^0 ~
Aq
(5.4)
where Ag is the waveguide wavelength, and t] is the impedance of free space (377 ohms).
The impedance of the RWCS (not including the effects the plasma tube or the short circuit at
PhD Thesis
107
J. W. Bethel
Chapter 5
Microwave Pumping Configurations
480
Q
'É 460
I
% 440
%
%
8
X
) 420
(D
t
d/b=0.2
400
0.2
0.4
0.6
0.8
Ratio of ridge to waveguide width, s/a.
Figure 5,6.
Impedance of the ridge waveguide against s/a for various d/b values
the end of the coupling structure) is plotted as a function of s/a for various d/b values in
figure 5.6, using data from figure 2.4 and equation 2.17.
The impedance of the rectangular waveguide (WGIO, «=7.2 cm and
b -3 .4 cm) for microwaves at a frequency of 3 GHz is 524 ohms. Therefore, in order to
reduce reflections at the boundary between the ridge and rectangular waveguides, we must
taper the impedance transition between the two waveguides. This can be done by linearly
tapering the ridge height from zero up to the height in the ridge waveguide itself. The curves
given in [20 ], show that the reflections produced by a lineai' taper are a function of the length
of the taper, and the magnitudes of these reflections are minimum for taper lengths equal to
multiples of Xt/2, where Xt is the wavelength of the microwaves in the tapered section. For
the case of the ridge waveguide, the taper length L should be made equal to
[Ag + Ai- ]
L —n
PhD Thesis
108
(5.5)
J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
where « is an integer and Xx is the wavelength in the ridge waveguide and can be obtained
from figure 2.4 and equation 2.17. However, it should be noted that the impedance
transformer was designed without considering the effects of the plasma tube. Figure 5.13
shows that the change in impedance of the rectangular* waveguide due to the plasma tube for
the expected electron densities is only around 10 percent.
5.4.3 Mechanical design o f the RWCS
Figure 5.7 overleaf shows the ridge waveguide coupling structure. The coupling structure
was constr ucted from standard WGIO brass waveguide. The design incorporated removable
ridges, so that a wide range of electr ic fields could be produced in the waveguide for given a
microwave power in the waveguide. Each of the ridges was fixed in position by Dowty seals
along the length of the waveguide. It is important to have good contact between the ridges
and the waveguide walls to prevent microwave power being coupled into this region. This
can result in arcing which damages the surfaces between the ridge and the waveguide wall,
hence leads to a further reduction in electrical contact in this area.
The plasma tube was sleeved in cylindrical brass tubing at the points where it
exited the coupling stnrcture, in order to prevent microwave leakage from the system. These
sleeves acted as waveguides with a much smaller cut off wavelength than the main
waveguide. The cut-off wavelength for the lowest order mode in a circular* guide (TEjj) is
given by [19],
%
(5.6)
where x=1.84 for TEjj modes and a' is the radius of the sleeve. Hence, due to the
exponential decay of the microwave frequencies below cut-off, using a length of 140 mm,
the field strength should be reduced by a factor of - 10'^® compared with that of the main
guide! However, any plasma in the quartz tube in this region would lead to the formation of
PhD Thesis
109
J. W. Bethel
i
Side view of the ridge waveguide
Ridge
taper
I
65 mm
Ridge length
---------------- 660 mm -----------------------------Ridge
taper
Ridges
End sheath
—14 m m ^
Waveguide pressurised with
3 bar of dry air
0 -rin
Quartz tube
Cross section of the ridge waveguide
Water-cooled
choke-flange
0 -ring
Water
channel
Dimensions
a - 1 2 mm
b = 34 mm
j = 20 mm
d = 22 mm
Tube dimensions
Id. = 8 mm
o.d. = 10 mm
Water cooling
Water cooling
I
?
s
I
Ridge fixing screws
a
Figure 5.7.
The ridge waveguide coupling structure
I
Chapter 5___________________________________ Microwave Pumping Configurations
a 'surface-wave' [21 ], which would propagate along the interface between the quartz tube
and the plasma. This effect would lead to a dramatic increase in the field strength outside the
waveguide and could therefore constitute a health risk. It was for this reason that such a long
sheath was employed.
The RWCS was water-cooled to provide maximum heat removal from the
tube and hence maximise the input power, and additionally to prevent softening of the brass
waveguide (at around 500°C) which is highly undesirable for a pressurised system.
5.4.4 Performance of the RWCS
The empty RWCS was initially designed with a ridge spacing d=10.5 mm and a width
of j=20 mm. The empty waveguide i.e. no plasma tube, should have a power handling
capability of ~ 1.8 MW with atmospheric air, according to equation 5.1 and 5.3. However,
with the plasma tube present, breakdown occurred at very low input powers even when
pressurised with 3 atmospheres of diy air. This ai'cing occurred between the ridge and quartz
tube in the vicinity of the ridge taper. The arc, as well as damaging the quartz tube and the
surfaces of the ridges, also acts like a short-circuit in the waveguide preventing further
propagation through the guide. The occurrence of aicing at such low input powers, can only
be explained by a significant enhancement of the electric field between the ridge and the
quartz tube. In the plots of the figure 2.19, which show the electric field distribution in a
rectangulai' waveguide containing a plasma tube, we can see an enhancement of the electric
field at the quaitz tube/air boundary. The increase in the electric field in this region will
increase as the distance between the quai'tz tube and the waveguide wall is reduced. As a
result, the ridge spacing d was increased to d=22 mm. This reduces the electric field in the
RWCS from 17 to 11.5 kV cm'^ for 1 MW peak power (see figure 5.4). However, this
reduction in field is more than compensated for by the increased power which could now be
deposited in the dischaige tube because of the elimination of arcing at the taper.
PhD Thesis
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J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
We first observed laser oscillation in a copper(l)chloride-neon discharge
using the RWCS described above. However, further experiments showed that the RWCS
would be poor a coupling stincture due to the standing waves that aie produced in the cavity,
as a result of reflection of microwaves from the short circuit at the end of the cavity (see
figure 5.7). The experiments using the RWCS aie presented in chapter 6 .
5.5 The tapered waveguide coupling structure
It followed from the initial experiments carried out with the RWCS, that a coupling structure
which provides an longitudinally uniform electric field in the plasma {i.e. no standing
waves) is necessary for efficient laser oscillation. This constraint obviously will result in
uniform power deposition along the length of the discharge tube, as can be seen from
equation 2.47. However, even if the standing waves were to be eliminated by placing a load
at the end of the RWCS, the electric field at the end of the cavity would still be significantly
reduced compaied with that at the input end, i.e. the field would still not be longitudinally
uniform. Therefore, a waveguide coupling structure which fulfils the condition of uniform
power deposition in the presence of a non-uniformly absorbing medium {i.e. the discharge
tube) was sought. This lead to our use of a tapered waveguide coupling structure (TWCS).
5.5.1 Theory of tapered waveguide containing plasma tube
The tapered waveguide coupling structure was first proposed by Slinko et al. [22] for
producing uniform power deposition in high pressure discharges, and has been used for the
pumping excimer laser discharges [23]. This coupling structure consists simply of
rectangular waveguide, with a tapered narrow wall, containing a discharge tube running
axially along the waveguide, as shown in figure 5.8.
PhD Thesis
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J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
If we return to theory of a rectangulai* waveguide containing a plasma tube in
chapter 2, the equation 2.70, for the attenuation constant of the microwaves travelling
thi’ough the waveguide can be rewritten as
2 kD^
Si Vm
g?
(where the symbols aie as defined in chapter 2 ) provided the outer radius of the plasma tube,
/?2 » satisfies the following condition (where Aq is the wavelength of microwaves in free
space):
I
k R.2
X0
{(1.
(5.8)
We can see from equation 5.7 thata is inversely proportional to the cross-sectional area of
the waveguide Sq>The electric
field, E(z>t),in the rectangular waveguide is given by
=
(5.9)
where the propagation constant 7rp=-7 Cfrp+Ap> and ftp is the phase constant (and can be
obtained from equation 2.69). For a TEjo mode the power in the waveguide is proportional
to the squai'e of the electric field. Therefore, following theory developed by Slinko [22], the
power tiansmitted thi'ough an arbitrary waveguide containing a discharge tube is given by
=
(5.10)
where Pq is the initial power entering the waveguide, P{z) is the power in the waveguide at a
distances along the waveguide and %p(z) is the variable attenuation constant, which at z=0
is given by equation 5.7 above. The condition corresponding to uniform deposition of
power along the waveguide is given by
cLP(o^ip(^),^)
constant.
(5.11)
dz
PhD Thesis
113
J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
Therefore, differentiating 5.10 twice with respect to z, we obtain the following differential
equation relating the attenuation constant ccip (z) to the longitudinal co-ordinate z.
f
dz
2 a^.^{zr = 0.
(5.12)
If at z=0, Oip(z)=«t) Le. (%p in equation 5.7, then the solution of this equation is
a
<^yp(z) = -r ~ :r — •
l~ 2aoZ
(5.13)
Hence, for uniform power deposition in the dischaige tube, we need to vary the attenuation
factor accordingly. It can be seen by rewriting equation 5.7 as
that this can be achieved by varying the dimension of the narrow wall b{z), where Z?(z) is
given by
b { z ) = bç) (1 ~ 2 a ç ) Z ) .
(5.15)
For complete absoiption of microwave power in the discharge tube, from equations 5.10
and 5.13, we find that
Œq = — ,
(5.16)
and hence
b ( z ) = bo
I
(5.17)
I
Therefore, it should be possible to obtain uniform power deposition (and hence a uniform
electric field) along the axis of the dischaige tube by uniformly tapering the narrow wall of
the rectangular waveguide from the input end to the distal end.
PhD Thesis
114
J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
5.5.2 Design o f the TWCS
The same basic principles governed the design of the TWCS as governed the design of the
RWCS described eaiiier (see section 5.4.3). The major difference between the two coupling
structures is that in the ridge waveguide the plasma tube was excited by a standing
microwave field, whereas in the tapered waveguide it was intended that a travelling
microwave field pump the discharge. Figure 5.8 shows the schematic diagram and
dimensions of the TWCS, along with the absorbing load and the impedance matching
transition between the coupling structure and the standard waveguide at the load end. To
ensure a travelling wave in the waveguide, the TWCS was designed with a load placed at its
end, to prevent un dissipated microwaves from being reflected back into the coupling
sti'ucture after their initial traversal.
According to theory outlined above, the length of the coupling structure is
determined by the initial attenuation constant, ao, i.e. there is complete absorption of
microwave power over a length / =/a given by
Figure 5.9 shows /a plotted as a function of electron density for various values of the
ratio Vm/û), and discharge tube radii as shown. It can be seen from these figures that for
small values of Vm/m and small plasma tube diameters, the tube length becomes inordinately
long. Therefore this type of coupling structure is better suited to pumping plasmas with a
high buffer gas pressure than those with a low buffer gas pressure. In a low buffer gas
pressure at the electron densities which aie optimal for metal vapour laser discharges, the
power dissipated in the plasma would be so low that it would be difficult to attain the tube
PhD Thesis
115
J. W. Bethel
I
Tapered waveguide side view
Taper length
750 mm
I
Matching
transition
> -< 222^
Î
H-plane
bend
mm
Water
channel
0\
O-ring
Water cooling
Cross-section of the tapered waveguide
Water-cooled
choke flange
Dimensions
a = 12 mm
b = 34 mm
Tube dimensions
Ld. = 8 mm
o.d. = 10 mm
Conducting rubber seals
Water cooling
Waveguide pressurised with
3 bar SIg
Quartz tube
S
I
a
Figure 5.8.
The tapered waveguide coupling structure
I
I
Chapter 5
Microwave Pumping Configurations
Pressure window
Conducting
rubber gaskets
Water-cooled
resistive-wall load.
Figure 5.8 (b).
Top view of the H-plane bend and the water-cooled load.
PhD Thesis
117
J. W. Bethel
g
f
d is c h a r g e tu b e J,
00
S
Chapter 5___________________________________ Microwave Pumping Configurations
operating temperatures necessaiy for laser operation. Therefore, the coupling structure was
not generally operated at pressures below 100 mbai'. Additionally, as expected /a is reduced
for increased tube radii because of the greater power dissipated in the larger volumes.
5.5.3 Electric fields in the TWCS
The TWCS, unlike the RWCS, was designed by taking into account the effects of the
plasma and the quaitz tube on the propagation of microwaves in the coupling structure
(under the assumptions made in chapter 2). The electric field in the dischaige region can
therefore be estimated, as a function of the plasma paiameters (election density, uq, collision
frequency for momentum transfer, Vm, and microwave frequency, co) following the method
outlined in section 2.5, using the measured microwave power in the waveguide.
Figure 5.10 shows the electric field in the dischai-ge region for the range of
electron densities relevant to SRLs and CHLs, and the dimensions of the quaitz tube used in
this work and for a power of 1 MW in the coupling structure. The electric fields, Ea, at any
value of power flow thiough the coupling structure, Pa, can be obtained from
(5.19)
where jEimw is the electric field in figure 5.10. However, this figure does not take the skin
depth (see section 2.4.3) into account, and this will be important for low buffer-gas
pressures. An estimate of the skin effect could be made by referring to figure 2.11
It can be seen from the graph that the electric fields for electron densities
of 10^0 m"3 are between 0.8 and 1.6 kV cm'i for Vm/A) ratios of 50 and 100 respectively.
These values are lower than those used in experiments on TE CuBr and SRL lasers [13, 16]
(although still higher than those in LE excited lasers). However it should be noted that prior
to the application of the microwave pulse, the electron density in the plasma will have fallen
somewhat due to vaiious losses such as recombination and diffusion [8 , 12]. Therefore the
PhD Thesis
119
J. W. Bethel
Chapter 5
Microwave Pumping Configurations
10
10
I
10
No plasma tube
3
2
I
Electron density cm 4
Figure 5.10.
The electric field against the electron density, for various values of Vm/û)
and a peak power of 1 MW in the TWCS. For a quartz tube t.d.=8 mm and
o.d. =10 mm.
initial electric field during the rf pulse is expected to correspond to that for a lower electron
density.
Figure 2.19 shows the electiic field distiibution in a cross-section of standard
WGIO waveguide containing a discharge tube (it should be noted that the above plot of the
electric field in the plasma remains very similar for the different tube diameters plotted in
figure 5.9). From this it can be seen that the electric fields in the waveguide, in the region
just outside the quaitz tube, can be enhanced by a factor of up to two by the presence of the
dischaige tube. This enhancement of the electric field in this region will be more pronounced
at the distal end of the TWCS, where the separation between the quaitz discharge tube and
PhD Thesis
120
J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
the waveguide is only about 0.5 mm. Initial experiments showed that compressed air of up
to 3 bar was insufficient to prevent breakdown from occurring toward this end of the
coupling structure. Therefore it was necessary to use pressurised (2 bar) sulphur
hexaflouride, SFg, to prevent breakdown from occurring in the waveguide. This is a highly
electron-attaching gas which has a dielectric strength of 4.5 times that of air [24]. However,
SFô is sensitive to surface imperfections and generally a value of the dielectric strength of
about 2.5 is used [25]. In addition, SFô is prone to slow thermal decomposition at
temperatures higher than about 200
when in contact with various metals, in pai’ticulai*
copper [25]. Therefore the waveguide coupling stmcture is water-cooled to prevent thermal
decomposition of the Sp 6 as well as to aid heat removal from the discharge.
5.5.4 The ratio o f the electiic field to the neutral particle density
The ratio of the electric field to the neutral number density {E/N ) is a very important
parameter in gas discharges and gas lasers, since it determines the char acteristic energy of
the electrons in the dischaige. The ratio is plotted, for both neon and helium, against p/T in
figures 5.11 and 5.12 respectively, where p is the pressure of the buffer-gas in mbai* and T
is the temperature in kelvin. It can be seen from these figures that the E/N ratio is lower for
discharges in neon than in helium, due to the lower collision frequency for momentum
transfer in neon (see figures 2.6 and 2.7). For both cases, at low electron densities the E/N
ratio is high (-10"^^ V cm^) at low pressures, but falls off almost linearly with increasing
pressure. This is because the electric field remains relatively constant with increasing
collisional frequency and hence with increasing pressure, as seen in figure 5.10. However,
at higher electron densities (-10^^ cm-3) the E/N ratio is lower (-10"^^ kV cm^) but
remains constant with increasing pressure. This is because the electric field increases at high
pressures for constant electron density, as a result of the increase in the collision frequency
at these higher pressures (see chapter 2 for a more detailed discussion on how the plasma
par ameters affect the propagation of microwaves).
PhD Thesis
121
J,W. Bethel
Chapter 5
2
Microwave Pumping Configurations
10 -1^-
n = 10 ^“^
n = 5x1014
Mg= 101^
10 ^
Ratio of p /T, where p is pressure in mbai*
and T is temperatme in kelvin.
Figure 5.11.
The E /N ratio against p /T where T is the average temperature of the gas,
for various electron densities (cm"^) in neon (T'e~5 eV). For a power of
1 MW in the TWCS and a quartz tube Ld.=S mm and o.d.=10 mm .
Typical values of the E/N ratio for optimum operation of conventional TE lasers are
-8.7 X 10'^^ V cm^ for SRLs [16], and -1.1 x 10"^^ V cm^ for CuBr lasers [14]. The
corresponding values for LE lasers are -1.1 and 6.0 x 10"^^ V cm^ for a high PRF CuBr
laser and a double-pulsed CuCl laser (/.£/.=10 mm) respectively [10, 26], and -0.7 and
4.5
X
10"^^ V cm^ for high and low PRF SRLs respectively [27, 28]. Figure 5.11 shows
that for an electron density of around 10^®
in neon, the E/N values in the tapered
waveguide are lower than those found in CHLs. On the other hand, the corresponding
values in helium are comparable to the values found in high PRF SRLs. Therefore the
tapered waveguide should be suited to producing the conditions found in SRLs, as long as
PhD Thesis
122
J. W. Bethel
Chapter 5
Microwave Pumping Configurations
10 -13
10rl4
<s •
g
10 15
>
10 -16
10
10 -17
10
-18
10
"
10
"
10
"
10'
10
10 ^
Ratio of p /T, where p is pressure in mbai'
and T is temperature in kelvin.
Figure 5.12.
The E /N ratio against p /T where T is the average temperature of the gas,
for various electron densities (cin‘^) in helium. For a power of 1 MW in
the TWCS and a quartz tube Ld.i=S mm and o.d.=10 mm.
the electiic field along the longitudinal tube axis remains constant. However, although the
E/N ratio in the taper is lower than in typical CHLs it remains constant with increasing
pressure. Therefore, it should be possible to operate the microwave-excited copper halide
and strontium recombination lasers at buffer gas pressures of up to several atmospheres.
