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Microwave reflectometry: Observing density layer motion in the Microwave Tokamak Experiment

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Microwave reflectometry: Observing density layer m otion in the
Microwave Tbkamak Experiment
Lopez, P atricia, P h.D .
The University of Michigan, 1993
UMI
300 N. Zeeb Rd.
Ann Arbor, MI 48106
MICROWAVE REFLECTOMETRY:
OBSERVING DENSITY LAYER MOTION IN THE
MICROWAVE TOKAMAK EXPERIMENT
by
Patricia Lopez
A dissertation submitted in partial fulfillment
o f the requirements for the degree of
Doctor o f Philosophy
(Nuclear Engineering)
in The University of Michigan
1993
Doctoral Committee:
Associate Professor Mary L. Brake, Co-Chairman
Professor Ronald M. Gilgenbach, Co-Chairman
Professor Ward D. Getty
Professor Y.Y. Lau
Physicist Thomas A. Casper, Lawrence Livermore
National Laboratory
RULES REGARDING THE USE O r
MICROFILMED DISSERTATIONS
Microfilmed or bound copies of doctoral dissertations submitted
to The University of Michigan end made available throufh University Micro­
films International or The University of Miehifan are open for inspection,
but they ate to be used only with due retard for the rights of the author.
Extensive copyinf of the dissertation or publication of material in excess
of standard copyright limits, whether or not the dissertation has been
copyrighted, must have been approved by the author as well as by the Dean
of the Graduate School. Proper credit must be given to the author if any
material from the dissertation is used in subsequent written or published
work.
For Jesus my Savior,
my Dad,
and my husband, Scott
ACKNOW LEDGEM ENTS
I would like to thank the University of Michigan and the Department of Nuclear
Engineering for taking me back into their graduate program and funding the completion of
this work. I would like to thank my doctoral committee and especially thank Professor
Brake for all her encouragement and help, for reading and providing insight to this work,
and for her support financially and emotionally. Also, Professor Gilgenbach for taking the
time to review this work and discuss specific ideas with me.
Foremost, I would like to thank those at Lawrence Livermore National Laboratory.
I received help and encouragement from the MTX group and especially my boss, Tom
Casper. I appreciate Tom for being part in this doctoral committee and for the efforts he
has made to help me along. Among the MTX group, I would especially like to thank Brad
Rice for his dissertation, completed in September of 1992, it was extremely helpful and is
referenced quite frequently in this thesis. Also, thanks to Bob Stever for constructing the
reflectometer, John Jolly for working with me to align equipment, Reg Wood for analyzing
SPRED data for me, Bill Meyer for keeping my acquisition software running and to Charlie
Lasnier, Jeff Moller, Bob Geer, Max Fenstermacher, all of whom helped describe some
element o f this thesis, thank you. MTX was a very large experiment and 1 could not
possibly list all my co-workers, but thanks for making the MTX tokamak work and for
making my experience at LLNL pleasurable.
Special thanks to my friends, those Ph.D.'s who showed me it could be done, and
those who labored beside me. And to my family, thank you. To my Dad and Mom, who
taught me all thing important, thanks and I love you. And not the least my husband, we
ran the Ph.D. race together, and I am glad we are both victors. Congratulations to you too.
PREFACE
The microwave reflectometer was one o f many diagnostics in the Microwave
Tokamak Experiment (MTX) at Lawrence Livermore National Laboratory (LLNL). MTX
combined a tokamak, originally known as Alcator-C and a free-electron laser (FEL)
developed at LLNL. This project was supported under a U.S. Department of Energy
contract and had collaborations with the Japan Atomic Energy Research Institute (JAERI)
to develop new diagnostics. The basic goals of this facility were to study the absorption of
very high power pulses from the FEL in a high plasma density, high magnetic field
tokamak, and to contribute to the fusion program by using this new electron cyclotron
heating (ECH) source to study heating, energy transport, noninductive current drive, and
MHD control [MTX-89].
Upon arriving at LLNL, a single frequency prototype reflectometer was being
tested and I became overseer of its developm ent. This author was not involved in the
design nor construction of the reflectometer, though Chapter 3 includes an extensively
discussion o f its design. My contributions to the study of reflectometry at MTX included,
testing the prototype and final reflectometer, conducting a computer study o f the transport
of these microwaves into the tokamak, operating the reflectometer on-line during MTX
experimental runs, and acquiring and analyzing the reflectometry data.