5.5.5 Impedance o f the TWCS
Just as in the case of the RWCS, we need to calculate the impedance of the TWCS in order
that the microwaves can be coupled into the system effectively (although in this investigation
PhD Thesis
123
7. W. Bethel
Chapters
Microwave Pumping Configurations
a suitable impedance matching device was not available, we can estimate reflected power
from the TWCS if we know the impedance). The impedance of a waveguide is given by
equation 5.4 as a function of waveguide wavelength Ag, however the wavelength of
microwaves in the TWCS is a function of the plasma par ameters and the dimensions of the
TWCS. In order to calculate /Lg, we must return to theory developed in chapter 2. Equation
2.69 relates the fractional change in propagation constant to the plasma par ameters and the
dimensions of the discharge tube. We can obtain the wavelength of the microwaves in the
TWCS, Aip from the following relationship
A.
^ rp - /
(5.20)
R e (4 ^
hence from equation 5.4, the TWCS impedance. Zip, can be written as
Z.^ = 3 7 7
g
1
(5.21)
0
— 7-------7\
Therefore, it can be seen that the impedance of the waveguide is a decreasing function of the
distance along the waveguide, z. Due to the length of the TWCS (75 cm), the change in
impedance with z can be assumed to be sufficiently slow to be adiabatic. Therefore, the
reflection of microwaves from within the coupling structure, due to this slow change in
impedance, can be assumed to be negligible. However, there will be an initial change in
impedance between the plain rectangular waveguide and the TWCS containing the discharge
tube. Therefore the initial value of the impedance of the TWCS at z=0 is plotted in
figure 5.13. The above graph shows that the impedance of the waveguide is less than the
impedance of the empty waveguide (524 ohms) for the plasma par ameters shown. Indeed, it
can be seen that as the electron density increases, the impedance decreases. Similarly, as the
plasma losses decrease (Vxn/o) decreases), the impedance of the TWCS also decreases. This
PhD Thesis
124
J. W. Bethel
Chapter 5
Microwave Pumping Configurations
is because the plasma acts as a shunt impedance in the waveguide and the effect becomes
greater for increasing plasma conductivity i.e. the plasma becomes more and more like a
metal rod.
510
Election density m 4
Figure 5.13.
Impedance of the TWCS for various values of Vm/û) for a quartz tube
with an inside diameter of 8 mm and an outside diameter of 10 mm.
5.6 Performance of the TWCS
The experiments in which the TWCS was used are presented and discussed in detail in
chapter 6 and 7. However, as expected the TWCS out-perfoimed the RWCS in so far as
higher laser output powers were obtained with this coupling stmcture. The pressurisation of
the waveguide with 3 bar Sp 6 was found to be sufficient when helium buffer gas was used.
However, there was some evidence that micro-dischai’ges had occurred towards the load end
of the coupling structure when using neon buffer-gas. This resulted in the appearance of
small 'pits' in the quartz tube which in some cases caused a leak to develop in the tube. This
PhD Thesis
125
J. W. Bethel
Chapters___________________________________ Microwave Pumping Configurations
was due to the lower collision rate of electrons with neon atoms, resulting in a higher
conductivity and lower power dissipation in the plasma. Therefore, the electric fields in the
region between the quartz tube and the waveguide wall at the narrow end of the TWCS
would have been very high.
PhD Thesis
126
J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
References
1.
Microwave Resonant-Cavity-Produced Air Discharges.
M. L. Passow, M. L. Brake, P. Lopez, W. B. McColl and T. B. Repetti.
IEEE Transactions on Plasma Science, vol. 19, No. 2, pp 219-228 April 1991.
2.
Novel methods of copper vapour laser excitation.
W. McColl, H. Ching, R. Bosch, M. Brake and R. Gilgenbach.
Proceedings of SPIE, vol. 1628, Intense Laser Beams, pp 22-31, 1992.
3.
Microwave resonant-cavity-produced air discharges.
M. L. Passow, M. L. Brake, P. Lopez, W. B. McColl and T. E. Repetti.
IEEE Transactions on Plasma Science, vol. 19, No. 2, pp 219-228, April 1991.
4.
Plasmas sustained by surface waves at microwave and r.f. frequencies:
Experimental Investigations and Applications.
M. Moisan and Z. Zakrzewski.
Radiative Processes in Discharge Plasmas, pp 381-431.
New York Plenum, 1986.
5.
A waveguide-based launcher to sustain long plasma columns through the propagation of an
electromagnetic surface wave.
M. Moisan, Z. Zakrzewksi, R. Pantel and P. Leprince.
IEEE Transactions on Plasma Science, vol. 12, No. 3, pp 203-214, September 1984.
6.
Slow-Wave Propagation in Plasma Waveguides.
A. W. Trivelpiece.
San Francisco Press, Inc., California.
7.
Time-resolved measurements of population densities in a Sr"^ recombination
laser.
R. Kunnemeyer, C. W. McLucas, D. J. W. Brown, A. L. McIntosh.
IEEE Journal o f Quantum Electronics, vol. 23, No. 11, pp 2028-2031, November 1987.
8.
Election density measurements in a stiontium vapour laser.
D. G. Loveland and C. E. Webb.
J. Phys. D: Applied Physics, vol. 25, pp 597-604, 1992.
9.
Pulse energy scaling charateristics o f longitudinally excited Sr'*' discharge recombination lasers.
M. S. Butler and J. A. Piper.
IEEE Journal o f Quantum Electronics, vol. 21, No. 10, pp 1563-1566, October 1985.
10.
High efficiency CuBr laser with interacting peaking circuits.
N. K. Vuchkov, N. V. Sabotinov and D. N. Astadjov.
Optical and Quantum Electronics, vol. 20, pp 433-438, 1988.
11.
Comparison of CuCl, CuBr, and Cul as lasants for copper-vapour lasers.
S. Gabay, I. Smilanski, L. A. Levin and G. Erez.
IEEE Journal o f Quantum Electronics, vol. 13, No. 5, pp 364-365 May 1977.
12.
A model for the dissociation pulse, afterglow, and laser pulse in the Cu/CuCl double pulse laser.
M. J. Kushner and F. E. C. Culick.
Journal of Applied Physics, vol. 51, No. 6, pp 3020-3032, June 1980.
PhD Thesis
111
J. W. Bethel
Chapter 5___________________________________ Microwave Pumping Configurations
13.
Stimulated emission due to transitions in copper atoms formed in tianverse discharges in copper
halide vapours.
G. V. Abrosimov and V, V. Vasil'tsov.
Soviet Journal of Quantum Electronics, vol. 7, No. 4, pp 512-513, April 1977.
14.
Operating characteristics of TE copper bromide lasers.
M. Brandt and J. A. Piper.
IEEE Journal of Quantum Electronics, vol. 17, No. 6, pp 1107-1115 June 1981.
15.
Microwave excitation of a XeCl laser without preionisation.
H. H. Klingenburg, F. Gekat, G. Spindler.
Proceedings on SPIE, vol. 1278, Excimer Lasers and Applications H, pp 43-50, March 1990.
16.
High-pressure high-cuiTent transversely excited Sr**"recombination laser.
M. S, Butler and J. A. Piper.
Applied Physics Letters , vol.42. No. 12, pp 1008-1010, June 1983.
17.
Pulse Power Foimulary.
R. J. Adler.
North Star Research Corporation, August 1991.
18.
Microwave Breakdown in Gases.
A. D. MacDonald.
John Wiley and Sons, 1966.
19.
Microwaves: An intioduction to microwave theory and techniques.
A. J. Baden Fuller.
2nd Edition. Pergamon Press, 1988.
20.
Reflection coefficient of E-plane tapered waveguide.
K. Matsumaru.
IRE Transactions on Microwave Theory and Techniques, vol. MTT-6 pp 143-149,1958.
21.
Plasmas sustained by surface waves at radio and microwave frequencies;
Basic processes and modeling.
C. M. Ferreira
Radiative Processes in Discharge Plasmas, pp 431-466.
New York Plenum, 1986.
22.
On producing an extended microwave discharge at liigli pressure.
V. N. Slinko, S. S. Sulakshin, L. V. Sulakshina.
Sov. Phys. Tech. Phys. Vol. 33, no. 3, pp 363-365, March 1988.
23.
Krypton flouride laser excited by high-power nanosecond microwave radiation.
V. A. Vaulin, V. N. Slinko, S. S. Sulakshin.
Sov. J. Quantum Electronics, vol. 18, no. 11, pp 1459-1461, March 1989.
24.
Equations aid breakdown-free component design.
T. Wilsey and G. Meggaugh.
Microwaves and RF. pp79-91, November 1991.
25.
Handbook of Electrical and Electronic Insulating Materials.
W. Tillar Shugg.
Van Nostrand Reinhold Company Inc. New York, 1986.
26.
Scaling a double-pulsed copper chloride laser to 10 mJ.
N. M. Nerheim, A. A. Vetter and G. R. Russell.
Journal of Applied Physics, vol. 49, No. 1, pp 12-15, January 1978.
PhD Thesis
128
J. W. Bethel
Chapters___________________________________ Microwave Pumping Configurations
27.
Pumping of a strontium-ion recombination laser in a system with a cut-off thyratron.
P. A. Bokhan and D. E. Zakrevskii.
Soviet Journal of Quantum Electronics, vol. 21, No. 8, pp 838-839.
28.
Discharge excited Sr"^ and Ca'^ plasma recombination lasers.
M. S. Butler, PhD. Thesis.
Macquarie University, Sydney, Australia. NSW.2109. March, 1986.
PhD Thesis
129
J. W. Bethel
CHAPTER
Experimental results of the
Microwave excited Copper Halide laser.
6.1 Introduction
This chapter presents the experimental results and discussions of the perfoimance of the two
coupling structures (RWCS and TWCS), which were described in chapter 5, for the
excitation of copper halide lasers. The first section describes the initial experiments
undertaken on the copper(l)chloride laser using the RWCS. In the next section we discuss
the effect of the buffer gas pressure on the absoiption of microwaves using the TWCS and
estimate the average electron densities and electric fields in the plasma tube. We also examine
the performance of the CuBr and CuCl laser using the TWCS and discuss the factors which
affect the laser's characteristics.
6.2 Preliminary experiments of the CuCl laser using the RWCS
6.2.1 Experimental details
The experimental layout is shown in figure 6.1 (see also figure 5.7 for details of the
RWCS). The source of microwaves was a tuneable S-band magnetron manufactured by
BEV (type M5193) which operates over the frequency range of 2.992-3.001 GHz. This
magnetron is capable of delivering peak output powers of 2.6 MW, and average output
powers of around 2.8 kW at an efficiency of 55 percent [1]. With the modifications to the
PhD Thesis
130
J, W. Bethel
I
Figure 6.1.
Experimental layout for the CuCl laser using the RWCS
Magnetron
EEV
M5193
f
Os
Water-cooled
load r
Circulator
Pressure
window
Directional —
coupler
To vacuum
pump À
Short
circuit
Quartz
tube
Point contact
diodes
Gas in
Pressure
window
S
to
I
Hat high
reflector
Ridge waveguide coupling structure,
RWCS.
Pressurised with 3 atmospheres of dry air.
Flat quartz output
coupler
I
I
Chapter 6________________________________ Microwave excited Copper Halide Laser
modulator which are detailed in section A2 of the appendix, the magnetron can produce
double pulses with a variable spacing of between 12-500 |xs, at a fixed recurrence-rate of
750 Hz. The magnetron must be isolated from the load in order to prevent damage to it by
microwaves reflected from impedance mismatches. Therefore the output of the magnetion is
delivered to the rest of the microwave circuit via a circulator. The circulator (model
10HD319) was manufactured by Albacom Ltd. and is a ferrite isolator which is supplied
with a resistive wall load and provides a minimum isolation of 20 dB and an insertion loss
of 0.17 dB at 3.0 GHz [2]. The power handling capacity was specified as being 3.5 MW
peak power, and 3.5 kW average power when operated into a short circuit of any phase. In
order to prevent breakdown due to the high electric fields which will be present, the
circulator was pressurised with 2 atmospheres of diy aii*.
A directional coupler (see figure 6.1) is used to distinguish between the
incident and the reflected microwave pulses to and from the RWCS respectively. It is a
narrow-wall coupler with a coupling factor of about 72 dB and was made 'in-house'.
Point-contact diodes in the secondary aim of the directional coupler were used to detect the
rf pulses, which were then viewed on a Tektr onix 2445B/2235 oscilloscope. It must be
noted, however, that the output of the point contact diodes was non-linear and therefore they
were not used to make any quantitative measurements of incident and reflected microwave
power.
The power reflected from the RWCS is transmitted back down the waveguide
and is dissipated in the water-cooled load of the circulator. Therefore the power can be
estimated by measuring the change in temperature of the water as it passes thr'ough the
circulator load. This was accomplished by the use of platinum temperature-sensitive resistors
[3] (Ft 100, B.S. 1904:1984 class B) which were placed in the input and output water pipes
of the load. The temperature dijference of the water could be measured using a calibrated
voltage bridge and a digital voltage meter. A GAP flow meter was used to measure the water
flow rates in the loads. Using this method the temperature difference could be measured to
PhD Thesis
132
J.W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
an accuracy of ±0.1 °C, corresponding to a power uncertainty of around ± 30 W. The
output power of the magnetron was calibrated against the input power by directing the
microwaves into the water cooled load and measuring the change in water temperature as
described above. Measurement of the input power to the magnetron was accomplished by
monitoring the voltage and current in the magnetron. Therefore the power absorbed in the
plasma tube could be monitored by simply subtracting the reflected power measured in the
circulator from the magnetion output power.
The RWCS (described in chapter 5) was pressurised with up
to 3 atmospheres of dry air to prevent ai’cing between the quaitz tube and the waveguide.
Pressure windows were constructed either of 5 mm thick High-Density Poly-Ethylene,
HDPE, or Teflon (PTFE) which was glued to a rectangular flange with silicon rubber or
Evo-stick. Both HDPE and Teflon have similai* permitivities and low loss at microwave
frequencies, however, pressuie windows made of HDPE were found to be superior because
Teflon has a tendency to 'flow' and therefore become distorted and eventually burst.
The quaitz tube (inside diameter, i.d.=S mm, outside diameter, o.d, = 10 mm
and active length 650 mm, see figure 5.7) was located centrally along the axis of the
RWCS. Copper(l)chloride powder was distributed evenly along the floor of the quaitz tube
in the region between the ridges (see figure 5.7). Neon buffer-gas could be flowed through
the tube at rates of up to 10 litre atm. hi" ^ and the pressure of the gas was measured on a
Leybold Inficon vacuum gauge using a capacitance manometer (type CM 100) as a gauge
head. The laser cavity consisted of a flat high reflector and a flat quaitz output coupler
(4 percent reflectivity) separated by 1.45 m. Laser output power was measured on a Photon
Control power meter which had a sensitivity of up to 1 mW full scale deflection. The
green (510.6 nm) and the yellow (578.2 nm) laser pulses were monitored through nairow
bandpass filters (Ealing Electro-optics) using an ITL vacuum photodiode which has a rise
time of 0.1 ns [4].
PhD Thesis
133
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
6.2.2 Performance of RWCS for pumping the CuCl laser
Laser oscillation was observed on the 510.6 nm (^p 3/2 to ^^>5 / 2 ) and 578.2 nm
(^^ 1/2
^ ^ 3/2) transitions of neutral copper, for neon buffer-gas pressures of between 40
and 400 mbar. The quartz tube was heated to produce the necessary vapour pressure of
CU3CI3 solely by the Joule heating effect of the microwaves. The pulse widths (FWHM) of
the microwaves were 1.8 (is for the dissociation pulse and 1.0 (is for the pumping pulse,
both with rise times of 20 ns (10 to 90 percent). Figures 6.2 and 6.3 show the laser pulses
for the 510.6 nm and the 578.2 nm tr ansitions respectively along with the second microwave
pulse at a pressure of 240 mbar and a flow rate of about 0.6 litre atm.hr"^ and a pulse pair
separation of around 35 (is. No stimulated emission was observed during the first
microwave pulse, just as in conventional double-pulsed copper halide lasers (CHLs).
Figure 6.4 shows the incident microwave pulses along with the laser pulse which occurs
during the second microwave pulse. The average output power obtained was about 3 mW
for the conditions shown in table 6.1. The optimum pulse pair sepaiation of aiound 35 (is, is
consistent with the trends observed by both Nerheim [5] (double-pulsed system) and
Chen [6 ] (multiply pulsed system) for a tube of this diameter.
Power incident
on RWCS, W.
Power absorbed
by discharge, W.
1000 ± 1 0 0
550 + 50
Pulse-pair
separation, ps.
35
Pressure, mbar.
240
Electric field in empty
RWCS, kV/cm.
Specific output pulse
energy, pJcni^.
Average output
power, mW.
Peak output
power, kW.
6.8 ± 1.0
0.16
3
200
Table 6.1.
Conditions for laser oscillation for the CuCl laser using the RWCS.
The electric field and the £>27 ratio was calculated using equation 5.1 (which
relates the electric field in an empty ridge waveguide to the power in the waveguide) and
seems to compare well with the values for conventional double-pulsed systems [7 ]
PhD Thesis
134
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
0.0
3,6 iim
«
I
c
3
Inci jen Microwave Pulse
(9
Q
<n)
(0
T im e (100 n s/d iv )
Figure 6.2.
Oscillogram showing laser the pulse at 510.6 nm with the
second, incident microwave pulse.
I
f «
si
i £
o (8
U
0.0
Laser Pulse 573.2 iim
ÎÎ
4
Inciqen Microwavd Pulse
r
.3
0
T im e (100 n s/d iv )
Figure 6.3.
Oscillogram showing the laser pulse (578.2 nm) along with
the second, incident microwave pulse.
2.0
Las er Fulse
<D
i2
1.0
S. B
si
0.0
a.
II
(A
I;
i'i
J|
V)
L_
Inc den t Mi Drov/avc ! Pu s e ^air 5
T im e (5 }xs/div)
Figure 6.4.
Oscillogram showing the incident microwave pulse-pairs and
the laser pulse (combined lines) occurring during the second
microwave pulse.
PhD Thesis
135
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
( 6 X 10" ^ ^
V cm^). The uncertainty in the given values aie due to the fact that it was not
possible to differentiate between the power reflected from the discontinuity formed by the
plasma tube in the H-plane bend, the pressure window, any impedance mismatch in the
RWCS, and the short circuit formed by the end of the RWCS. Therefore the upper and
lower limits of the power used in the electric field calculation are the incident power
delivered to the RWCS, and the power absorbed in the waveguide. However, as noted in
chapter 5, equation 5.1 does not take the effects of the plasma tube into account and these
result in a reduction in the electiic field in the plasma. We can estimate the electiic field in the
plasma if we assume an electron density in a typical CHL of between 10^^ and 10^^ cm-3,
by using equation 2.47 (rewritten below) which equates the power absorbed to the Joule
heating in the plasma.
.2
where the terms aie as defined in section 2.4.4. This gives a much lower electric field of
between 677 and 215 V cni'l for electron densities in typical CHLs of 10^^ and lO^^cm'^,
respectively. The corresponding E/N ratios are 2.35 x 10'^^ and 8.2 x 10"^^ V cm"^
which aie substantially lower than Nerheim's double pulsed laser [7].
The efficiency of the laser is very low and this is due to many factors. The
most obvious is the fact that the peak of the laser pulse occurs about 150 ns after the peak of
the second microwave pulse. Therefore the remaining 850 ns of the pulse just heats the
plasma. Hence, reducing the pulse length and increasing the peak power in order to maintain
the same average power to the dischaige, will increase the electric fields and lead to more
efficient laser oscillation. Secondly, due to the significant fraction of microwaves which
were reflected from the short at the end of the cavity, a large standing wave was formed in
the cavity. This leads to regions of high and low electric field along the axis of the plasma
tube. Therefore, in the regions of low electric field, the lower laser level is likely to be
PhD Thesis
136
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
populated in preference to the upper levels. This will then lead to areas of strong absorption
and hence the effective gain length of the system is drastically reduced.
Further confirmation for the existence of a standing wave became evident
when the quartz tube was removed after laser oscillation ceased following only a few hours
of operation. Inspection revealed that the copper chloride powder had been redistributed into
approximately equally spaced regions similar to the powder in Kundt’s sound tube
experiment, where regions with no powder correspond to pressure antinodes produced by
the standing waves. In the case of the laser tube the antinodes will correspond to regions of
high electric field. Therefore laser action ceases because there is no copper chloride in the
high field regions. The wavelength of the microwaves in the RWCS could be estimated from
the positions of the minima of the CuCl distribution. This gave a value of 10.7 ± 0.6 cm,
which corresponds to an impedance of 400 Ql (the ridge waveguide wavelength without the
plasma tube is 12.3 cm, and the impedance is 460 Q from figure 5.6). Therefore, as
expected from the theory in chapter 2 , the effect of the plasma tube (for these plasma
conditions) on the propagation of microwaves is a reduction in wavelength and this results in
a reduction in impedance of the waveguide. However, this reduction in impedance is not
large enough to account for the measured reflected power, therefore a significant proportion
of the incident power is reflected from the short at the end of the cavity, the plasma tube, the
H-plane bend and the waveguide window.
In conclusion, it is evident that the RWCS is unsuitable for pumping a
microwave-excited metal vapour laser due to the nonunifonn electric field along the axis of
the laser tube. Therefore in order to effectively pump a metal vapour laser using
microwaves, a coupling structure which deposits power uniformly along the length of the
dischai’ge tube is required.
PhD Thesis
137
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
6.3 Measurements of the absorption of microwaves in discharges occurring
in helium and neon buffer gases.
Buffer-gas effects on the performance of copper lasers are discussed in section 4.2.3. The
effects of the buffer-gas on the absorption of power in a microwave pumped laser add an
extra dimension to the operating characteristics of a microwave pumped system. These
effects have been discussed in chapter 2. It was shown that the Vir/ct>ratio in the plasma was
very important for both the fractional transmission and the depth of propagation of
microwaves into a plasma. For the range of pressures between 100 and 1000 mbar both
the fractional tiansmission and the skin depth increase with increasing Vm/co. It has also been
shown that the attenuation of microwaves in a waveguide containing a plasma tube increases
with increasing Vtj/ o). Therefore experiments were cairied out to measure the absolution of
the microwaves in the plasma for various buffer gas pressures and input powers, for both
neon and helium.
6.3.1 Experimental details
The experimental layout for the TWCS is shown in figure 6.5 (see also figure 5.8 for details
of the TWCS) and is similai' to that used for the RWCS, except that the ridge waveguide is
replaced by the tapered waveguide and a load is situated at the end of the cavity to prevent
the reflection of undissipated microwaves. The TWCS is described in detail in chapter 5, the
dimensions of the quartz tube are Ld>= 8 mm, o.d.= 10 mm and the length of the tube
inside the active region {i.e. in the tapered section and H-plane bend) is 900 mm. Due to the
high electric fields present in the TWCS during operation, especially towaids the end of the
coupling structure where the waveguide wall is in close proximity to the quartz tube, the
TWCS was pressurised with two atmospheres of Sulphur Hexaflouride, SFô. This is a
highly electron attaching gas and has a much higher breakdown voltage than dry air (about a
factor of four).
PhD Thesis
138
/ W. Bethel
I
I
Figure 6.5.
Experimental layout for the absorption measurements
in helium and neon using the TWCS.
Water-cooled
load
Magnetron
- EEV
M5193
Os
Circulator
Pressure
window
Water-cooled
load
U)
VÛ
Point
contact
diodes
Directional
coupler ■
Pressure
window
Brewster angled
window
Waveguide
transition
^—
Quartz
tube
I
Pressure
window'
I
n_L
I
S
S’
I
Y
To vacuum
pump
I
Tapered waveguide coupling structure
TWCS
Pressurised with 2 atmospheres of SR
Gas in
Chapter 6________________________________ Microwave excited Copper Halide Laser
The experimental and monitoring apparatus is the same as that described in
section 6.2.1. However, in order to measure the power absorbed in the dischai'ge, we must
also measure the power dissipated in the load at the end of the microwave cavity. Therefore
platinum temperature sensitive resistors (described in section 6 .2 . 1) were placed in the
water-cooling pipes connected to this load. The power absorbed in the buffer gas is then
calculated by subtracting the power dissipated in the loads from the output of the magnetron
as in section 6 .2 . 1 .
Measurements of the absorbed power were undertaken for both neon and
helium buffer gases, using microwave pulse-pairs of each 0.9 jis duration, for pressures
from 100 mbar to 900 mbar. Representative figures 6.6 to 6.8 show the power absorbed in
the plasma, the power reflected from the TWCS and tiansmitted to the load at the end of the
TWCS. Measurements for the reflected powers were corrected for the insertion loss of the
circulator (0.17 dB) and the power reflected from the waveguide window in the circulator;
the combination of both amounted to approximately 10 percent of the magnetion output.
The figures show that for both helium and neon, the fractional absorbed
power increases for increasing pressure. This is to be expected because the conductivity of
the plasma is reduced at the higher electi'on-atom collision frequencies which occur at higher
pressures (see figures 2.6 and 2.7). However, whilst the transmitted power decreased with
increasing pressure, the reflected power remained relatively constant over this range of
pressures for neon buffer gas. In addition, the reflected powers are much higher than would
be expected from the change in impedance in going from the empty waveguide to the TWCS
(reflected powers should be less than about five percent for these plasma conditions, see
figure 5.13). Later measurements undertaken using just a microwave load and the pressure
window revealed that the windows reflected about 30 percent of the incident microwaves.
This reflected power could be eliminated by placing a stub tuner before the waveguide
window, although at the time of the measurements a tuner was not available.
PhD Thesis
140
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
1 lOi
800-
— □— Power absorbed in plasma, W.
—A
Power reflected, W.
— o— Power tiansmitted, W.
Pressure=100 mbar helium.
I
I
6 00-
400-
200
Duty cycle of the
microwave pulses=0.00135.
-
600
800
1000
1200
Average power incident on TWCS, W.
1400
Figure 6.6.
600
500 -
I
I
-a
Power absorbed in plasma, W.
-A— Power reflected, W.
-o— Power transmitted, W.
400 Duty cycle of the
nucrowaves=0.00135
300 -
Pressure=100 mbar neon.
200
100 1
600
800
1000
1200
Average power incident on TWCS, W.
1400
Figure 6.7.
Graphs showing the power absorbed in the plasma, power reflected from
the TWCS and the undissipated power transmitted to the load at the
distal end of the TWCS against the incident power on the TWCS, for
helium (figure 6.6) and neon (figure 6.7) at 100 mbar.
PhD Thesis
141
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
1 10
“
800
I
600
I
— B— Power absorbed in plasma, W.
—A
Power reflected, W.
— o— Power transmitted, W.
Pressure=900 mbar neon.
Duty cycle of microwave
pulses=0.00135.
□ □
□
400
200
600
800
1000
1200
Average power incident on TWCS, W.
1400
Figure 6.8.
Graphs showing the power absorbed in the plasm a, power
transmitted to the load at the distal end of the TWCS against the
incident power on the TWCS, for neon (figure 6.8) at 900 mbar.
The power absorbed in the plasma using helium buffer gas is greater than that in the neon
for the same gas pressures. This is because the collision frequency for momentum transfer
Vm in helium, at the electron energies expected (around 5 or 6 eV [8 ]), is about factor of two
greater that in neon (see figures 2.6 and 2.7). For the case of neon buffer gas, the ratio of
the absorbed power to the input power for the lower pressures (100 mbar) is only aiound
50 per cent and this ratio decreases for increasing input powers (see figure 6.9). This
reduction in the ratio of absorbed power to incident power is due to the increase in ionisation
of the neon buffer gas, resulting in higher electron densities and hence conductivities, which
occur as the power absorbed and hence the electric field in the plasma is increased. The
effect is reduced at the higher buffer gas pressures; at a pressure of 900 mbar theratio of
power absorbed to input power is almost constant (and between 0.6 and 0.7). In helium
buffer gas, the reduction in this ratio is only noticeable for the measurements taken at
100 mbar. Above this pressure for the range of measurements taken, the ratio remained
PhD Thesis
142
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
0.8
0.7
0.6
I
Typical error bar. —
0.5
I
0.4
I
0.3
Neon buffer gas.
Duty cycle of microwave
pulses=0.00135.
a------Pabs/Pincident 100 mbar.
6------ Pabs/Pincident 500 mbar.
o— Pabs/Pincident 900 mbar.
0.2
0.1
600
400
800
1000
1200
1400
Average power incident on TWCS, W.
Figure 6.9.
1
0.8
I
0.6
I
Pabs/Pincident, 100 mbar. Typical enor bar
Pabs/Pincident, 500 mbar.
Pabs/Pincident, 900 mbar.
0.4
Helium buffer gas.
0.2
0
Duty cycle of microwave
pulses=0.00135.
600
800
1000
1200
Average power incident on the TWCS, W.
1400
Figure 6.10.
Ratio of power absorbed in the plasma to the incident power
on the TWCS for neon (figure 6.9) and helium (figure 6.10).
PhD Thesis
143
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
greater than 0.7 (see figure 6.10). This is because at higher pressures, the system is
dominated by the Vm/û) ratio. At lower pressures on the other hand, when the Vm/<wratio is
smaller, the û)p/m ratio is dominant (see figure 2.19) and therefore a small change in the
electron density has a greater effect upon the conductivity of the plasma.
Discharge at lower
pressures (less than around
200 mbar)
Discharge at higher
pressures (greater than
around 500 mbar)
Intense glow gj
Constriction
Weak glow 0
(a)
(t)
Figure 6.11.
The end-light emission from the discharge tuhe
The discharges in both helium and neon were stable for all the above
pressures. Observation of the end light emission revealed that the discharge intensity had an
appearance similar to that shown in figure 6.11 (a). This intensity profile is probably a
manifestation of the plasma skin effect (see section 2.4.3) which will become evident in a
tube of 8 mm in diameter for electron densities of above 1 x 10*'^ cm'^. (The electron
density in the plasma is the subject of the next section). At higher pressures (above around
300 to 500 mbar) the discharge appeared to form a kind of constriction as shown in figure
6.11 (b). Constrictions are observed in high pressure pulsed systems under dc excitation,
especially at higher pressures. They are the result of an increase in electron temperatures on
the axis of the plasma (due to the Bessel function distribution of current in the discharge)
which increases the E/N ratio in this region and this in turn reduces the electron-atom
recombination rate [9]. Therefore the occurrence of such an arc in the microwave pumped
discharge is probably the result of the ratio Vm/O) » 1 at these higher pressures and hence
the plasma behaves like a dc discharge.
PhD Thesis
144
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
6.3.2 Estimation of electric field and electron density in the plasma
In order to make comparisons of the operating parameters of the microwave pumped
discharge/laser with conventional dc dischaiges/lasers we need to be able to estimate the
electric field in the dischai'ge. Equation 6.1 shows the relationship between the electron
density, electric field and the power absorbed in the plasma. However it was shown in
section 2.5.1, that in a rectangular waveguide containing a plasma tube, the electric field in
the plasma for small diameter plasma tubes could be estimated from the electric field in the
empty waveguide by applying the necessaiy boundaiy conditions. The rms electric field in
the centie of the empty rectangular waveguide (from equation 2.19) is given by
2P
Eq =
ab.
P-)
( 6 .2 )
Ac J
where the tenus are as defined in section 2.2 and the electiic field in the plasma tube, Erp, is
(6.3)
^ rp =
+ l ) + g2 - l ] ( / + £p)
where gp is the relative permittivity of the plasma (see equation 2.32), and is a function of
Vm and the electron density. It should be noted that this expression for Erp assumes that
there aie no radial valuations of the electiic field in the plasma. The other terms are as defined
in section 2.5.1. By assuming that the power deposited in the plasma is constant along the
length of the discharge tube (see section 5.5), we can use equation 6.3 along with equation
6.1 as simultaneous relationships for the average electric field and the average electron
density in the plasma tube during the microwave pulse. The collision frequency for
momentum tiansfer Vm is taken from figures 2.6 and 2.7 to be
1 .9 x 1 0
/7 for He,
(6.4)
0 .9 X 10^/7 for Ne,
PhD Thesis
145
7.
Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
where p is the pressure in mbai*. It must be noted that for helium, Vm is fairly constant for
election temperatuies above approximately 6 eV; however, for neon it is a slowly increasing
function of electron energy. Therefore for this estimation, we assume an electron
temperature of around 5 or 6 eV [8 ], which is typical of the values found in copper halide
lasers. The simultaneous equations are then solved using an equation solving routine in
MathCad on a PC. It should be noted that the electron densities and electric fields estimated
in this way are averaged over the duration of the pulse and over the volume of the plasma.
Representative graphs showing the results of these calculations are presented
in figures 6.12 to 6.15. Figures 6.12 and 6.13 show that the increase in electron densities
for a fixed pressure in neon ar e small compared to the variation in absorbed power, the same
behaviour was observed for helium. This is because the electric field is proportional to the
squai'e root of the absorbed power (from equation 6 . 1) and the electron density will not be
expected to change much for small changes in the electiic field.
However the estimated election densities for constant power absorbed in the
plasma, at various pressures, show an increase in the electron density with increasing
pressure (see figure 6.14). Although reference [10] suggests that the electron density should
scale linearly with increasing pressure (Vm/o) ratio), the basis for this occurrence is the
increased power loading necessary to maintain the plasma at the higher pressures. In our
case, the increase in electron density with increasing pressure (at constant absorbed power)
could be explained by reference to figure 6.15 and equation 2.47 rewritten below, for the
case where Vm »to and the volume, V, is constant
Figure 6.15 shows that the electric field in the plasma remains relatively constant, therefore
the electron density must increase if the absorbed power, P, remains constant. The
consequence of this is that the skin depth only increases from about 4 to 6 mm for an
PhD Thesis
146
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
1.4
Duty cycle of microwave
pulses=0.00135.
Typical error bar.
1.2
'o
r-4
1
X
I
0.8
.S
•t
0.6
J
0.4
I
A
Neon buffer gas.
A
A
e-density in plasma, 100 mbar.
e-density in plasma, 500 mbai\
e-density in plasma, 900 mbar.
0.2
0
200
300
400
500
600
700
800
Average power absorbed in plasma, W.
900
Figure 6.12.
0.7
□
_ A
o
0.6
0.5
E-field in plasma, 100 mbar.
E-tield in plasma, 500 mbar.
E-field in plasma, 900 mbar.
A
°
®A A O
A
O
Neon buffer gas.
Typical error bar
0.4
I
□
0.3
Duty cycle of microwave
pulses-0.00135.
0.2
0.1
0
200
_L
300
400
500
600
700
800
Average power absorbed in plasma, W.
900
Figure 6.13.
Graphs showing the variation in electron density (figure 6.12)
and the electric field (figure 6.13) against absorbed power in the
discharge for neon buffer gas.
PhD Thesis
147
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
] — ■e-density, 550 W in helium.
^
e-density, 800 W in helium.
D— e-density, 550 W in neon.
1.5
Duty cycle o f microwave
pulses=0.00135.
0
Typical error bar.
1
I
0.5
400
600
Pressure, mbar.
200
800
1000
Figure 6.14.
0.7
0.6
I
0.5
Typical eiTor bar.
â
1“
.S 0.3
□
A
G
W 0.2
Duty cycle of microwave
pulses=0.00135.
I
E-field, Pabs=550 W helium.
E-field, Pabs=800 W helium.
E-field, Pabs=550 W neon.
0.1
0
200
_L
400
600
Buffer gas pressure, mbar.
800
1000
Figure 6.15.
Graphs showing the variation in electron density (figure 6.14) and
electric field strength (figure 6.15) with pressure for constant
absorbed power in the plasma for helium and neon buffer gases.
PhD Thesis
148
J. W, Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
increase in pressure of 100 to 900 mbar in a buffer gas of helium (for a constant power
power absorbed of 800 W). This should be compared to an increase of 4 to 16 mm for the
same increase in buffer gas pressure but with a constant election density. Therefore in order
to scale the plasma to larger diameters whilst still maintaining radially uniform electric fields,
it will be necessary to increase the Vm/<y ratio by reducing m and not simply by increasing
Vm- The gradient in the plot of the electric field against pressure for constant absorbed power
in neon reduces for pressures above about 500 mbar (see figure 6.15). In helium this turn
off appears to occur at lower values of the pressure. The effect could be due to greater
dissipation of microwave power in the early part of the coupling structure, at these higher
pressures, resulting in a lower electric fields at the end of the waveguide. Tliis would mean
that the average field (which is what was estimated using this method) is reduced and would
lead to non uniform power deposition in the plasma. The effect is expected to be greater in
helium buffer gas than in neon. This is because Vm and hence the attenuation of the
microwaves is greater in helium than in neon.
The errors in the above measurements come for the uncertainty in the power
absorbed measurements, the uncertainty in the volume of the plasma and the nonuniformity
of the electric field. The volume uncertainty is due to incomplete power absorption in the
TWCS resulting in plasma forming in the impedance tr ansforming section of waveguide and
the second H-plane bend at the end of TWCS (see figure 6.5). In addition, the effect of the
skin layer (see section 2.4.3) will also have the effect of reducing the electric field in the
plasma, when the skin layer is less than the diameter of the discharge tube. For the above
estimations of the maximum electron densities at each pressure, the estimated skin depth
calculated from equation 2.4 (this equation is strictly only valid for a TEM wave propagating
in an infinite medium) was between 5 and 6 imn for the case of helium and between 4 and
5 mm for neon. However it maybe reasonable to expect that the method described
underestimates the electron density for the case when radial electric field variations are
significant i.e. when the electron density is large and hence the skin layer is smaller than the
PhD Thesis
149
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
tube diameter. This is because for a fixed power absorbed in the plasma, equation 6.1 shows
that an increase in the election density will result in a decrease in the electiic field strength.