The contents o f this thesis include, in Chapter I, an introduction into the use of
reflectometry and background information on tokamaks. Information specific to MTX was
taken from the thesis o f Brad Rice [Ric-92] and other LLNL publications. Chapter II is
based on derivations found in Ginzburg, [Gin-70], and describes the theory of wave
propagation in a plasma. Chapter m contains a description and diagrams of the
reflectometer system provided by R. Stever and tests performed on the instrument by
Stever and myself. The methods used to propagate the microwaves into the tokamak were
tested theoretically using a computer model, MTH code, and experimental tests in sidelab
studies. Chapter IV displays results from the operation o f the reflectometer on the MTX
tokamak. Included are shots verifying the accuracy o f the reflectometer measurement and
its detection of plasma disturbances. And lastly, Chapter V contains an ending discussion
and conclusions.
Patricia Lopez, May 1993.
TABLE OF CONTENTS
D E D IC A T I O N
............................................................................................. ii
A C K N O W L E D G E M E N T S .....................................................................
iii
PREFACE
iv
.....................................................................................................
L IS T O F
F I G U R E S ..................................................................................
viii
L IS T O F
T A B L E S ......................................................................................
xi
CH APTER
I.
IN T R O D U T IO N
1.1
1.2
.................................................................
1
The Use of Reflectometry in Plasma R e s e a rc h
2
1.1.1 Microwave Reflectometry on M T X ...................
2
1.1.2 Other Tokamaks Using Reflectometry ............
3
.................................................
9
1.2.1 The Microwave Tokamak Experiment (MTX) .
9
1.2.2 Turbulence in Tokamaks
14
Tokamak Introduction
...................................
1.2.3 Other Diagnostics on M T X ................................ 20
II.
III.
T H E O R Y O F W AVE P R O PA G A T IO N
IN A PLA SM A ......................................................................
25
2.1
Wave Equations
...........................................................
26
2.2
Phase C o m p a riso n .........................................................
29
2.3
Uses of O-mode and X-mode Waves in Reflectometiy. 35
D E S IG N AND S U P P O R T IN G R E S E A R C H
3.1
.............
39
Design o f the JAERI R eflecto m eter...........................
41
3.1.1 Hardware and Setup in the V a u l t .....................
41
3.1.2 Control Room Processing and Acquisition . . .
47
3.2
Side-lab T e s ts ..................................................................
50
3.3
MTH Code Analysis
56
....................................................
3.3.1 Test Cases A and B
..........................................
59
3.3.2 Results from Case A and B S tu d ie s .................
61
...................
62
The Reflectometer on MTX (no p lasm a).....................
68
3.3.3 Side-lab Results of MTH Studies
3.4
3.4.1 Sensitivity o f the Reflectometer Setup on MTX . 68
3.4.2 Non-Plasma MTX Operation
...........................
69
IV. EXPERIMENTAL R E SU L T S.................................
71
4.1
4.2
4.3
V.
Validity of the Reflectometer ......................................
71
4.1.1 Sensitivity to Cutoff D e n s ity .............................
72
4.1.2 Smooth Plasma Motion .....................................
79
4.1.3 Large Scale Plasma Motion
.............................
80
Disturbances in the MTX T o k a m a k ............................
86
4.2.1 The Detection o f Plasma Oscillations ..............
86
4.2.2 The Detection o f M inor D isru p tio n s................
92
Discussion o f R e s u lts ....................................................
98
DISCUSSION AND CONCLUSIONS ...................
APPENDIX
105
....................................................................................
110
REFERENCES ...............................................................................
126
vii
LIST OF FIGURES
F ig u re
1.1
Overhead photo of the MTX tokamak as shown in the LLNL,
Energy and Technology Review catalogue, July 1990.........................
1
1.2
A schematic of the MTX tokamak cross section. [R ic -9 2 ]..................
11
1.3
An drawing o f the overall MTX facility. [R ic-92]................................
13
1.4
Illustration o f an (a) m=0 sausage instability, (b) m =l kink
instability and (c) m=2 instability on a straight circular cylindrical
plasma are shown without magnetic field lutes from
Bateman, Instabilities, page 6 ................................................................
15
1.5
A Hugiil plot showing the nondisruptive operating regime for
Alcator-C. [Tho-86].................................................................................... 16
1.6
A diagram o f the position loops. [Pri-83] .............................................
2.1
A drawing of the reflectometer optical relay path. The signal
is shown entering vertically through the top B port. The axis
shown represents the electromagnetic field direction of the
propagating signal........................................................................................25
2.2
A picture of the boundary conditions used for the full-wave
solution o f the wave equation................................................................... 32
3.1
The progression of the microwave reflectometer setup..........................40
3.2
The JAERI reflectometer intermediate frequency (IF) assembly
for frequencies 75 to 107 GHz. (from R. S te v e r ) ............................... 42
3.3
The JAERI reflectometer front end assembly for an operating
frequency of 75 to 107 GHz. (from R. Stever) ..................................43
3.4
A schematic of the optical coupler used to split the reflected
signal is shown above along with sidlab tests o f its directivity.
Distances on the coupler diagram are in cm ...........................................45
3.5
The JAERI reflectometer vault and control room setup.........................49
3.6
Power and phase tracking sidelab experimental setup..........................
22
51
3.7
3.8
3.9
3.10
Testing the prescale option of the phase comparator by
tracking phase off a hexagon wheel.........................................................
53
Electric field radiation patterns as measured by the x-y scanner
in the sidelab. The plots shown are behind a slot (3 cm x 12 cm
x 14 cm) at distances of (a) 2 cm, (b) 4 cm and (c) 12 cm ....................
55
The study using the MTH code modeled the transmission of the
reflectometer microwave signal through the top B port of MTX. . . .
58
The radiative contours from the MTH code for the large illumination
case A study. Refer to figure 3.9 for position of stage numbers
(0,0), (0,1), (1,2) and (2,3). Stage (2,3) is at a minor radius of
8.5 cm...........................................................................................................
63
3.11
Vertical and horizontal planes exiting the duct for case A ......................
64
3.12
A comparison study o f the phase front in case A and B.
Results are from the MTH code................................................................
65
The radiative contours from the MTH code for the small
illumination case B study. Refer to figure 3.9 for position of
stage numbers(0,0), (0,1), (1,2) and (2,3). Stage (2,3) is at
a minor radius o f 8.5 cm ............................................................................
66
3.13
3.14
A comparison o f case A and B using the x-y scanner. The E-field
profiles are positioned at (a) 4 cm and (b) 8 cm behind the
sidelab duct.................................................................................................... 67
3.15
Non-plasma reflectometry data obtained during normal MTX
operations....................................................................................................... 70
4.1
Displayed is an idea profile o f the reflectometer phase
measurement through t the shot....................................................................72
4.2
The onset time of the critical density is shown in (a) the
reflectometer plot and (b) the FIR interferometer plot for shots
12353 and 13732 (dashed line in plot b). The phase data in
13732 is offset by +1.2 volt so as not to overlay with 12353...............
74
4.3
The IF power return of a delayed onset shot 13732...............................
77
4.4
Displayed is shot 13982 in which the critical density layer is
only present for an intermediate time between 0.033 to 0.217 sec. . .
4.5
4 .6
78
Shot 11864, comparison o f radial motion as measured by the
(a) FIR interferometer and (b) reflectometer........................................
80
A comparison of (a) reflectometry, (b) and (d) position loop,
and (c) line density data for shot 11858. This comparison
of large plasma oscillation favorably shows the reflectometer's
sensitivity to plasma motion.......................................................................
83
ix
4.7
4.8
4.9
A comparison of (a) reflectometry, (b) and (d) position loop,
and (c) interferometer line density data for shot 11859.......................
84
A comparison of (a) reflectometry, (b) and (d) position loop,
and (c)interferometer line density data for shot 11860........................
85
A comparison of the (a) reflectometry, (b) visible bremsstrahlung
and (c) an interferometer line density for shot 12416. The
signal VBREM_2 and FIR[13] are at a minor radius of 10.5
and 10.25 cm, positioned on the inside o f the tokamak......................
87
4.10
A display o f FIR interferometer line density data for shot 12416. . . .
89
4.11
Shot 12353 shows a burst 20 ms before the plasma terminates.
Shown is data from (a) the soft x-ray, (b) the reflectometer and
(c) the visible bremsstrahlung diagnostics. Reflectometry data
was acquired at 200 kHz........................................................................... 91
4.12
Shot 11885 displays multiple disruptions in a shot that lasts
330 ms. For comparison plotted are (a) the soft x-ray, (b) the
reflectometer, (c) the visible bremsstrahlung and (d) the H R
interferometer line density........................................................................