6.3.3 Summary
The above measurements on the absorption of microwave power in the plasma in neon and
helium show that the power absorbed in the plasma increases as the conductivity of the
plasma is reduced (either by increasing the pressure or by using a buffer gas with a higher
Vm value). The use of a simple method of estimating the electric fields and electron densities
implies that a plasma with a high Vm/d) ratio can support higher electron densities for similar
electric fields than a plasma with a low Vm/d) ratio, for the same absorbed powers. In
addition, these measurements would suggest that in order to scale the plasma to large
diameters, it would be more effective to reduce the angular frequency of the microwaves (u)}
rather than to increase the buffer gas pressure (Vm). Figures 6.11 (a) and (b) show that the
skin depth could be important especially at lower pressures (less than 200 mbar or so).
6.4 Results of laser oscillation in CuCl and CuBr using the TWCS
The experimental set up for the experiments undertaken with CuCl and CuBr is shown in
figure 6.16 and is essentially the same as that for the measurements taken with pure neon
and helium buffer gas. Copper halide (copper(l)chloride or copper(l)bromide) was placed at
approximately 5 cm intervals along the floor of the quaitz discharge tube in the region of the
tapered section of the waveguide coupling structure. Neon buffer gas was flowed through
the quartz tube at rates of between 1 and 3 litre.atm.hr-k The optical cavity consisted of a flat
high reflector and a flat quartz output coupler separated by a distance of 1.7 m. Average
output powers of the lasers at 510.6 nm and 578.2 nm were measmed on a Photon Control
power meter using narrow bandpass filters, as functions of the microwave pulse pair
PhD Thesis
150
J. W, Bethel
I
i
I
0\
Microwave
pulse-pairs
Water-cooled
load
Photodiode
or
Power meter
Narrow band-pass
filter
Brewster
angled window
Pressure
window
Quartz
tube
Pressure
window
J1
IT
I
To vacuum
Flat high P™P
reflector
I
I
II
I
I
Tapered waveguide coupling stracture, TWCS
Pressurised with 3 atmospheres of SI%.
Waveguide
transition
coupler
Figure 6.16.
Experimental set-up for the CuCI/CuBr laser.
I
I
Chapter 6________________________________ Microwave excited Copper Halide Laser
sepai'ation, as described in section 6.2.1. The peak output powers were measured on the ITL
vacuum photodiode. The pulse width of both the microwave pulses was 0.9 |Lis and the
risetime was 20 ns (10 to 90 percent).
6.4.1 Performance of the TWCS for CuBr and CuCl with neon buffer gas
Figures 6.17 and 6.18 show the average output powers of the 510.6 and 578.2 nm
transitions respectively, for copper( 1)bromide (CuBr) at a fixed incident power on the
TWCS of 1.28 kW. Figure 6.19 shows the peak power (in arbitraiy units) for the case of
the copper( 1)chloride (CuCl) for a fixed incident power of 1.2 kW. The power absorbed,
reflected and transmitted to the load for the conditions in figure 6.17, 6.18 and 6.19 for
CuBr and CuCl aie tabulated in table 6.2. The coupling efficiency of the microwaves into the
discharge is between 55 and 75 per cent for the conditions at which laser oscillation was
observed. Plates 6.1 and 6.2 show laser action at 510.6 nm and 578.2 nm, respectively.
It can be seen from figure 6.20 that the optimum pulse-pair separations at a
specific pressure are longer for the 510.6 nm tiansition than the 578.2 nm transition. This is
because the lower laser level of the 510.6 nm transition (^D^/2) is below the corresponding
level for the 578.2 nm transition (^0 3 /2)- Therefore, by equation 3.1, the electron collisional
de-excitation rate of the metastable ^Dg/2 level will be slower than for the ^Dg/2 level. In
addition, these sepaiations decrease with increasing pressure (see figure 6 .20 ) which is a
direct result of the increased rate of cooling of the electrons (by collisions with buffer gas
atoms) which occurs at these higher pressures. As expected, the rate of decrease of the
optimum pulse sepaiation approximates to an exponential decay and the relative decay rate
for the 510.6 nm transition is slower than the corresponding 578.2 nm transition (see
equation 3.2). The optimum pulse-pair separation for the case of CuCl is less than for CuBr,
as is observed in conventional dc-excited systems [11]. This is consistent with the fact that
the chlorine atom is more electronegative than the bromine atom and therefore recombines
more rapidly with the copper atoms than the bromine atom. The output power of the laser
PhD Thesis
152
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
6
Neon flow rate =
5
i
I
I
I
l.OdtD.l litre.atni.lir " .
— □— p=100mbar, 510.6 nm.
■ à
p=500mbai', 510.6 nm.
,
\ d
o
p=900mbar, 510.6 nm.
4
Duty cycle of
microwave pulses=0.00135.
3
2
1
0
0
20
40
60
80
Pulse-pair separation, p,s.
100
120
Figure 6.17.
Neon flow rate = 1.0 ±0.1 litre.atm.hr
Duty cycle of
microwave pulses=0.00135.
I
I
p=100mbar, 578.2 nm.
p=200mbar, 578.2 nm.
p=500mbar, 578.2 nm.
p=900mbar, 578.2 nm.
1.5 -
1
.
-
t
I
0.5
0
20
40
60
Pulse-pair separation, fis.
80
100
Figure 6.18.
Average output powers of the 510.6 nm (figure 6.17) and the
578.2 nm (figure 6.18) transitions as a function of pulse-pair
separation for the CuBr laser for various neon buffer gas pressures.
PhD Thesis
153
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
1.4
Neon flow rate = 0.9 ±0,1 litre.atm.hr
1.2 -
§
p=100 mbar, 510.6
p=100 mbai', 578.2
— p=500 mbar, 510.6
— p=900 mbar, 510.6
1 -
.
nm.
nm.
nm.
nm.
I
I
Î
I
0 .8 -
0 .6 0 .4 0 .2 0
20
30
40
50
60
Pulse-pair sepai'ation, |lis.
70
80
Figure 6,19.
Peak output powers of the CuCl laser 510.6 and 578.2 nm
transitions as a function of pulse-pair separation for various neon
buffer gas pressures.
50
« — Pulse separation, 510.6 nm.
45
■A
Pulse separation, 578.2 nm.
=i
I
35
30
t
Typical eiror bar.
25
20
15
0
200
400
600
Pressure, mbar.
800
1000
Figure 6.20.
Variation in pulse-pair separation with pressure for the CuBr-Ne
laser.
PhD Thesis
154
J. W. Bethel
î
i
I
Os
Table 6.2.
Conditions for laser oscillation for the CuBr-Ne and CuCl-Ne laser
corresponding to the curves in figures 6.17 to 6.19.
Pressure
in mbar
Ux
Power incident Power
Power
Power
Estimated electron
on TWCS, W. reflected, W. transmitted, W. absorbed in density, cm"3.
plasma, W.
CuBr-Ne discharge.
100
1280 + 130
114 ±40
466 ±40
700 ±90
1.5 ±0.5x10^^
3.0 ± 1.0 X 10^^
Estimated
electric field,
V/cm.
500 ±80
4.6 + 0.7x10’16
500 ±80
2.3 + 0.4 X 10 -16
1.0 ± 0 .2 x 10
200
1280 ±130
141 ±40
435 ±40
703 ±90
500
900
1280 ±130
1280 ±130
168 ±40
168 ±40
352 ±40
269 ±40
760 ±95
842 ±100
1.1+0.3x10^^
550 ±90
650 ±100
6 .6 ± 2 .0 x 1(/^
E/Wratio
V cm2
-16
16
0.6 + 0 . 1 x l(J
CuCl-Ne discharge.
S
16
100
1200 ±120
113 ±40
321 ±40
721 ±90
1.4 ±0.5x1013
521 ±80
4 .8 ± 0 .8 x l0
200
1200 ±120
113 ±40
352 ±40
733 ±90
2 .7 ± 0 .9 x lrf^
538 ±90
2.5+ 0.4x10'!^
500
1200 ±120
113 ±40
248 ±40
837 ±100
5.9 ±1.9x10^3
611 ± 1 0 0
1.1 ± 0 .2 x 10
900
1200 ±120
166+40
113+40
920 + 113
9 .5 + 3 .0 x l(/3
676 + 110
0.7 +0.1
-16
X
Ifl
16
I
I
I
Chapter 6________________________________ Microwave excited Copper Halide Laser
Plate 6.1.
Laser oscillation at 510.6 nm.
PhD Thesis
156
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
Plate 6.2.
Laser oscillation at 578.2 nm.
PhD Thesis
157
J. W. Bethel
À
il -
V**
Ü
4Y.X
%,j-^*-.
.VÆ:.
y
'U^
i J T ' : ''i K
U>
'T
"E r
Chapter 6________________________________ Microwave excited Copper Halide Laser
was observed to increase significantly with increasing flow rates. The total output power of
the green (510.6 nm) and the yellow (578.2 nm) transitions combined increased to 18 mW
on increasing the neon flow rate to 3.0 litre.atm.hr‘l. This corresponds to a specific output
energy of 0.6 )LiJ cm'3 and a peak power of 1.2 kW. Although this is very low compared
with double-pulsed systems, which can produce specific output pulse energies of around
45 jiJ cm“3 [12], high recurrence rate CHLs have much lower typical specific output pulse
energies of between 2 and 8 |iJ cm'^ [13]. The performance of the present system would
be expected to fall somewhere between that of double-pulsed and high PRF systems. This is
because the microwave pumped system is dischaige heated and therefore will be prone to
number density variations in the dischaige, as a result of the radial temperature gradients in
the plasma tube, whereas temperature gradients in double-pulsed systems will be less
because they aie externally heated. However in the microwave excited CHL, number density
gradients of species in the plasma due to incomplete relaxation of components in the
inteipulse period will not be as severe as in high PRF CHLs (see reference [12]). The
maximum efficiency of the microwave excited system (based on the power output from the
magnetron and considering only the exciting, second microwave pulse) was around 0.003
percent. Conversion efficiencies of the excitation pulse alone for double-pulsed systems are
around 0.27 percent [12] and for discharge heated, high PRF CHLs up to 1.5 percent [14]
(with the addition of hydrogen). However, the low efficiency of the microwave pumped
system is to be expected if we consider that the laser pulse occurs within the first 50 to
100 ns of the beginning of the microwave pulse (see figure 6.21). The remaining
component of the microwave pulse just heats the plasma, therefore the efficiency quoted
above could be 10 to 20 times higher if we disregard this pait of the rf pulse. Nevertheless,
even this efficiency is low compared to the double-pulsed systems and therefore other
factors must also contribute to the present low value. The estimated E/N ratios (see
table 6.2) are lower than for both conventional double pulsed and high PRF CHLs (1.1 and
6.0 X 10-15 Y cm2) by over an order of magnitude. This would result in
PhD Thesis
158
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
Figure 6.21.
O scillogram show ing the onset o f the laser pulse
(510.6 nm) with respect to the microwave pump pulse.
both a reduction in the fraction of dissociation of the copper halide molecules during the first
microwave pulse and inefficient excitation of the upper laser levels of neutral copper.
However probably the most significant factor which is responsible for the
low efficiencies measured was the indication that there was a nonuniform temperature
distribution along the length of the quartz tube. This was inferred from the fact that the
output power of the laser increased significantly at higher neon flow rates. In addition, later
observations of the sidelight emission of the discharge with the copper halide and neon
buffer gas using screened windows in the narrow wall of the tapered waveguide confirmed
this. It appeared that the copper halide vapour only occurred in a very small region of the
discharge. Therefore the active length of the laser medium was very much shorter than the
length of the coupling structure. The beam quality of the laser was very poor and this is also
likely to be the result of a small nonuniform active medium. The laser beam profile often
appeared to contain a lot of scattered light and frequently had an annular appearance.
PhD Thesis
159
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
Although this annulai’ appearance could be due to the skin effect, annular beams are often
observed in metal vapour lasers which aie operating close to their threshold input powers
{Le, low vapour pressure). The estimated electron densities would imply that the skin layer
is approximately the same as the radius of the discharge tube therefore the electric field
should not var y too much across the plasma cross section.
6.4.2 Effects of the copper halide on the discharge
In order to gain a more complete understanding of how the temperature variations affect the
performance of the microwave pumped laser, we need to look at how the copper halide
vapour can affect the discharge. If we compare the data for the power absorbed in the
discharge of neon in the presence of CuCl or CuBr vapour (given in table 6.2) and the
corresponding measurements for pure neon (figure 6 .6 ), we can see that at a pressure
of 100 mbar there is an increase in the absorbed power of around 150 W for both CuCl
and CuBr. The estimated election density for the pure neon case appears to be around
25 percent higher than in neon with copper halide vapour present. Experimental
measurements taken during the laser chaiacterisation have shown a sharp drop in the power
transmitted to the load, hence an increase in the absorbed power in the discharge, as the
input power to the CuX-Ne discharge was increased. This is accompanied by the termination
of laser oscillation as the concentration of copper halide particles in the dischar ge exceeded
the maximum permissible value for laser oscillation.
The increase in the absorbed power could be explained by a combination of
two effects occurring in the discharge, which are both related to the vapour pressure of the
copper halide. Firstly, an increase in the number of electron-heavy body collisions arising
from the presence of the copper atoms, halogen atoms or the CU3X 3 molecules in the
dischar ge could account for this increased absorption. However, it is unlikely that the copper
and halogen atoms will significantly affect the collision rate in the plasma. This is because
PhD Thesis
160
J. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
8
Fixed peak power in the TWCS of IMW.
Duty cycle of microwave pulses=0.00135.
7
Electron density of IxlO^'^cm'-^.
Electron density of SxlO^^cm'^.
Electron density of IxlO^^cmr^
6
01—j
X
5
4
1
I
3
2
1
0
0
200
400
600
800
1000
Average power absorbed in plasma, W.
1200
Figure 6.22.
Calculated variation in the absorbed power in the plasma with
collision frequency, for a constant power in the TWCS of 1 MW.
the electron-atom collision frequencies for momentum transfer for copper and bromine will
be at least a factor of five less than for pure neon, at the expected partial pressures of the
copper halide (around 0.15 mbar) [14]. Nevertheless, the corresponding collision
frequencies for the trimer CugXg could well be significant. Figure 6.22 shows the increased
power absorbed in the discharge with increased collision frequency in the discharge for a
constant microwave field in the TWCS, calculated using the method described in section 6.3
(by solving for the collision frequency at a fixed electron density). The second mechanism
for the increased power absorbed in the dischaige could be due to a reduction in the electron
density in the discharge, as a result of the presence of the highly electron attaching halogen
atoms in the plasma. Figure 6.23 (again calculated using the method described in
section 6.3) shows that only a small reduction in the electron density can result in a dramatic
PhD Thesis
161
J. W. Bethel
Microwave excited Copper Halide Laser
Chapter 6
12
Electron density, 100 mbar neon.
Electron density, 500 mbar neon.
Electron density, 900 mbar neon.
10
"o
%
I
I
8
6
4
2
0
0
200
400
600
800
1000
Average power absorbed, W.
1200
1400
Figure 6.22.
Calculated variation in the absorbed power in the plasma with
collision frequency, for a constant power in the TWCS of 1 MW.
increase in the power absorbed in the plasma, especially at lower pressures. In both
scenarios described above, we will have a runaway effect because the increase in power
absoiption will result in an increase in the vapour pressure of the copper halide. However, it
seems plausible from figures 6.22 and 6.23 that the second explanation, (reduction in
electron density) is likely to be the more dominant mechanism.
Observations of the sidelight emission in the CuBr-Ne or CuCl-Ne
discharges showed that in extreme cases, when the halide vapour pressure became too high
in one region of the laser tube (indicated by a very blue dischaige), breakdown of the gas in
the remaining sections of the tube (furthest from the input end of the TWCS) would cease
altogether. The sensitivity of the absorbed power on the vapour pressure of the halide made
operation of the laser very difficult to manage, especially in view of the fact that copper
PhD Thesis
162
/. W. Bethel
Chapter 6
Microwave excited Copper Halide Laser
halide lasers operate over a veiy naiTOw temperature range. This problem is compounded by
the poor thermal conductivity of the quartz tube.
6.4.3 Experiments to reduce the temperature variation along the tube
It clear' from the above discussions that in order to successfully operate a microwave excited
copper halide laser it is necessary to have a uniform vapour pressure of the halide thr oughout
the laser tube. Using insulation in the waveguide around the quartz tube is inconvenient and
impractical because it would be necessary to rearrange it for any change in the dischar ge
--------------------------------------750m m ------------------------------------
490 mm
Quartz tube
Choke flange
Alumina tube
Dimensions
in mm
Figure 6.24.
The alumina tube sleeved in quartz inside the TWCS.
conditions. An experiment undertaken to test the compatibility of Saffil fibrous insulation, in
a waveguide resulted in complete charting of the Saffil within a few seconds, at very low
microwave power levels.
Therefore in order to reduce the temperature nonuniformity, the straight
quartz tube was replaced by an alumina tube sleeved in quartz (see figure 6.24). The higher
thermal conductivity of the alumina (10.47 W .m'kK"! at 500°C [15]) compared to
PhD Thesis
163
J. W. Bethel
Microwave excited Copper Halide Laser
Chapter 6
Choke flange
Neon flow
Quartz tube
Figure 6.25.
Neon buffer gas flowing over CuBr or CuCl in the coldest part of the discharge tube.
quartz (1.4
[15]) should reduce any temperature gradients along the axis of the
tube. Experiments were undertaken using flowing neon buffer gas and CuBr as the copper
donor. However, the observed laser oscillation was very weak and too small to measure and
appeared to be the result of some CuBr in the quartz tube outside the alumina section.
Observation of the alumina tube through the side windows in the waveguide showed that
copper halide vapour was present along the whole length of the alumina section, but the
dischaige was bluish rather than the usual chaiacteristic green colour. A blue discharge is
observed in conventional electrically excited CHLs when the electric field strength is
suddenly reduced. The lack of stimulated emission occurring in the alumina tube is therefore
probably due to the reduction in the electric field in the plasma in the alumina section of the
tube. This could be the result of attenuation of the electric field in the discharge which occurs
in tlie plasma formed in the region between the quartz and the alumina tubes, suggesting that
the electron densities could be higher than estimated using the method based upon the
absorption of power in the plasma.