95
4.13
Shot 11873 detects a disruption at 190 ms which stabilizes the
plasma. Shown are (a) the soft x-ray, (b) the reflectometer, (c)
the visible bremsstrahlung and (d) an FIR interferometer line
density............................................................................................................96
4.13
Shot 13694 displays a major disruption which terminates the
plasma at approximately 220 ms. Plotted are (a) the soft x-ray,
(b) the reflectometer, (c) the visible bremsstrahlung and (d) the
MHD position loops....................................................................................97
4.15
A shot review o f shot 12416......................................................................... 100
4 .16
A shot review of shot 12353...................................................................... 101
4.17
A shot review of shot 11885...................................................................... 102
4.18
A shot review of shot 11873...................................................................... 103
4.19
A shot review of shot 13694...................................................................... 105
A .l
These files are input, i-files, for the MTH code. The file
shown in (a) creates a rectangular waveguide source and (b)
propagating that source a specified distance..........................................
116
The flies shown are in (a) an i-file to propagate a plane
through a duct and in (b) an example ispecs file for the
postprocessor..............................................................................................
117
A.2
x
LIST OF TABLES
Table
1.1
Range of operating parameters for MTX. [Ric-92]...............................
12
2.1
O-mode and X-mode characteristics compiled from Nazikian and
Biglow...........................................................................................................
36
3.1
Power returns in the sidelab setup............................................................. 52
3.2
Power return through the reflectometer setup......................................... 68
4.1
A list o f values pertaining to figure 4.4 for shot 13982. The
cutoff density, nco, is equal to 0.75 xlO20 n r 3.................................... 78
A .l
Compile and run commands......................................................................
112
A.2
Read statements in the MTH code for the i-file......................................
114
CHAPTER I
INTRODUCTION
To study plasmas many imaginative diagnostics have been implemented. Lately
renewed interest in reflectometry has been shown on such tokamaks as DIXI-D (San Diego,
CA), JET (Culham, England), TEXT (Austin, TX), TFTR (Princeton, NJ), and our MTX
(Livermore, CA), plus many others. Among the reasons reflectometry is popular are:
(1) its ability to provide a local density measurement, as opposed to a line averaged
measurement, (2) it can probe edge plasmas, (3) it does not require a large window but
only one small port, and (4) in comparison to other diagnostics, it is straightforward to
analyze since no inversion techniques are required in O-mode. The physical properties of
Figure 1.1:
Overhead photo of the MTX tokamak as shown in the
LLNL, Energy and Technology Review catalogue,
July 1990.
1
2
the plasma that may be studied with a reflectometer are plasma fluctuations, density
profiles, magnetic profiles and edge plasmas.
The experimental setup, reflectometer operation, and research presented in this
thesis were conducted at Lawrence Livermore National Laboratory (LLNL) on the
Microwave Tokamak Experiment (MTX). This tokamak produces high plasma densities
and magnetic fields and was used to study new means of plasma heating. Unfortunately
MTX operations ended August 1992. The reflectometer installed late in 1990 operated
during 3 experimental runs, for a period o f 8 months, on MTX and was designed to study
density fluctuations. In the following sections o f this chapter, section 1.1 will introduce
the reflectometer, funded in pan by the Japanese Atomic Energy Research Institute (JAERI)
and used on MTX, and in general mention other work in reflectometry. In section 1.2, the
MTX tokamak and several diagnostics used in comparison with the reflectometer will be
described. Also, there is a general presentation on tokamak turbulence in section 1.2.
1.1
The Use o f Reflectometry in Plasma Research
1 . 1.1 Microwave Reflectometry on MTX
Reflectometry, originally pioneered to study the stratified ionosphere using the
reflection o f radiowaves [Pit-59], is used to study plasmas by use o f microwaves. The
reflectometer for the MTX tokamak experiment operates in ordinary mode, O-mode, with a
variable frequency range o f 75 to 110 GHz. The microwaves reflect off the plasma at a
critical density and, for this frequency range, the cutoff density is between 0.7 and 1.5 x
1020 n r 3. By measuring the travel time, phase, and amplitude o f the microwaves,
information about the plasma can be determined. The quantity measured in our
experiments is the change in phase of the reflected signal. This phase change is equivalent
to a change in the reflective region of the plasma and implies motion of the density layer.
3
This measurement therefore monitors the motion of a particular density layer or local
fluctuations, at cutoff layers in excess of 0.7 xlO20 n r 3. Fluctuation measurements are
important to the fusion program since they provide information on anomalous transport and
turbulence. Insight into the causes o f this enhanced transport, responsible for decreased
confinement time o f the plasma, can be gained by using reflectometry. By monitoring and
gaining a better understanding of transport mechanisms and turbulence in the tokamak,
better operation regimes and techniques to increase the confinement time can be determined.
Therefore, the main purpose of the reflectometer was to study density fluctuations.
The reflectometer was developed at LLNL with the assistance of the Japan Atomic
Energy Research Institute (JAERI). The experimental setup of this reflectometer was
unique in its use o f an optical relay system to transport microwaves from the transceiver
located in a low magnetic field region near the tokamak and to provide beam focusing
through the port. An optical splitter/coupler provided approximately 40 dB separation
between the transmit and receive signals. Our design provided for two independent,
continuously variable transceivers for radial correlation reflectometry measurements. Due
to the of MTX operations, this goal for the reflectometer system was not reached.
Data from the reflectometer will be presented in this work and compared with
density profiles provided by a 15 channel far-infrared (FIR) interferometry system,
temperature fluctuations noted by soft x-rays, bremsstrahlung radiation and impurity
fluctuations from a visible bremsstrahlung diagnostic, and bulk plasma motion as measured
by position loops. These additional diagnostics are only a few of the instruments operating
on the MTX tokamak and they are described in section 1.2.3.
1. 1.2 Other Tokamaks Using Reflectometry
At present there is great interest in the field of reflectometry. Progress in the early
1980's in the advancements in broadband microwave components and promotion o f swept
frequency microwave sources, has led to new uses for the reflectometer. The following is
4
a synopsis o f some work, past and present, that has been instrumental in the field o f
reflectometry.
Density Profiles
Cano and Cavallo [Can-80] proposed the application of a swept frequency radar in
reflectometry to obtain a plasma density profile in large tokamaks. The concept is simple;
when the frequency is changed, the cutoff density from which reflection occurs also
changes. The first step is to sweep the incident wave frequency and measure the derivative
o f the phase shift with respect to the wave frequency, dd>/dco. A change in phase is
equivalent to a change in position and a change in frequency indicates a change in critical
density; therefore dO/dcu is directly related to dr/dne. The position o f the reflective layer in
the plasma using ordinary mode transmission is obtained by integrating the derivative,
d<J>/dto, multiplied by a propagation term and the index o f refraction [Sim-85],
( 1. 1)
where the applied frequency to ranges from zero to the corresponding cutoff frequency
cOpg. Density profile measurements using the reflectometer have been active on TFR [Sim85], Petula-B [Bot-86], JET [Sip-90] and upcoming on Alcator C-Mod [Ste-90], As stated
by Simonet,
"The advantage of reflectometry compared with interferometry is that the farmer
gives local density measurements, does not need Abel inversion and any
assumptions about the plasma cross section. Another advantage is the need for
only modest access to the plasma."
Reflectometry does have the advantages stated above except when correcting for changes in
the density profile during the sweep. In this case, an Abel inversion is used by Sips [Sip90] to correct for this delay.
5
Fluctuation Studies
Reflectometry has most commonly been used for fluctuation studies. Research in
this area dates back to Mazzucato's successful experiments on the ATC in 1975 [Maz-75],
When the source frequency is held constant, the reflectometer will measure changes in the
phase difference resulting from variations in the electron density. Work by Mazzucato,
using a fixed frequency reflectometer, first yielded a frequency spectrum of density
fluctuations in 1975. Further work by Mazzucato and the TFR group, [TFR-85], revealed
a decrease in the frequency o f the spectrum by moving the reflecting layer towards the
plasma center. This result was expected from drift wave theory. The TFR group also
measured large scale MHD instability modes which were localized on resonant magnetic
surfaces of the reflective layer and thus precisely located magnetic modes in the plasma.