Further attempts to homogenise the vapour pressure of the halide by placing
the copper halide in the coolest point in the tube and flowing neon over it (see figure 6.25)
failed to produce higher output powers (8-9 mW using CuCl and 10 mW using CuBr). The
PhD Thesis
164
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
discharge again showed that the distribution of the halide vapour was not uniform. At
maximum output power, the length of the plasma tube containing copper halide vapour was
only 5 to 10 cm. Bearing this in mind, the effective specific output pulse energies would be
increased to 3-6 jj,J cnr^ which is comparable to high PRF CHLs. Observations of the
discharge in the region containing the copper halide showed that the discharge became
unstable as the halide vapour is released into the dischai ge zone. Discharge instabilities are
also observed in conventional copper halide lasers [16] and are attributed to an increase in
the copper halide pressure in the vicinity of the tube wall resulting in an increase in the
number of negative ions, and hence a reduction in electron density. The solution to this
problem in conventional CHLs is confine the discharge using apertures in the quartz tube
(see figure 4.8). However the use of apertures in the present system would be impractical
because the apertures would not constrain the dischaige and the effect of the skin layer
would result in a reduction of the electric field in the apertured region.
6AA Perfo finance of TWCS as a coupling structuréefor the copper halide laser
Although the TWCS out-performed the RWCS as fai- as output powers aie concerned, the
overall performance of the laser was poor when compared with conventional electrical
excitation. The primary aim of the coupling structure was to produce an axially uniform
electiic field by using a travelling wave to excite the dischaige in the plasma tube. However,
the power absorption in the plasma and hence the uniformity of the associated electric field is
greatly affected by the intioduction of electron attaching species into the dischaige. A method
of controlling the vapour pressure of the halide independently of the tube temperature is
necessary if the TWCS is to be used effectively in future experiments.
There was some evidence for the existence of a standing wave in the cavity,
in the region towards the end of the TWCS. When the quartz tube was removed after a few
hours of operation, there was a noticeable regular variation in the deposited copper on the
inside of the quartz tube. This variation extended over a length of about 15 cm towards the
PhD Thesis
165
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
end of the active region. The standing wave could have resulted from an incorrect length of
the impedance matching transition, which was designed assuming that there would be no
plasma in that section of the quartz tube. However, the presence of a plasma could alter the
wavelength of the microwaves in this region and the extent to which wavelength is changed
will depend on the electron density and the pressure of the buffer gas. Therefore an
impedance transition which is not strongly dependent on wavelength {e.g. by using long
linear taper or quarter wavelength steps) will be necessary for optimum performance.
Reflection of microwaves could also occur at the end of the TWCS where the outside
diameter of the quaitz tube equals the height of the waveguide (see figure 6.26). Therefore
the plasma in this region of the waveguide could act like a short circuit, especially at high
electron densities. This problem could be overcome by the use of tuning stubs on the H-field
in the TWCS.
Waveguide wj
Quaitz tube
Plasma
Figure 6.25.
Cross-section of the distal end of the TWCS.
Inspection of the quaitz tubes after operation also revealed that a substantial
fraction of the copper halide diffuses out of the laser medium into the cold regions of the
tube, at each end of the TWCS, where there is no plasma. This problem is also encountered
in conventional systems and can be reduced by raising the temperature of the whole system
to greater than that corresponding to condensation of the halide. However raising the
temperature of the whole waveguide structure to over 400°C could pose some problems.
There was also evidence of the microdischarges occurring in the TWCS
between the quartz tube and the waveguide wall, in particular near the distal end of the
PhD Thesis
166
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
TWCS, where the quaitz tube is in close proximity to the waveguide wall and electric field is
likely to be the highest in this region. These microdischarges resulted in 'pitting' of the
quartz tube and in one extieme case resulted in complete perforation of the tube. However
this problem could be solved by increasing the pressure of SFg in the coupling structure.
The low E/N ratios could be increased simply by reducing the pulse length of
the microwaves. The microwave pulse should ideally be terminated as the laser pulse is
terminated, otherwise energy is wasted in heating the discharge. However, due to the
limitations imposed by the magnetron power supply (see appendix), the pulse lengths in the
present system were limited to at least 700 ns.
6.5 Conclusions
Laser oscillation has been demonstiated on the cyclic transitions of neutial copper using both
CuBr and CuCl as the copper donors. Although low efficiencies have been obtained at low
specific pulse energies, the effective specific pulse energies are comparable to those of
conventional high PRF CHLs. There is no fundamental reason to suggest that the
performance of a small bore (less than around 1 cm in diameter) microwave excited CHL
should be worse than that of a conventional electrically excited system given a suitable
coupling structure. However for lai'ger bore systems the skin depth of the microwaves in the
plasma will introduce unacceptable radial electric-field profiles, unless the angular
frequency, CO, of the microwaves is reduced (see figure 2.11). One would expect that the
skin depth would be increased by operating at higher buffer gas pressures. In practice,
however, this is not the case because the higher buffer gas pressures require higher electric
fields to maintain the dischaige and therefore result in increased power absoiption in the
plasma. This in turn leads to higher electron densities, so the skin depth is not significantly
increased [10]. Alternatively, by using a magnetic field the skin depth of the microwaves can
PhD Thesis
167
L W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
be increased (see reference [10]) albeit by using very high field strengths (greater than
1 tesla for a microwave frequency of 2.45 GHz and election densities of 10^^ cm"3).
It is evident from the measui'ements taken that in order to obtain efficient laser
oscillation using microwave excitation the following criteria must be fulfilled.
1. The electric field must be uniform throughout the whole dischaige volume. Ideally it
should be possible to be able modify the electiic field within the waveguide to accommodate
changes due to different plasma conditions.
2. The vapour pressure of the copper donor must be uniform throughout the discharge
volume and independent of the input power to the dischaige (e.g. by using a heated reseiwoir
of the copper halide).
A successful, stable long-lived microwave excited copper vapour laser could
be operated at higher pressures than the conventional dc excited counterparts (as long as
sufficiently high pump power densities can be obtained). This could allow a greater paitial
pressure of the halide and hence an increase in the copper number density, providing higher
gain. The electrodeless system could also be an advantage for a sealed-off laser because the
electrodes in conventional CHLs are prone to chemical reactions with the laser medium.
Such a system would be highly desirable from a commercial point of view.
PhD Thesis
168
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
References
1.
Data sheet A1A-62-M5193.
Issue 1, July 1991.
EEV Ltd.
Caiholme Road, Lincoln, LNl ISF.
2.
Isolator 10HD319.
Data sheet MIC203 C490.
Albacom pic (now Trak Europe), 29 Dunsinane Avenue, Dundee. DD2 3PN.
3.
Platinum Resistance Thermometer Inserts (4-wire).
Data sheet 3914.
R.S. Components.
4.
Data sheet.
Instiument Technology Limited.
29 Castleham Road, St. Leonards-on-Sea, East Sussex.
5.
A parametric study of the copper chloride laser.
N. M. Nerheim.
Journal of Applied Physics, vol. 48, No. 3, pp 1186-1190, March 1977.
6.
High-efficiency multiply pulsed copper vapour laser utilising copper chloride as a lasant.
Che J. Chen and Gary R. Russell.
Applied Physics Letters, vol. 26, No. 9, pp 504-505, May 1975.
7.
Scaling a double-pulsed copper chloride laser to 10 mJ.
N. M. Nerheim, A. A. Vetter and G. R. Russell.
Journal of Applied Physics vol. 49, No. 1, pp 12-15, January 1987.
8.
Electron temperature measurements utilising a microwave radiometer.
E. Sovero, C. J. Chen and F. C. Culick.
Journal of Applied Physics, vol. 47, No. 10, pp 4538-4542, October 1976.
9.
Gaseous Electronics and Gas Lasers.
B. E. CheiTington.
Pergamon Press, 1979.
10.
Magnetically enhanced electromagnetic wave penetration in weakly ionised plasmas.
S. P. Bozeman and W. M. Hooke.
Plasma Sources Science and Technology, vol. 3, No. 1, pp 99-107, February 1994.
11.
Comparison o f CuCl, CuBr and Cul as lasants for copper vapor lasers.
S. Gabay, I. Smilanski, L. A. Levin and G. Erez.
IEEE Journal of Quantum Electionics, vol. 13, No. 5, pp 364-365, May 1977.
12.
Kinetic processes in continuously pulsed copper halide lasers.
C. S. Liu, D. W. Feldman, J. L. Pack and L. A. Weaver,
IEEE Journal of Quantum Electionics, vol. 13, No. 9, pp 744-715, September 1977.
13.
Copper bromide lasers-discharge tubes and lifetime problems.
N. V. Sabotinov, N. K. Vuchkov and D. N. Astadjov.
Proceedings of SPIE High Power Gas Lasers, vol. 1225, pp 289-298, 1990.
PhD Thesis
169
J. W. Bethel
Chapter 6________________________________ Microwave excited Copper Halide Laser
14.
Parameti’ic study of the CuBr laser with hydrogen additives.
D. N. Astadjov, N. K. Vuchkov and N. V. Sabotinov.
IEEE Journal of Quantum Electronics, vol. 24, No. 9, pp 1927-1935 September 1988.
15.
Multi-Lab Data
Tynevale works, Newham, Newcastle.
16.
Proceedings of the Lebedev Physics Institute, Academy of Sciences of the USSR.
'Metal Vapour and Metal Halide Vapour Lasers'.
Edited by G. G. Petrash, tianslated by S. A. Stewai t.
Nova Science Publishers, Inc. New York, 1989.
PhD Thesis
170
J.W. Bethel
CHAPTER
7
Experimental results of the
Microwave excited
Strontium-ion recombination laser,
7.1 Introduction
In this chapter we describe the experimental observation of laser oscillation on the 430.5 nm
recombination transition (6^Sy2“5^p3/2) of
ions with microwave excitation, using the
TWCS. The operating char acteristics of the laser are discussed with reference to the kinetics
of strontium lasers. The electron density in the plasma is estimated by analysis of the
time-resolved spontaneous emission of the 430.5 nm transition. The results of this method
are compared with the values estimated by the method described in section 6.3.3, which was
based on the conductivity of the plasma tube in the waveguide.
7.2 Experiments using the TWCS for the strontium laser
7.2.1 Experimental details
The experimental arrangement is shown in figure 7.1 and is similar to that used for the
experiments on the copper halide lasers and was discussed in section 6.4. The dimensions of
the quartz tube and the waveguide are the same as in section 6.4 (i.d.=S mm, o.d.=lO mm,
active length =900 mm). However, in this case the buffer gas used was helium instead of
neon (laser oscillation has never been observed on the recombination tr ansitions of strontium
PhD Thesis
171
J. W. Bethel
I
I
.
Figure 7.1.
Experimental arrangement for
the microwave excited SRL.
Magnetron EEV
M5193
Photo-naultiplier
tube
Water-cooled
load
Water-cooled
load
Circulator
Pressure
window
Monochromator
Directional
coupler ■
Brewster
angled
window
Point contact diodes
Pressure
window
Quarz flat
To vacuum
pump
to
I
Flat high-reflector
Tapered waveguide coupling structure
TWCS
Pressurised with 2 atmospheres of SR.
Waveguide
transition
Gas
in
Curved
high-reflector
Ï
I
I
I
I
Chapter 7_____________________ Microwave excited Strontium-ion recombination laser
ions in a pure neon buffer gas because the rate of cooling of the electrons in the discharge
afterglow is too slow, see chapter 3). Again, double pulses of microwaves were used as in
chapter 6, but this was only to obtain the necessary average power from the magnetron
{i.e. to double the PRF) and not because of any fundamental excitation requirements of
strontium lasers. Measurements of the power absorbed in the dischar ge were carried out in
the same way as described in chapter 6 for the experiments on copper halide lasers.
The laser cavity used consisted of a flat high reflector and a curved high
reflector (two metre radius of curvature) separated by 1.7 m. An output coupler was not
used because the laser was operating close to threshold. A quartz flat, placed in the laser
cavity at about 45 degrees to the optical axis, was used to couple out the intia-cavity
spontaneous and stimulated emission. This radiation was passed through a monochromator
and monitored using a photomultiplier tube (Hamamatsu model R636) and displayed along
with the microwave pulses on a Tekti'onix 2445B oscilloscope.
7.2.2 Preparation of the laser tubes
Sti'ontium metal is highly reactive and rapidly oxidises in air to produce a white oxide which
has a very high melting point of 2420 °C [1]. Therefore strontium is usually stored under oil
to prevent oxidation. In these experiments, the strontium metal was flattened in a vice
between two stainless steel plates and cleaned with a scalpel under petroleum spirit. The
metal was then cut into small pieces (about 5 x 3 x 0.5 mm) and quickly loaded into the
quartz tube under a flow of helium, with a spacing of around 5 cm between the metal pieces.
The strontium metal was then melted onto the floor of the quaitz tube in the presence of
helium buffer gas, using nichrome wire which was insulated with Saffil and wrapped
around the outside of the tube. It was necessaiy to melt the metal into place because loose
pieces of strontium tend to migrate from the discharge region when the magnetron is
switched on, due to the low pulse recurrence frequency of the microwaves which can induce
acoustic resonances in the laser tube.
PhD Thesis
173
J.W. Bethel
Chapter 7
Microwave excited Strontium-ion recombination laser
7.3 Results of experiments with strontium
Laser oscillation was observed on the 430.5 nm transition in singly ionised strontium for
helium buffer gas pressures of between 500 and 900 mbai\ Table 7.1 shows the conditions
at which stimulated emission was observed for the pressures 500 and 700 mbai\ The widths
of the microwave pulses were 1.75 and 0.9 ps and the pulse-pair separation was
around 35 p,s. Laser oscillation and spontaneous emission of the 430.5 nm transition were
independent of the pulse-pair separation, for spacings of between 15 and 500 ps. The
electron densities and electric fields are estimated using the method described in
section 6.3.2.
Pressure
Power incident on
TWCS, W:
Reflected power, W.
500 mbar
700mbar
2540 ±250
2630 ±260
560 ±40
674 ±40
Transmitted power, W.
217 ±40
96 ±40
Absorbed power, W.
1852 ±190
1860 ±190
Estimated
electron density, cm
1.1 + 0.4x10^4
1.4 ±0.5x10*4
Estimated electric
field, V/cm.
E / N ratio Vcm^.
810 ±130
1.9 + 0.3x10''®
840 ±129
1.4±0.2xl0'*®
Table 7.1.
Conditions for laser oscillation for the microwave excited SRL.
Figures 7.2(a) and (b) show the incident microwave pulse with the associated spontaneous
and stimulated emissions at 700 mbar respectively. Laser oscillation occurs after the
PhD Thesis
174
J. W. Bethel
Chapter 7
Microwave excited Strontium-ion recombination laser
Figure 7.2 (a).
Incident microwave pulse (2nd pulse) upper trace and the
spontaneous em ission of the 430.5 nm transition lower
trace, for a helium buffer gas pressure of 700 mbar.
V s
500n,V ^
Figure 7.2 (b).
Incident microwave pulse (2nd pulse) upper trace and the
stim ulated em ission of the 430.5 nm transition lower
trace, for a helium buffer gas pressure of 700 mbar.
PhD Thesis
175
J. W. Bethel
Chapter 7_____________________ Microwave excited Strontium-ion recombination laser
end of the microwave pulse, as is characteristic of recombination lasers. However in this
case, stimulated emission was only observed at the end of the second microwave pulse and
not at the end of the first microwave pulse. This is because the temiination time (90 to 10
percent) of the second microwave pulse was 440 ns as opposed to around 170 ns for the
second pulse. Therefore, for these conditions, the termination time for the first microwave
pulse was too slow to allow laser oscillation to occur. The lack of stimulated emission after
the first microwave pulse could also have been brought about by a low strontium vapour
pressure. This is because the average power to the magnetron could not be raised much
above 5.4 kW, which corresponded to the conditions in figures 7.2 (a) and (b), which were
taken just at the onset of laser oscillation. Therefore we may reasonably suspect that the
vapour pressure of strontium in the discharge was lower than the optimum required for
powerful laser oscillation.
The power absorbed in the dischaige is over 70 percent for both the 500 and
700 mbai* cases (disregarding losses in the circulator). As expected, the power transmitted
to the load at the end of the microwave cavity is reduced at higher pressures due to the
increase in the election atom collision frequency (hence Vm)- The majority of the power lost
to the discharge is due to reflections from the TWCS. This reflected power could be
eliminated by the use of tuning stubs, which were not available at the time of these
experiments. Therefore it should be possible to match over 90 percent of the microwave
power into the dischaige. The electron density estimates given in table 7.1 ai*e low compaied
to those measured in conventional LE SRLs (6.8 i 0.4 x 10^^ cm”^) [2]. This would
suggest that the electron densities in the microwave excited system aie close to the threshold
values. These low values could be the result of the low strontium vapour density because
strontium is much more easily ionised than helium. Indeed, in conventional electrically
excited SRLs the peak value of the current pulse can increase by a factor of two when
strontium vapour enters the dischaige. The E4V ratios are much lower than those obtained in
TE SRLs (8.7 x 10"^^ V cm^) [3] although they are compaiable to the high PRF, LE SRLs
PhD Thesis
176
7. W. Bethel
Chapter 7_____________________ Microwave excited Strontium-ion recombination laser
(7 X 10“^^ V cm^) [4]. The E/N ratios in the present system would be increased by the use
of shorter microwave pulses because in order to maintain the same average power, the peak
power of the microwaves will have to be increased, resulting in higher electric fields.
Figure 7.2 (b) shows that there is an approximately 100 ns delay between
the termination of the microwave pulse and the onset of laser oscillation and this does not
correspond to the peak in the spontaneous emission at 430.5 nm, which occurs close to the
termination of the microwave pulse. In conventionally excited strontium-ion recombination
lasers, the onset of laser emission usually occurs immediately after the current pulse
terminates, except when there is ringing in the current pulse. (In fact at high buffer gas
pressures, above about 300 mbai\ the onset of the laser pulse can occur before the current
pulse has fully terminated [5]). The delay observed in our case appears to be a metastable
(4 ^Dg/2 5/2)
lower laser level (5 ^Pj/2 3/2) effect rather than an upper level effect. This is
evinced by fact that the peak of the spontaneous emission at 430.5 nm doesn't coincide with
the onset of the laser pulse. The spontaneous emission at 430.5 nm is proportional to the
recombination rate of the
ions and is therefore essentially the pump rate of the upper
laser level, because the radiative decay of the lower laser level is much more rapid than the
electron de-excitation rate of the upper level (see section 3.2). Therefore, the delay obseiwed
could be the result of a high initial Sr^ ground state population (and hence high metastable
and lower laser level populations, see chapter 3 and figure 3.1) resulting from direct
excitation of these levels during the rf pulse and a lower than optimum electron density. The
latter factor would result in a reduction in the electron collisional de-excitation rate of the
lower laser levels and hence prevent a population inversion from being established until later
in the discharge afterglow. The spontaneous emission of the 430.5 nm transition shows that
no recombination occurs during the microwave pulse, even for the first 1.75 |Lis pulse (the
emission observed during the pulse is due to direct pumping of the upper laser level). This is
because the electron temperature during the pulse will be too high to allow three-body
PhD Thesis
177
J. W. Bethel
Chapter 7_____________________ Microwave excited Strontium-ion recombination laser
recombination of the
ions to occur (fast three-body electron ion recombination only
occurs when the electron temperature drops below about 5000 K [6]).