On DIII-D, Doyle and his group, using two reflectometers, a 7 discrete channel Omode unit and a tunable X-mode unit for fluctuation measurements, have determined that
high frequency, > 50 kHz, density fluctuation are invariably suppressed at the L-H
transition near the edge of the plasma [Doy-90]. This L-H transition in tokamaks involves
a fast change, an improvement, in the particle and electron energy confinement and an
increase in edge electron and ion temperature. Previous measurements during this
transition on ASDEX indicated thru at high heating power both the ion and electron
collisionality parameters at the plasma edge were close to one in the L-phase and fell below
one in the H-phase [Wag-85]. Thus, the reflectometer may have measured this decrease in
collisionality. In the near future, this group is planning to add a second tunable X-mode
reflectometer for correlation studies [Doy-90].
The study of density fluctuations is an integral part of correlation reflectometry and
particle transport theory. Correlation reflectometry is important because it investigates
global mode versus localized density fluctuations. Groups involved in these areas of
research include those working on correlation studies at ATF [Han-90] and at 'I F I K [Naz92], and performing transport studies, those at JET [Sip-90].
6
Correlation Studies
Correlation reflectometry is accomplished with two reflectometers that study the
coherence between closely positioned reflective layers. The TFTR group [Naz-92] using
X-mode reflectometry have noted,
*
"From a plasma cutoff in the core region (r/a-0.2) o f an ohmic discharge
within the sawtooth region, several highly coherent spikes at low
frequencies (<10 kHz) indicate regular MHD activity, whereas a previously
unobserved quasi-coherent feature oscillating at "SO kHz is also evident
This high frequency feature is commonly observed on the multichannel
reflectometer system in the core region o f ohmic plasmas."
*
There is an "observed trend towards shorter correlation lengths with
increasing minor radius. The data suggests that the turbulent correlation
length may indeed depend on the local density scale length and that this
scaling may be similar for both ohmic and beam heated plasm a"
Hanson performing two-frequency correlation reflectometry on ATF found radial
correlation lengths from 0.5 to 1 cm in ECH plasmas [Han-90]. At some frequencies the
correlation length was up to 3 cm. In plasma with neutral beam injection (NBI), the radial
correlation lengths in the edge region were found to be 0.1 - 0.2 cm. This supports the
TFTR group’s measurements of decreasing correlation lengths with increasing minor
radius. The TFTR group noted that very short coherence lengths are typical of edge plasma
measurements and stated the frequency spectra of the scattered signal from the plasma
edge was typically broad for both NBI and ECH plasmas. ATF found a highly coherent
frequency structure in ECH plasma in the edge gradient. This structure has a correlation
length approximately equal to the gradient length.
Transport Studies
Using a multichannel reflectometer or a high resolution multi-chord interferometer,
density pulses can be measured to deduce particle transport. Particle transport, unlike
7
energy transport which is measured from election temperature fluctuations for which there
are several diagnostics, has been immeasurable until recent advancements in reflectometry
and interferometry. Using such a multichannel reflectometer, density pulses propagating
inward have been observed in JET [Sip-89]. The measurements were made in the
horizontal midplane o f the tokamak in the region 0.5 < r/a < 1.0 on the outboard side o f the
plasma. A heat pulse, measured by monitoring the changes in electron temperature with a
12 channel ECE polychromator, was observed to reach the limiter in advance of the density
pulse and generated an inward propagating density pulse caused by an increase in the
recycling at the edge. The perturbation of the electron density evolved much slower than a
perturbation of the election temperature. Also observed was a small temporary decrease in
local density when the heat pulse passed by. Values of the particle diffusion coefficient,
DltK, from density perturbations induced using different methods were also determined
using reflectometry. This important aspect of thermonuclear research is aimed at
attempting to understand anomalous transport and improve particle confinement.
Precision of Reflectometry Measurement
Also a subject o f interest and continual study are the principles and plausible
limitations in reflectometry. The ability to obtain a spatially localized measurement is not
well understood. It is known that wave scattering by density fluctuations is enhanced if
the density fluctuations are localized near the reflective layer. In a side lab experiment
Baang [Baa-90] observed that the reflectometer signal was highly spatially localized in the
plasma. However in another paper, [Bre-91], a one dimensional full wave calculation was
used to investigate phase fluctuation measurements in reflectometry and how they relate to
localized density fluctuations in typical tokamak experiments. The following notes were
made by Bretz,
8
•
Drift waves and the reflected phase and amplitude depend on the density
gradient scale length, Lfl=nc/(dne/dr). From reflected waves off density
fluctuations with magnitude and frequencies typical of drift waves, the
surface appears rough and amplitude variations are always large.
•
"Density perturbations with wavelengths near the free space wavelength of
the probing beam are not resolved."