The output beam of the laser, taken from the quartz flat in the cavity (see
figure 7.1), appealed to have an annular profile. The estimated skin depths calculated from
the electron densities quoted in table 7.1 aie ai'ound 5 mm, for the conditions at which laser
oscillation occuiTcd. Therefore the annular output beam could be the result of the electric
field profile in the plasma. (However it must be noted that the electron densities quoted are
estimates, in the next section we discuss an alternative method for calculating the electron
densities and compare the values). Alternatively, it could be due to the fact that the laser was
operating close to threshold input power, election densities and electric fields. It is well
known that the output beam profiles of metal vapour lasers are annular* when the vapour
pressure of the metal is low. The laser pulse width is also narrow compared with strontium
lasers operating at or near to optimum conditions and this would also suggest that the vapour
pressure in the microwave pumped system was low.
7.4 Estimation of the electron density from the duration of the spontaneous
emission of the 430.5 nm transition
In chapter 3 we saw the importance of the electron temperature on both the recombination
rate of
ions (equations 3.13 and 3.14) and the subsequent stimulated emission on the
430.5 and 416.2 nm transitions of singly ionised strontium. The energy balance equation
for the electrons in the discharge afterglow of a helium buffer (equation 3.16) gas indicates
that the temporal decay of the election temperature will be sti ongly dependent upon the initial
electron density. Therefore, the spontaneous emission of radiation from the 430.5 nm
transition should also be strongly dependent on the initial election density in the plasma (this
method of calculating the electron density was first used by McIntosh and McLucas [7]).
Consequently we should be able to estimate the electron density in equation 3.13, by
PhD Thesis
178
J.W. Bethel
Chapter 7
Microwave excited Strontium-ion recombination laser
matching the time vaiiation of the calculated dSi'^'^/dt (which is effectively proportional to
the spontaneous emission intensity) for various starting values of the electron density, with
the observed spontaneous emission in figures 7.2 (a) and 7.3 (a). We can then compare the
results with those obtained in section 6.3.3 and examine the validity of the electron density
obtained using that method.
7,4.1 Calculation of the recombination rate
In order to calculate the recombination rate of the
ions, we need to calculate the
variation in electron temperature and electron density with time. We can rewrite
equation 3.16 as
( ^ e ^ e ) = = - ^ ^ t o t ( ^ e “ ^ g j + — ^7— (^ m + ^ ^ r )> C7.1)
3 A:
because for high values of «e, the helium metastable number density may be approximated
by [8]
,2
CA2)
=
{(y'Oe)'
where the terms are as defined in section 3.4. The change in electron density can be
accounted for by calculating the populations of the various ions present in the plasma. We
need only consider the time dependencies of the
and He'^ ions, and we can ignore
the diffusion of electrons losses for these short time scales (about 2 |is). Therefore the time
dependencies of the ionic species in the discharge can be written as follows, where the
squai'e brackets indicate number densities
d [S r+ +
Sr
df
dr
PhD Thesis
Sr ++ n e ’
—
I
179
CA3)
+
(7.4)
J, W. Bethel
Chapter 7
Microwave excited Strontium-ion recombination laser
(7.5)
dr
where the recombination coefficients for the strontium and helium ions, according to
Caiman [6], are given by
= 3 . 5 5 x l 0 ^ r ; / \ Te > 3 1 00 K
C7.6)
= 4 X 10“ ^^
Sr
'Sr'
, Te < 3100 K
= 7.16 X 10“ ^^ pT:^-^ Te > 3 1 0 0 K
(7.7)
= 4 X 10"^^ pT :^, Te < 3100 K
p = Z e ^ ln (V z 7 7 I)
where Zc is the electronic chai'ge on the ions. These values of the recombination rates were
used by Carman in his self-consistent model of an SRL, in order to give a better fit to
experimentally observed recombination rates at high temperatures, rather than the more
commonly quoted
dependence used by McIntosh and McLucas in their calculations of
electron density [7]. Bearing this in mind we decided to cany out the calculations using both
the recombination rates quoted in Carman's paper (equations 7.6 and 7.7) and the more
general equation 3.14 (applicable to ions of any element) rewritten below.
(%r = 1 .8 x 1 0 - 2 0
(7.8)
Using Carman's rates, the electron density in the immediate afterglow becomes
dn^
dt
where the specific recombination rates,
equation 7.8 for the calculations using the
«sr+» ^He+» would be replaced by
dependence. The electron density changes
much more slowly than the election temperature, therefore we can rewrite equation 7.1 as
PhD Thesis
180
J. W. Bethel
Chapter 7_____________________ Microwave excited Strontium-ion recombination laser
— ( î ’e ) = - ^ 1 ^ to t( î’e ~ ^ g ) + —
+^ e r ) >
(? 10)
and we can integrate this equation numerically, as long as the time steps are short enough.
The linear differential equations 13-1.5 and 7.10 were solved using the fourth-order
Runge-Kutta method, with 100 time steps over a period of 1.5 |Xs.
The initial conditions were taken as 5r++=0.2/îe»
5r+=10l^ cm'3 [6] and the starting value of the electron density was varied until a good fit
was obtained between d^r+^/dr and the observed spontaneous emission in figure 7.2 (a).
An initial electron temperature of Te= 10,000 K was chosen, although variation in this
star ting value had very little effect on the overall shape of the rate of decay of d5r++/dr. The
gas temperature Tg of 1480 K was the radially averaged value calculated by assuming a tube
wall temperature of 873 K and the absorbed powers as given in table 7.1. This temperature
was assumed to be constant throughout the integration period. The initial number densities
of the ions were taken from Carman [6] who found that during the current pulse, about 60
percent of the electrons in the dischaige were the result of ionisation of helium and that the
population corresponded to around 98 percent of the original Sr population. Although
there is likely to be a discrepancy between the conditions used in Carman's model and those
in the present investigation, the effect of varying the initial conditions of the ions present also
had very little effect upon the shape of the resultant d5r++/dr, as expected. However, small
variations in the electron density had a substantial effect upon the shape of the calculated
spontaneous emission.
Figures 7.3 and 7.4 show the best fit of the calculated spontaneous emission
along with digitised data of the spontaneous emission at 500 and 700 mbar for the
recombination coefficients used by Carman. The corresponding curve fits of the digitised
data with the recombination coefficient given in equation 6.8 are shown in figure 7.6 and
7.7. The peak intensity of the observed spontaneous emission was normalised to that of the
PhD Thesis
181
J. W. Bethel
Chapter 7
Microwave excited Strontium-ion recombination laser
200
4-.4A
+ +
§
+
Spontaneous emission, 500 mbar.
^
Calculated d Si*"^/dt for
electron density, n e =1.3x10^^ cin^ .
150
A+
I
+
+
100
+
+
A
50 h +
+
A
A +
+
+
+
§
±
500
0
^
^
A t |A
A + A ,,A
A
1000
1500
Time in ns.
Figure 7.3.
250
-ZPT
+
A
■i 200
■f
A+ +
+
4-
+
Spontaneous emission, 700 mbai\
A
Calculated d S&Vdt for
election density, n q =1.3x10^^ cm“^.
4
150
%
+
"+
§
100 - +
i
A+
(D
I
+
Ah
A+
A
50
A+
A+
i
■ £■ + |A +
500
1000
A +
A
a l-
1500
Figure 7.4.
Measured spontaneous emission at 500 mbar (figure 7.3) and 700
mbar (figure 7.4) along with the best fits for the calculated
d5|.++/d^ at the electron densities shown, using the recombination
rates quoted by Carman [6].
PhD Thesis
182
/. W. Bethel
Chapter 7
Microwave excited Strontium-ion recombination laser
200
1
4A A
+ +
■§ 150
+
Spontaneous emission, 500 mbar,
A
Calculated d &
A
+
+
c
for
electron density, n q = 6 x 1 0
A
+A
+
§ 100
+
+
+
50 "+
I
+
+
+
+
+A
0
200
400
600
A+ Ah|
I
^
800 1000
Time, ns
I
A 4-
1200
aI
1400
1600
Figure 7.5.
250
—T■i
+
B 200
4- Spontaneous emission, 700 mbar.
-
^
+
i
CO 150
nd
+
t
A
§
■k
100 h 4-
&
%
4a
(D
4-
I
Calculated dSr
for
electron density, n g =5x10 ^^cm“^.
50
44A
+
±
200
400
600
800
Time, ns.
1000
1200
_Æ
1400
Figure 7.6.
Measured spontaneous em ission at 500 mbar (figure 7.5) and
700 mbar (figure 7.6) along with the best fits for the calculated
dSr'^'^/dt at the electron densities shown, using the recombination
rates in equation 6.8.
PhD Thesis
183
/. W. Bethel
Chapter 7_____________ ._______ Microwave excited Strontium-ion recombination laser
calculated values and the time at which this peak occurred was adjusted so they were both
coincident.
It is interesting to note that with the recombination rates used by Caiman, we
see that the electron density required to give the best fit with the observed spontaneous
emission (1.3 x 10^^ cnr^ for both 500 and 700 mbar of helium) agrees very well with the
estimates obtained using the method described in section 6.3.3 (1.1 and 1.4 x 10^^ cm“^
for 500 and 700 mbar respectively). However, the corresponding estimates using the
recombination rates given equation 7.8 (6 and 7 x 10^^ cm~3 for 500 and 700 mbar) are
higher than those predicted using Carman's data (as expected due to the weaker electron
temperature dependence of equation 7.8) and the estimated values given in table 7.1. These
higher electron densities would result in a skin depth of aiound 2 and 3 mm for buffer gas
pressures of 500 and 700 mbai*. Thus indeed would lead to a substantial radial profile of the
electric field sti'ength in the dischaige tube and could therefore be responsible for the annulai'
beam observed. The values calculated by using equation 7.8 are also more consistent with
those quoted for conventional electrically excited SRLs [8, 9]. This increased electron
density would result in a substantial decrease in the electric field given in table 7.1, due to
the increased conductivity of the plasma. This reduced electiic field could possibly result in a
low
ion density in the discharge afterglow and hence lower than optimum laser output
power.
Equation 7.1 does not take into account the effect of electron reheating due to
the recombination of str ontium ions or the effect of Hybrid-Penning ionisation of the neutral
strontium by the helium ions (although this effect is small for the time scale in this
calculation [6]). The effect of omitting of these terms would be to underestimate the initial
electron density. Therefore it would seem plausible that the electron density estimate
obtained using Carman's recombination rates would represent a lower limit of the electron
density in the discharge. (It has already been suggested in section 6.3.3 that the electron
densities calculated by the method described therein, which appear' to agree well with those
PhD Thesis
184
J. W. Bethel
Chapter 7_____________________ Microwave excited Strontium-ion recombination laser
calculated using Caiman's recombination rates, are likely to give an underestimate of the true
electron density).
On the other hand, Bibermann et a l [10] claims that the
dependence of
the recombination rate of group 2 elements is obeyed up to relatively high electron
temperatures (80,000 K). However, for the case of inert gases, the recombination coefficient
falls much more rapidly with rising Tq (greater than about 2500 K [10]). Hence, the
corresponding estimates using the classical
dependence for the recombination rate
could be expected to give an over estimate of the electron density. Other sources of error
could arise from the uncertainty of the strontium vapour pressure. It was noted in chapter 6,
that the wall temperature was nonuniform along the length of the tube, this could result in
lai'ge variations in the vapour pressure of strontium. However, as has already been stated the
shape of the calculated emission was fairly independent of the starting values of the
strontium and helium ion densities. In addition, in the region of the tube where laser
oscillation takes place the conditions are likely to be similar to those in Carman's model.
7.5 Conclusions
Laser oscillation has been observed on the recombination transitions of
ions for a
self-heated, microwave pumped discharge. The laser was operated at what appeared to be
threshold input powers, resulting in a low strontium vapour density. Much higher output
powers should be possible if higher average microwave pump powers could be used, or if a
tuner was used to eliminate the reflected power. Using such a tuner, the coupling efficiency
of microwave power into the discharge is expected to exceed 90 per cent.
The upper and lower limits to the electron density estimated by analysing the
spontaneous emission of the 430.5 nm transition aie in relatively good agreement with those
measured in section 6.3.3. These values would suggest that scaling a microwave excited
PhD Thesis
185
J. W, Bethel
Chapter 7_____________________ Microwave excited Strontium-ion recombination laser
laser to lai'ger tube diameters (greater than 1 cm in diameter) would result in the occurrence
of large radial electric field gradients. In order to overcome this problem it would be
necessary to use a magnetic field or reduce the microwave field frequency, in order to
increase the depth of propagation of microwaves into the plasma. However the magnetic
fields required for the plasma conditions in occurring in SRLs would be large (over 1 T for a
microwave frequency of 2.45 GHz at an electron density of 10^^ cm“^). On the other hand
reducing the microwave field frequency would increase the Vm/û) ratio rather than just
increasing Vm, because according to reference [11] the skin depth remains constant for
increasing Vm as higher absorbed powers aie required to maintain the discharge at these
higher pressures. These higher absorbed powers result in higher electric field strengths in
the plasma and this in turn results in an increase in the electron density.
However, despite the problems associated with the plasma skin effect, the
advantage of operation at high buffer gas pressure (see chapter 3) and the fact that the
microwave pulse shape can be regaided as independent of the dischai'ge paiameters makes
the prospect of a microwave pumped system very attractive. In addition, the electrodeless
nature of the microwave discharge will result in a reduction in both contaminants and
electrode induced dischaige instabilities.
PhD Thesis
186
J. W. Bethel
Chapter 7_____________________ Microwave excited Strontium-ion recombination laser
References
1.
Handbook of Chemistry and Physics.
Edited by R, C. Weast.
57th edition, CRC press, Inc. 1976-7, U. S. A.
2.
Electron density measurements in a strontium vapour laser.
D. G. Loveland and C. E. Webb.
J. Phys. D: Applied Physics vol. 25, pp 597-604, 1992.
3.
High-pressuie high-current transversely excited Sr’*' recombination laser.
M. S. Butler and J. A. Piper.
Applied Physics Letters, vol. 42, No. 12, pp 1008-1010, June 1993.
4.
Pumping of a strontium-ion recombination laser with a cut-off thyratron.
P. A. Bokhan and D. É. Zakievskii.
Soviet Journal o f Quantum Electronics, vol. 21, No. 8, pp 838-839, August 1991.
5.
Forced aii-cooled strontium recombination laser,
J. W. Bethel.
MSc. Thesis, Strathclyde University, 1990.
6.
Self-consistent model for a longitudinal discharge excited He-Sr recombination laser.
R. J. Carmen.
IEEE Journal of Quantum Electronics, vol. 26, No. 9, ppl588-1608 September 1990.
7.
Investigation of laser emission in Sr"^ and Ca"**.
C. W. McLucas and A. I. Macintosh.
J. Phys. D; Applied Physics vol. 20, pp 591-596, 1987.
8.
Recombination lasers utilising vapours of chemical elements.
2. Laser action due to transitions in metal ions.
V. V. Zhukov, V. S. Kucherov, E. L. Latush and M. F. Sem.
Soviet Journal of Quantum Electronics vol. 7, No. 6, pp 708-714, June 1977.
9.
Electron density measurements in a strontium vapour laser.
D. G. Loveland and C. E. Webb.
J. Phys. D: Applied Physics, vol. 25, pp 597-604, 1992.
10.
Kinetics of the impact-radiation ionisation and recombination.
L. M. Bibermann, V. S. Vorob'ev and I. T. Yakubov.
Soviet Physics Uspeklii, vol. 15, No. 4. pp 375-531, January-Februaiy 1973.
11.
Magnetically enhanced electromagnetic wave penetration in weakly ionised plasmas.
S. P. Bozeman and W. M. Hooke.
Plasma Sources Science Technology, vol.5. No. 1, pp 99-107, February 1994.
PhD Thesis
187
J. W, Bethel
CHAPTER
8
Conclusions and future work
8.1 Summary of the work in this thesis
We have designed and built two microwave coupling stmctures, the ridge waveguide and the
tapered waveguide coupling structures, for producing relatively high electron densities at
high buffer gas pressures. Using these coupling structures, we have demonstrated laser
oscillation on the cyclic transitions of neutial copper (^510.6 and 578.2 nm) using copper
halides (CuCl and CuBr) and on the recombination transition of singly ionised strontium
(/U=430.5 nm), for the first time in a microwave pumped system. Although the performance
of the both laser systems was poor when compared to conventional electrically excited
systems, this could be attributed in pai't to the non-ideal nature of the pump source (long
duration of the microwaves pulse, the fixed, relatively low recurrence rate of the modulator
power supply and the high angulai' frequency of the microwaves).
During the course of the investigation we have estimated some of the more
fundamental plasma parameters (electron density, electric field and E/N ratios) in the laser
discharges. These estimates appealed to be lower than those in conventional electrically
excited systems, however this could be remedied by the use of shorter, higher peak power
microwave pulses.
The major fundamental factor contributing to the poor performance of the
copper halide lasers was the problem of producing a uniform electric field along the length of
the active medium of the laser. This will be particulaiiy important in metal vapour lasers in
general because the vapour pressure of the elemental metal or metal compound (such as the
PhD Thesis
188
J. W. Bethel
Chapter 8_________________________________________ Conclusions and future work
metal halide) is often determined by the tube wall temperature and hence the absorbed
microwave power at that point in the tube. The addition of these vapours can drastically
change the properties of the plasma, resulting in run-way instabilities (see section 6.4.2). It
is for this reason that resonant microwave structures (such as Asmussen cavities), or
standing wave fields (such as those occurring in the ridge waveguide coupling stiucture used
in the initial experiments on the copper chloride laser) are of no use for exciting metal vapour
lasers.
The consequence of the nonuniform temperature distribution in the dischaige
tube of the copper halide laser is a diastic reduction in the effective active volume of the laser
(see section 6.4.3). By estimating the volume of the discharge where laser oscillation
occuiTcd, we found that the effective specific output power for the microwave excited copper
halide laser is comparable to that in conventional electrically excited high PRF systems.
Therefore there would seem to be no fundamental reason to suggest that the performance of
a small bore (where the skin depth is not important) microwave excited copper halide laser
should not compare favourably with a conventional electrically excited system. Although we
cannot say for certain whether the performance of the lasers studied in this investigation was
affected by the skin depth of the microwaves, it is apparent that for larger bore tubes the skin
layer will be detrimental to the operating char acteristics of these lasers.
The poor performance of the strontium-ion recombination laser was due to
the threshold average input power absorbed in the plasma tube. This absorbed power could
be increased by the use of a suitable tuning element in the cavity, which was not available at
the time of the measurements. We have shown that coupling of the microwave power into
the discharge should exceed 90 per cent for high buffer gas pressures, if an impedance
matcher is used. This compares very favourably to dc electrically excited systems.
PhD Thesis
189
J. W. Bethel
Chapter 8_________________________________________ Conclusions and future work
8.2 Suggestions for future work
There is a wide range of coupling structures and excitation schemes which could be used
with microwave excitation. However, from the experience gained in this investigation we
can identify the important properties which an effective coupling structure should possess.
In order to effectively pump a metal vapour laser using microwave excitation a coupling
stiucture which has the following fundamental properties must be used.
1. A uniform electric field for a wide range of dischaige conditions. This would probably
involve using a coupling structure in which it is possible to manipulate the electric field to
accommodate the vaiious plasma conditions.
2. Unifoim vapour pressure of the elemental metal or metal donor, the paitial pressure of
which should be independent of the microwave pump power.
It would also be advantageous to be able to use a coupling structure in which the active
medium is confined in a metallic container. This would result in a more robust laser tube
with lower outgassing rates and a higher thermal conductivity to reduce temperature
gradients in the active medium. Some promising coupling structures are discussed below.
8.2.1 Surface-wave coupling structures
In recent years a great deal of research effort has been put into plasma generation using
'surface-waves' [1]. In these systems the electromagnetic wave generated propagates along
the interface between a plasma column and a surrounding dielectiic tube. Surface waves can
be effectively launched in a plasma tube placed in holes peipendiculai* to both broad walls of
a rectangulai* waveguide, see figure 5.3. However as the wave propagates along the plasma
column, it becomes attenuated and hence the power absorbed in the plasma will be reduced
along the length of the column. Therefore in order to produce a uniform plasma along the
length of the discharge tube it will be necessary to use two magnetrons as shown in
figure 8.1. A magnetic field, directed along the propagation direction of the microwaves,
PhD Thesis
190
J. W. Bethel
Chapter 8
Conclusions and future work
Sliding short
Cii'culai* waveguide
Plasma
Beiyllia tube
Solenoid
Rectangulai* waveguide
Microwaves in
Microwaves in
Figure 8.1.
A surface wave coupling structure using two magnetrons to obtain a uniform field
could also be used to increase the skin depth of the microwaves at the high electron densities
chaiacteristic of copper and strontium vapour lasers. This magnetic field could be created
using high peak current pulses, rather than a continuous field which would create a lot of
heat. A bei*yllia dischaige tube would be more suitable than an alumina tube because the
higher conductivity of beryllia would result in reduced temperature gradients along the tube
axis.
8.2.2 A// metal waveguide coupling structure
An all metal waveguide structure based on a plasma guide is shown in figure 8.2. In this
system the vapour pressure of the metal vapour could be accurately controlled by the use of
external ovens. The mesh over the ovens will prevent any interaction of the microwaves with
the metal or metal donor and hence allow the vapour pressuie to be totally independent of the
microwave field in the tube. However in this system, the use of a magnetic field is
mandatory (unlike the previous suggestion) because in the absence of a magnetic field, the
PhD Thesis
191
J. W. Bethel
Chapter 8
Conclusions and future work
Sliding short
Circulai' waveguide
Plasma
Mesh
External /
heated ovens
Solenoid
Rectangular waveguide
Metal or
metal donor
Microwaves in
Microwaves in
Figure 8.2.
An all metal microwave coupling structure.
plasma frequency of the discharge produced will be limited to the angular frequency of the
exciting field. Possible problems with this system could result from the 'slow wave' formed
in the dischaige (in plasma filled waveguides the wavelength of the microwaves, and hence
their velocity, can be very much less than in free space). This could mean that the
propagation time of the microwave field along the length of the discharge tube is longer than
the upper laser level lifetime.
8.2.3 Transmission line coupling structure
In a transmission line system the microwave power would be coupled out of the rectangulai*
waveguide via a rectangular waveguide to coaxial cable transition. The microwave or radio
frequency field will be applied to one of the parallel plates from the coaxial cable whilst
leaving the other either at ground or floating. In this way a transverse electric field will be
produced in the plasma. Figure 8.3 (a) shows a coupling structure consisting of two parallel
plates separated by a ceramic spacer (in this case alumina). One of the ceramic spacers also
acts as an external oven containing the metal or the metal donor. Obviously in this situation
PhD Thesis
192
J. W. Bethel
Chapter 8
Conclusions and future work
Zemrex CR50
conducting gasket
Alumina
spacer
Metal plates
Alumina
rf application
Metal or
metal donor
Heaters
(b)
(a)
Figure 8.3.
Coupling structure based on a parallel plate transmission line.
the whole of the coupling structure will have to be at a very high temperatures to prevent the
active vapour from condensing out. Therefore in this scenario we propose to use a carbon
composite gasket (Zemrex CR50 [2]) which can be exposed to temperatures in excess of
KXX) ®C, to seal the alumina to the parallel plates. Using this configuration we can scale the
discharge in one dimension (the width) whilst keeping the height constant thereby
maximising the heat removal from the system. In addition, this method can bypass the
problems resulting from the small skin depths which could occur in microwave excited
pulsed metal-vapour laser discharges. A similar configuration is shown in figure 8.3 (b),
however in this case the transmission line is external to the discharge which is located
PhD Thesis
193
J. W. Bethel
Chapter 8_________________________________________ Conclusions and future work
entirely inside the alumina slab. A similar device to that shown in figure 8.3 (b) has been
used to pump a small excimer laser and is now commercially available [3]. It would be
interesting to compaie the performance of the two devices in figures 8.3 (a) and (b).
Possible problems in these systems could aiise from the coupling of the
coaxial cable to the transmission line plates at the high peak powers necessary for laser
oscillation. Therefore it may be necessary to place the transmission line section under oil.
The impedance matching of the microwaves into the transmission line can be accomplished
by using a tuner in the rectangulai* waveguide before the waveguide to coaxial transition.
Finally, the size of the structure will be determined by the propagation constant of the
microwaves in the tiansmission line. For optimum performance, the size of the active region
should be chosen to be small compaied to the propagation constant in the system. However
the propagation constant will be detei*mined by the plasma paiameters and hence will change
with buffer gas pressures.
8.2.4 Waveguide with plasma tube operating close to cut-off
If the dimensions of the waveguide are chosen so that the microwave field is close to the
cut-off frequency for waveguide then the wavelength of the microwaves in the waveguide
will be lai’ge compaied to the dimensions on the active medium of the laser. Such systems
have been used to pump CO2 lasers [4] in a system based on a hybrid-T-junction. In this
case the axial distribution of the electric field produced should be relatively uniform along the
length of the dischaige tube. Figure 8.4 shows the hybrid-T-junction along with the plasma
tube in the section of waveguide which is close to cut-off.
In this system, there is a high possibility that arcing could occur where the
H-plane junction joins the waveguide due to the lai'ge electi'ic field distortion which occurs in
this region. This problem could be reduced somewhat by using rounded edges and
pressurising with SFô-
PhD Thesis
194
J. W. Bethel
Conclusions and future work
Chapter 8
Waveguide section
neai' cut-off
Dischaige
Plasma tube
Microwaves
in
Figure 8.4.
Waveguide coupling structure based on a hybrid-T.
8.2.5. Microwave pulse compression
The compression of microwaves pulses is a well known technique for producing very high
peak power microwave pulses of short duration from a source of lower power microwaves
with a longer pulse duration [5]. Compression of the pulses is achieved by resonantly
charging a waveguide cavity and then Q-switching this cavity by changing its effective
length (usually by a quarter of a wavelength of the pumping microwaves). This technique
has been applied to microwave excited excimer lasers [6, 7], where self Q-switching occurs
due to the transition of no plasma, to plasma in the laser tube as the microwave field builds
up in the waveguide coupling structure (see figure 8.5). However these lasers were operated
at low recurrence rates (10 Hz [6]). The application of this technique to metal vapour laser
systems would depend upon the electron density falling substantially between microwave
pulses so that a significant change in the Q of the cavity can occur. This appear s to happen in
copper halide lasers (see chapter 6) and therefore this technique could possibly be applied to
PhD Thesis
195
J. W. Bethel
Chapter 8
Conclusions and future work
these lasers. The duration of the compressed microwave pulses is related to the length of the
waveguide by the following relationship
CT«
(8.1)
^w “
where /w is the length of the resonant cavity Tp is the duration of the compressed pulse and c
is the speed of light. Therefore the size of the laser system will become very lai'ge for pulse
lengths of over 20 ns or so. However, the very high peak powers possible could allow
Sliding short
Resonant iris
Microwaves in
Rectangular waveguide
resonant section
Plasma tube
Absorbing load
Figure 8.5.
Scheme for producing short pulses in a plasma tube.
operation at substantially higher buffer gas pressures (tens of atmospheres) than is currently
possible with conventional electrical methods. In addition the rapid rise and fall times
available will be advantageous for the copper and strontium based systems respectively.
PhD Thesis
196
J. W. Bethel
Chapter 8_________________________________________ Conclusions and future work
8.4 Conclusions
As we have shown in the previous sections in this chapter, the work in this thesis has only
scraped the surface of possibilities available for pumping metal vapour lasers using
microwaves. Operating regimes which are outwith the capabilities of present electrically
excited discharges can be accessed using microwaves pumping and these could lead to
substantially improved performances of these lasers. However, in recent years, the advent of
high power, reliable solid-state devices has meant that metal vapour lasers could well
become overshadowed. These advances in solid-state devices have come about largely as a
result of the vast resear ch effort which has been put into this field during the past decade or
so. With such a large research environment, new ideas are bound to arise and advances in
the technology will be rapid. The extent of the research undertaken in the field of metal
vapour lasers is substantially smaller. However significant improvements in metal vapour
lasers could be made if more research is carried out and the full range of current technologies
available from other fields are exploited.
PhD Thesis
197
7. W. Bethel
Chapter 8_________________________________________ Conclusions and future work
References
1.
Plasma sources based on the propagation of electromagnetic surface waves.
M. Moisan and Z. Zakrzewski.
J. Phys. D: Applied Physics, vol. 24, pp 1025-1048, 1991.
2.
Electromagnetic Shielding Products and Themially Conductive Insulators.
Issue 0592.
Warth International Ltd., Charlswoods Business Centre, Charlswoods Road, East Grinstead, Sussex,
RH19 2HH.
3.
Potomac UV Waveguide Lasers.
Potomac Photonics, Inc., 4445 Nicole Drive, Lanaham, MD 20706.
4.
Excitation of COg lasers by microwave discharges,
B. Freisinger, H. Frowein, M. Pauls, G. Pott, J. H. Schaffer, J. Uhlenbusch,
Proceedings of SPIE, CO2 Lasers and Applications II, vol. 26, pp 29-40, 1990.
5.
Some properties of microwave resonant cavities relevantto pulse-compression power amplification.
R. A. Alvarez.
Review of Scientific Instruments, vol. 57, No. 10, pp 2481-2488, October 1986.
6.
1.3 mJ XeCl laser pumped by microwaves.
H. H. Klingenberg and F. Gekat.
Applied Physics Letters, vol. 58, No. 16, pp 1707-1708, April 1991.
7.
Laser system based on a commercial microwave oscillator with time compression of a microwave
pump pulse.
M. S. Arteev, V. A. Vaulin, V. N. Slinko, P. Yu. Chumerin and Yu. G. Yushkov.
Soviet Journal of Quantum Electronics, vol. 22, No. 6, pp 562-563, June 1992.
PhD Thesis
198
J. W, Bethel
APPENDIX
A
Magnetron power supply.
A l Magtest modulator power supply for the magnetron
The power supply used to drive the magnetron (M5193) (see data sheet, [1]) was an
alternator charged Magtest modulator on loan from EBV Ltd., Lincoln. It is a 'line-type
modulator' Le. voltage pulses are applied to the magnetron by chaiging up a pulse forming
line or network (in this case a lumped inductor-capacitor network), and dischai'ging it with a
gaseous switch {e.g. a thyratron), through the magnetron via a pulse transformer. The
modulator is required to produce voltage pulses of up to 47 kV with corresponding peak
currents of up to 110 A [1] with a maximum average power of about 6 kW (at the recurrence
rate of 750 Hz, which the modulator is fixed at). The full details of the charging system aie
complicated, but a simplified circuit diagram is shown in figure 1. In addition to chaiging the
pulse forming network (PEN), the main alternator and the auxiliaiy alternator aie required to
provide the necessary heating currents for the thyratrons, the magnetron and for the
electro-magnet. However, we will only concern ourselves here with the main alternator and
the chaining circuit.
A 1.1 Alternator charging of the PFN
The modulator employs a system of chaiging known as 'ac non-resonant charging', (see [2]
and [3] for a comprehensive treatment of ac non-resonant and ac resonant charging). This
system of charging has been used for high power radar applications for over 50 years, and
has some advantages over direct current (dc) chaiging methods. Foremost is the fact that this
method requires no high voltage rectifiers, smoothing condensers, or hold-off tubes.
PhD Thesis
199
J. W. Bethel
Î
PFN t = 2.2 jis
i
I
C = 7x5nFL =6x3.53|iH
f
'V’WV'V^
Inverse diode
CX1140
T
T
-p_______T
De-spiking section
Anode inductor
29 pH
Charging chokeLc
2.7 mH
6xl200pF
i
A
R=40a
800 W
Main switching
thyratron CXl 140
750 Hz
) Alternator
Transformer
1:25
12 kV max.
400 Q
200 W
Magnetron
M5193
Peak power
2.6 MW
Average power
-2.7 kW
Impedance 427 O
Pulse transformer
1 :4
Figure A l
Simplified circuit diagrm of the charging system used in the modulator.
s
I
I
Appendix A
Magnetron power supply
In addition, the charging voltage obtained with ac charging methods can be made higher
than with dc chaiging methods for the same supply voltage [2]. However, as we shall see,
ac chaiging is less flexible and limited to a fixed recurrence rate.
Alternator
Inductance
.rw - v A .
7^=1.3mH
Alternator
Chaiging
Choke
Transformer
leakage inductance
jA T V A A = 2.7 mH
- T V A A O ___
= 0.3 mH
Effective inductance of
transformer
%> =21.9|xF
= 80 mH
Capacitance of
PFN referred to
primary
1:25 Step-up
Chaiging tiansformer
Figure 2.
Equivalent circuit for the charging of the PFN via the step-up transformer, with all the
component values referred to the primary.
The charging circuit for the modulator (as supplied by EEV) is shown in
figure 1, for the charging of a 2.2 |xs (PFN). An equivalent circuit for the charging of the
PFN is shown in figure 2, along with the component values referred to the primary. The
total effective inductance of this circuit is given by
(La + L^, ) Lj
^e =
(La +Lc +Ljn)
+ Lc,
(A.1)
and the total capacitance of the pulse forming network (PFN) referred to the primary of the
step-up charging transfonner (turns ratio n~25) is
Cn
PhD Thesis
p
= ^ CpFN-
201
(A.2)
J, W. Bethel
Appendix A
Magnetron power supply
The alternator produces a sinusoidally vaiying voltage at a fixed recurrence
rate of 750 Hz and chai ges the PFN to a voltage of up to 25 kV, via the step-up transformer.
For ac non-resonant charging, there aie two conditions which must be met. Firstly,
dV ^ ^
2k
= 0, dX.t = ----dt
(O^
(A.3)
where cOq, is the angular frequency of the alternator and V is the charging voltage. Le. the
main switching thyratron (CXI 140) fires when the voltage on the PFN is at a maximum.
Secondly,
2k
(A.4)
0
because the PFN is supplied directly from the transformer. In addition to these conditions,
the voltage on the PFN at the beginning of each charging cycle is zero. This is achieved
using a triggered inverse diode (see figure 1) which fires a few |as after the main switching
thyratron has fired. This ensures stable operation of the charging circuit. Therefore the
chaiging wavefomi at the PFN following a dischaige of the thyratron (obtained by applying
Laplace transforms to the equivalent chcuit in figure 2 and then using Duhamel's integral as
in reference [2]) is given by equation A.5 below
r
V = V q sin(ft)a^ + ^f ) “
sinj^c^ Pc
where
v-ti \
sin Of +
V
^0
J
cosp^t
Vq =
(A.5)
(A.6)
(/^c^ - ® a ^ )
1- K
= tan -1 ( ®a
tan
^a
V Pc 1 + K
I
and the natural frequency of the circuit, Pç. =
jy
(A.7)
(A.8)
NP
PhD Thesis
202
J. W. Bethel
Appendix A___________________________________________Magnetron power supply
coa is the angular frequency of the alternator, 0f is the firing angle (which can occur at
^f=^±7F so that V can have either polaiity), ÆVr is the overswing following the switching
of the thyratron (for instance due to an impedance mismatch) and Vac is the alternator
charging voltage. Equation A.5 is plotted in figure 3 for the case where there is no negative
overswing (KVt:=^0) and for Pc/coa. = 0.7. The ratio pc/coa ~ 0.7 is generally regarded as
being the optimum for alternator chaiged systems [2], as lower values of pc/(Oa require
higher alternator voltages (see figure 4) and higher values (Pc/C0a>lA) lead to a distortion in
the charging waveform. This distortion manifests itself in a positive swing in the charging
voltage immediately after the thyratron fires (see figure 3), which could result in latching of
the thyratron. Choosing Pc/coa, = 1, the resonance condition, is generally avoided due to
the danger of overvoltage and subsequent component damage occurring, if the main
thyratron fails to conduct.
The role of the inverse diode in the circuit is to allow stable operation of the
charging circuit (as described above) and to prevent over-voltages from occurring on the
PFN as a result of a short circuit in the magnetron. When a short circuit occurs in the
magnetron, the tr ansformer is also short circuited and therefore the voltage on the PFN will
swing to -V. Therefore, the subsequent voltage maximum in the charging cycle will be
greatly increased (see figure 5). The inverse diode is triggered by a current transformer in the
anode lead of the main thyratr on and is arranged to trigger at the end of each voltage pulse.
PhD Thesis
203
J. W. Bethel
Magnetron power supply
Appendix A
Curve 3
0.5
Curve 2
Curve 1
2
Curve 2
o
>
Curve 3
a=0-7 -
1 .5
— Curve 1
s
I
B 0.5
I
I
0
I
-0.5
>
4
Curve 2
1
Curve 3
a
i
Curve 1
I
0
%
2%
Time period
Figure 3.
The voltage charging cycle for ac non-resonant charging for
various values of the ratio j8c/ft)a* Curve 1 is the PFN voltage F t »
curve 2 is the alternator charging voltage F a o and curve 3 is F q.
PhD Thesis
204
J. W. Bethel
Magnetron power supply
Appendix A
4
I
3
I
2
1
0
0
0.5
1
The ratio
1.5
2
Figure 4.
The ratio of the terminal charged voltage F x to the alternator
voltage Fac> for a range of values of j3c/û)a<
-2
7t/2
37T/2
Time period
Figure 5.
Plot of the subsequent charging voltage after magnetron has
shorted.
PhD Thesis
205
/. W, Bethel
Appendix A
Magnetron power supply
A 1.2 Discharge of the PFN through the pulse transformer
When the voltage on PFN has reached a maximum voltage, the main thyratron is fired and a
voltage pulse of half the PFN charging voltage (when the load is matched to the PFN)
appears at the primary of the pulse transformer (turns ratio 1:4). Therefore, a voltage pulse
which is twice the PFN charging voltage is produced at the magnetron. The equivalent
circuit of the discharge of the PFN through the pulse transformer is shown in figure 6, again
with all the components values referred back to the primary, and their origin given in table 1.
A full analysis of the equivalent circuit of the pulse transformer and a biased
diode load, i.e. a magnetron, is complicated. This is because the response of the magnetron
is nonlinear, the usual equivalent circuit representation of a magnetron is a battery, a series
resistance and a switch which closes when the voltage across the load is greater than or equal
to that of the battery [3]. Therefore any voltage fluctuations which occur after the magnetron
has turned on (begun oscillating) produce much greater variations in the current (about a
factor of 10). However, during the rising edge of the voltage pulse, the magnetron resistance
is essentially infinite and exhibits a capacitance of around 5 pF [4]. Therefore, the equivalent
^2
PFN
L2
mag
Figure 6 (a).
Full equivalent circuit of a pulse transformer.
PhD Thesis
206
J. W. Bethel
Magnetron power supply
Appendix A
ag
Figure 6 (b).
Simplified equivalent circuit for calculating the voltage risetime.
Parameter
Origin
Value
«P
Primary winding resistance
0.4 n
Rs
Secondary winding resistance
3,4 0
Rq
Transformer core resistance
2mag
Magnetron impedance
427 0
Primary winding inductance
1.1 mH
4
Secondary winding inductance
16.9 mH
Ll I
Primary leakage inductance
8.5 |liH
^L2
Secondary leakage inductance
144|liH
Cl
Primary winding capacitance
Negligible
C2
Secondary winding capacitance
Negligible
Cl2
Interwinding capacitance
1.1 nF
Qnag
Capacitance of the magnetron
~5pF
n
Transformer turns ratio
oo
4
Table 1
Pulse transformer parameters.
PhD Thesis
207
J. W. Bethel
Appendix A___________________________________________Magnetron power supply
circuit for the front edge of the pulse reduces to figure 6 (b), where the primary winding
resistance can be neglected. Hence the voltage rise is given simply by
^rise(0 = M^s _
where (5^ =
1
.
,
V ^ e ff^ e ff
^m ag
(l-cos^ e0>
(A.9)
L
C
Lgff = L ^ + L ^ + - ^ andC g^ = —--------n
^1 + ^PFN
,(A.10)
n is the transformer turns ratio (in this case 4), La is the anode inductor (see figure 6(a)),
and Vs is given by
7
-^mag
//
Vs “ 7 ------- 7-------------- ^PFN^mag /
+ ZpFN
(A. 11)
y^2
2mag is the steady state impedance of the magnetion after it has switched on and Zpfn is the
impedance of the PFN, Equation A.5 shows that the voltage pulse would ring up to twice
the value of nVs, as expected from this type of resonant charging. However when the
voltage on the magnetron reaches nV^fl, the magnetron switches on and the subsequent
oscillations which would have occurred are damped out by the application of the steady state
magnetion impedance. The characteristic time (10 to 90 percent) taken for the voltage pulse
to reach this value {nV^H) is given by
^rise ~ 'V'^eff ^eff •
(A. 12)
This value of the risetime corresponded well (± 5 percent) to the measured values.
The top of the current pulse on a biased diode load (such as a magnetion) is
very sensitive to changes in the voltage on the load. The voltage pulse shown in figure 7
shows that the top of the pulse is relatively free from oscillations and spikes. However the
corresponding current pulse shown in figure 8 shows that there is a considerable current
spike on the leading edge of the pulse. These spikes can generally be reduced by the use of
PhD Thesis
208
J. W. Bethel
i
Appendix A
Magnetron power supply
Figure 7.
Voltage pulse at the magnetron for the 1.75 |is PFN.
Figure 8.
Current pulse at the magnetron for the 1.75 |is PFN,
20 Amps per division.
PhD Thesis
209
J. W. Bethel
Magnetron power supply
Appendix A
chosen to approximately match the period of the current spike. The voltage and current
pulses (figures 7 and 8) are relatively free from droop, even though the droop on a
magnetron load is expected to be much greater than for a linear load [3]. The magnetron
output pulse tends to follow the current pulse quite closely and hence current oscillation tend
to produce oscillations on the rf pulse. The oscillations generally observed in this work
tended to originate from the pulse forming hnes used.
Figure 9.
Voltage pulse at magnetron showing the back swing due to
the demagnetisation of the pulse transformer core.
The rate of fall of the voltage pulse tends to be much slower than the rate of
rise of the voltage pulse. However, oscillation in the magnetron usually ceases when the
voltage pulse drops below about 80 percent of the peak value and the width of the rf pulse
corresponds to the width of the current pulse at half its maximum. In a biased-diode load or
magnetron a back swing voltage occurs after the voltage at the secondary has reduced to zero
(see figure 9). This is a result of demagnetisation of the core of the pulse transformer.
Usually the area under the voltage pulse will be equal to the area under the backswing region
because the flux density in the pulse transformer core must return to the same remanent point
before the next pulse is applied. The oscillations at the end of the current pulse tend to be
PhD Thesis
210
J. W. Bethel
Appendix A___________________________________________Magnetron power supply
comparatively larger than the corresponding voltage oscillations. Strong oscillations at the
end of the current pulse can result in the resumption of oscillation of the magnetron (and
probably in a different mode from the fundamental mode, which could result in damage to
components e.g. the circulator, so this should be avoided).
A2 Modification of charging circuit
The modulator used in this work is limited to a recurrence rate of 750 Hz. In order to obtain
laser oscillation in a copper halide vapour, the halide molecule must be dissociated and the
free copper atoms excited to the upper laser levels before they can recombine with the
halogen atoms (see chapter 4). Ideally, a continuous train of pulses, of recurrence rates of
between 5 and 30 kHz, should be applied to the dischai’ge tube. However, due to limitations
of the charging system, it would not be possible to charge up the PFN on a time scale
required for the high recurrence rates necessaiy for a copper halide laser. However, by
charging up two PFNs in parallel and switching them sequentially, we can create the
conditions required for generating a population inversion in the laser. To do this, it was
necessaiy to replace the existing PFN (which has a 2.2 |Xs duration) and to design and
construct PFNs of varying pulse durations which would produce adequate pulse shapes for
use in the circuit. Hence before describing the double-pulse circuit used in this work we will
outline the some of the criteria for PFN design.
A2.1 Pulse Forming Network design
The main points to consider for designing PFNs for use with magnetions aie the impedance,
the risetime of the voltage pulse and the pulse duration. The risetime of the leading edge of
the voltage pulse applied to the magnetion above 80 percent of the amplitude must not
exceed 150 kV/j.is [4]. Rise times greater than this can lead to the magnetron oscillating in
higher order modes. Many forms of pulse foiming lines can be used to generate high voltage
PhD Thesis
211
J.W . Bethel
Appendix A
Magnetron power supply
squai'e pulses, ranging from simple coaxial cable, to various elaborate inductor-capacitor
(LC) configurations (see reference [3] for more details). The pulse forming lines used in this
work were lumped inductor-capacitor (LC) networks based on the type E lumped LC lines
(see reference [3] and figure 10). In these PFNs, the inductor can consist of a continuous
winding whose total inductance, Lpfn> is
LpFN =
tZ,
'mag
(A.13)
2n 2 ’
and equal capacitances whose sum is given by
CpFN =
(A.14)
2 Z mag
where t is the pulse length. The inductor is then divided up equally, except that the two end
stages have about 25 percent higher inductance and the capacitances are attached to the
corresponding points along the solenoid (see figure 11). In this way the mutual inductances
between adjacent coils replace the negative self inductances which occur in series with the
1.25 L n
'N
LN
1.25 L n
C]sf
Cn -
Cn
Cn
oFigure 10.
Type E pulse forming network.
capacitors in type D Guillemins line [3]. The value of the total inductance was estimated
using the well known Wheeler foiinula [5]
LpFN =
9r + 10/
(A. 15)
where L here is in |iH, n is the number of turns, r is the radius and / is the length of the
PhD Thesis
212
J. W. Bethel
Appendix A
Magnetron power supply
Enamelled copper wire
Nylon former
Aluminium plate
Bleed resistor
Capacitors
Figure 11.
Pulse forming network showing the continuous winding of the inductor.
solenoid in inches, for />0.8r. This was then measured using a Marconi bridge or an LCR
Avometer.
Very good pulse shapes for lumped lines are usually obtained for PFNs with
five stages, although it is possible to produce adequate pulse shapes with less stages if the
pulse lengths aie not too long (less than around 2.5 |Xs [3]). The capacitors used in the PFNs
were ceramic, manufactured by Murata or TDK and were rated to 40 and 50 kV peak
voltage, respectively.
As mentioned above it is important to limit the rate of rise of the voltage pulse
delivered to the magnetron. This is usually achieved by placing an additional inductor (La) in
the vicinity of the thyratron anode (see figure 1). This leads to a slight increase in the
impedance of the PFN. However this is not a problem because it results in a slight negative
voltage swing after the thyratron has fired, which allows the thyratron to recover more
quickly. The value of the inductor to be used can be calculated by referring to equations
A. 10 and A. 12.
PhD Thesis
213
/. W. Bethel
H
Appendix A__________________________________________ Magnetron power supply
The pulse duration of the microwaves ideally should be less than aiound
100 ns for efficient laser operation (see chapters 3 and 4). Unfortunately, there is a limit (of
about 0.8 |xs) to how short the pulse width can be made without incurring too great an
impedance mismatch (which would result in strong oscillations at the end of the current
pulse). This is due to the primaiy and secondary inductances of the pulse transformer and
the risetime constraint of the magneti on.
Due to the high-peak currents and short pulse duration generated in the PFNs
(up to 400 A peak) it is necessary to consider the rms current values and the skin effect of
these pulsed currents in the copper wire, so that the maximum current density in the wire is
not exceeded. The skin effect of cuiTcnt pulses in metal is given by
8 — ^ I—^ « 0 . 1 V t m m , for copper,
(Ojl
(A. 16)
where pr is the resistivity of the metal, m is the frequency of the electromagnetic field, p is
the permeability of the medium and Tis the duration of the current pulse in ps. The rms
heating effect of squaie wave pulses is given by [6]
Ams “ ^pk
’
(A. 17)
where /pk is the peak current (a maximum of 400 A for this magnetron) and D is the duty
cycle. Therefore the approximate minimum radius of the wire which must be used is
where
is the maximum current rating of the wire. The value of 7r vaiies with wire diameter
but is greater than around 10.5 A/mm for wire areas of less than 4 mm^ [7]. Copper wire
(14 SWG) of about 2.1 mm diameter was used in the construction of the PFNs in this
work. The PFNs were immersed in an oil bath to prevent electrical breakdown and a bleed
resistor
PhD Thesis
214
7. W. Bethel
Appendix A__________________________________________ Magnetron power supply
Figure 13.
Charging voltage of PFN l, voltage scale is 5 kV/division.
of around 20 MH was placed across the PFN to allow slow discharge of the line when not
in use.
A2.2 Double-pulse circuit
The double-pulse circuit used this work is shown in figure 12. This is very similar to the
double pulse discharge circuit described in Pulse Generators' by Glasoe and Lebacqz [3].
In our case, the charging resistors in the circuit described in [3] are replaced with charging
diodes. In both cases, the charging diodes and the resistors serve to prevent PFN2 from
discharging through thyratron 1 when it fires, and vice-versa. However, in our case the
diodes serve an additional purpose. Thyratron 1 is triggered at 750 Hz by the thyratron in the
firing tray. By adding another PFN to the circuit, we change the natural frequency of the
circuit, pc (see section Al.l). This results in either reduced voltage pulses from the PFNs,
or as is more likely, failure of the thyratron to switch altogether. The use of diodes in the
circuit solves this problem and leads to charging waveforms as shown in figure 13. The
charging diodes consist of about thirty solid state, BYW96E [8] diodes in series. Each diode
PhD Thesis
215
J.W. Bethel
Magnetron power supply
Appendix A
has a hold-off voltage of 1 kV, an average current rating of 3 A and a recovery time of 300
ns. This method of charging is known as ac rectifier charging and is described in detail in
reference [2]. The charging voltage is given by A.5 for values of V>0, ie.
V=
(A.19)
s i n P ^ t - P q sincOaO-
The chaining circuit becomes essentially open circuit when dV/d^=0, hence the charged
voltage remains constant until the thyrati'on fires. This terminal charging voltage Vr is given
by
(A.20)
Pc “ ^ a
and the charging angle (j)is
2
kco,
(A.21)
(l>
Pc +
I
0.5
The ratio
Figure 14.
The variation of the ratio of terminai charged voltage T j and
the alternator voltage T a c with 0 c / # a , for the ac diode
charging, with no overswing (i.e, Æ=0).
PhD Thesis
216
J. W. Bethel
Appendix A
Magnetron power supply
From figure 14, which shows the relationship between Vt and the ratio
we can see
that ac-rectified charging can result in lower charging voltages than the ac nonresonant case
(see figure 4). Therefore it is necessary to choose Pc so that the value of Vt is not too low
that the required charging voltage (Le. 25 kV) cannot be obtained. In addition, if Pc/coa is
too small, the charging time will become longer than the alternator oscillation period (see
figure 15). Therefore care needs to be taken in choosing pc/C0a>
400
300
I 200
I
u
100
The ratio p^/co^.
Figure 15.
Charging angle ^ against j8c/®a-
Finally, we need to consider the rms and maximum charging currents
flowing in the circuit. The rms current is given by
cosec (j)
4ms = VjCO).
(A.21)
and is plotted in figure 16 along with the peak current [2]. For the example of 1.7 |Lis and
0.9 |is PFNs (total capacitance of 25^x47 nF, when referred to the primary) we have an
7rms of 1.5 A and an /max of 3.0 A.
PhD Thesis
217
J. W. Bethel
Magnetron power supply
Appendix A
0.8
0.6
0.4
0.2
0.5
1
2
1.5
Ratio Pç/Cû^.
2.5
3
Figure 16.
Plot showing
I rms
and /m ax against
Pc^Cû^.
Figure 17.
Charging voltage on the PFNs when the triggered inverse
diode is in use, 5 kV per division, 500 |is per division.
PhD Thesis
218
J. W. Bethel
Appendix A
Magnetron power supply
The triggered inverse diode (see section A l.l) of the original circuit was found to be
unsuitable for use in the double pulse circuit. This was because the negative swing in the
charging waveform on PFNl was removed by the inverse diode, which is triggered when
thyratron 2 switches. This leads to alternately high and low, charging voltages of the PFNs,
as can be seen in figure 17 and hence to alternately 'missing' microwave pulses from the
magnetron. Therefore the triggered inverse diode was replaced by thirty BYW96E solid state
diodes in series with a 480 O high-voltage resistor across each PFN, to provide a decay
time constant of about 14 ps (for the 1.7 ps PFN).
During operation, thyratron 1 is triggered by the pulse it receives from the
modulator's firing tray and this is synchronised with the main alternator charging cycle.
Thyratron 2 is triggered by a separate thyratron trigger unit whose output can be delayed
with respect to thyratron 1, by between 10-500 ps. This variable delay is achieved by using
a potential divider in the output pulse from the thyratron in the firing tray, to produce a
-15 volt pulse, and then feeding this into a delay circuit (figure 18) and from there to a
sepai’ate thyration triggering unit (see figure 19).
•o +18 V
|~~[ Inpm
J —1^ Output
Cj=0.1 nF
C =1.0nP
=8.3
Figure 18.
Delay circuit use in the double-pulsed system.
PhD Thesis
219
J. W. Bethel
Appendix A
Magnetron power supply
Main
Alternator
Double pulse
circuit
PFNl
Vaiiable
delay
Trigger
generator
PFN2
Pulse
ti'ansformer
Magnetron
Figure 19.
Block diagram of the modified charging system.
A3 Performance of the double-pulse circuit
The charging waveforms for the double-pulse circuit aie shown in figure 13. It can be seen
from this figure, that the output pulse from thyratron 1 appears at the anode of thyratron 2,
and vice-versa. These pulse voltages are negative and therefore pose no problems in
operation as long as large post-pulse oscillations do not occur. Note that the use of solidstate diodes as an inverse diode, as opposed to the triggered thyratron, has two main
disadvantages. These aie both related to the fact that there is no negative swing in the chaige
up of the PFNs. Usually the negative voltage swing on the thyratron anode would be around
2 kV depending on the impedance mismatch. Firstly, this could present a problem for
operation at high recurrence rate, because a negative voltage swing is normally used to aid
thyratron recovery. However, in the present system, the thyratrons discharge in the negative
half-cycle of the charging voltage and there is ample time, ~500 jus, for the thyratron to
recover. Therefore no latching was observed during this work. Secondly, as we have seen
in section A l.l, the negative voltage on the PFNs at the beginning of the cycle results in a
higher charging voltage on the PFNs than would be the case for zero initial voltage.
PhD Thesis
220
J. W. Bethel
Appendix A__________________________________________ Magnetron power supply
Therefore, slightly higher alternator voltages were required when the solid-state diodes were
used to achieve the same output voltages as before.
When the pulses from the PFNs are separated by less than around 15 |Lis or
so, the second voltage pulse occurs before the transformer core has time to demagnetise (see
figure 19). This results in a reduction in voltage for the second pulse which causes a slight
decrease in the output of the magnetron (and probably affects the frequency of the
microwaves too). However, under normal laser oscillation conditions the pulse pair
separ ation was greater than 15 |is so no problems occurred.
PhD Thesis
221
J, W, Bethel
Appendix A
Magnetron power supply
R eferences
1.
Data sheet A1A-62-M5193. Issue 1, July 1991.
EEV Ltd.
Carholme Road, Lincoln, LNl ISF, England.
2.
Some developments in high-power modulators for radar.
K. J. R. Wilkinson.
lEE Journal, vol. 93, No. Ilia, pp 1090-1112, 1946.
3.
Pulse Generators.
G. N. Glasoe and J. V. Lebacqz.
McGraw-Hill Book Company, Inc., U.S.A., 1948.
4.
Private communication with Tudor Bell.
EEV Ltd., Carholme Road, Lincoln, Lincs., LNl ISF.,
5.
Pulsed Power Formulary.
R. J. Adler.
North Star Research Corporation, August 1991.
6.
Transfomiers.
R. Lee.
7.
Technical Formulae
G. and R. Gieck.
Gieck-Verlag, D-8034 Germany.
8.
Farnell Electronic Components.
Canal Road, Leeds, West Yorkshire, April 1994.
PhD Thesis
222
J. W. Bethel
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