•
For small amplitude waves, numerical solutions o f the one-dimensional full
wave equation for the propagation near cutoff frequencies showed,
1.
For density perturbations with wavelengths near the density scale
length, (A~Ln), the phase change can be interpreted near the cutoff
layer.
2.
The amplitude of the phase response falls substantially as the
fluctuation wavelength approaches the free space wavelength,
( A—
The location o f reflection moves out in front o f the cutoff
layer following the wave matching condition, kA = 2,n(x)k0.
3.
•
Resolution o f correlation lengths less than 4 X0 are not possible.
Because poloidally propagating waves cause significant angular scattering
of the reflected beam, even reflectometer systems using well collimated
antenna patterns to minimize the reflection spot size can experience rapid
amplitude changes in the reflected beam and difficulty in tracking the phase.
It is recommended the spot size be larger than 1/2 the poloidal wavelength,
thus putting on upper limit on the range o f kg which can contribute to the
fluctuation spectrum.
Bretz found that if the density perturbation wavelength, A, is comparable to the probe
wavelength, A*,, the reflectometry measurement can not resolve drift waves and thus is not
a localized measurement, that is, maximum phase change takes place far from the cutoff,
for small amplitude waves. He tries to make the point that localized measurements are not
certain and that a small spot size can lead to difficulty in tracking the phase. His statement
concerning correlation lengths dispute measurements which were previously listed in this
section. Correlation lengths of less than 3 cm with the reflectometry system on ATF, and 1
cm on TFTR, are considered by Bretz to be impossible. However, correlation
9
measurements in the millimeter range were noted by both groups. Thus, overall, his
conclusions convey the need for future research to clarify these conflicting points.
1.2
Tokamak Introduction
In the fall of 1991 the Joint European Toms (JET) reported narrowing the gap
towards reaching breakeven, a "Major step toward their dream of tapping a limitless supply
of cheap and comparatively safe energy through nuclear fusion (The Detroit News)."
Fusion, which has often been described as "an inexhaustible resource o f energy", has been
an important area o f research for almost 40 years. The first series of tokamak experiment
occurred during the 1960's at the Kurchatov Institute, USSR.
In the study o f fusion there are two rather different approaches in containing the
fusion process, one involves electromagnetic confinement and the other compression by
laser beams or by beams of charged particles. Since the ionized fuel is very hot, so as to
overcome coulomb repulsion, it cannot be easily confined. Because the particles are
charged however, electromagnetics can be used for confinement. At present both
confinement methods are active areas of research, though noting recent events at JET,
electromagnetic confinement using a tokamak appears more readily feasible.
An outline o f section 1.2 is as follows: section 1.2.1 gives a description of the
Microwave Tokamak Experiment, section 1.2.2 presents general information on turbulence
observed in tokamaks, and section 1.2.3 describes other diagnostics on MTX, which will
be used in support of reflectometry measurements.
1.2.1 The Microwave Tokamak Experiment (MTX)
The primary aim of the Microwave Tokamak Experiment was to combine a tokamak
moved from MIT, previously known as A lea tor-C, and a firee-electron laser (FEL) to
10
investigate plasma heating and confinement [Ric-92]. A t the Massachusetts Institute of
Technology (MIT), a successful investigation o f confinement scaling laws for high density,
circular, ohmic plasmas using Alcator-C was conducted in the mid 1980's. Modifications
made to Alcator-C by the MTX group included additional heating mechanisms and various
new diagnostics. The original goal for MTX of studying the nonlinear absorption o f
extremely high-power microwaves (gigawatts) produced by the FEL broadened to include
the study o f electron cyclotron heating (ECH) by absorption of long-pulsed gyrotron
microwaves at a few hundred kilowatts. Also investigated by MTX has been pellet
injection, transport, MHD fluctuations, sawtooth oscillations and disruptions [Ric-92].
A brief physical description of the MTX tokamak as described by Rice [Ric-92] is
as follows. The vacuum vessel of the tokamak is 40 cm in diameter and is constructed
from sections o f stainless-steel bellows. It is supported by three legs and elevated to a
height of 3 meters as measured to the machine's center line. The entire vacuum vessel and
magnet set is enclosed within a dewar of liquid nitrogen to provide magnet cooling between
shots and reduce resistivity. The toroidal field coils are o f a copper Bitter plate construction
producing fields to 12 Telsa with less than a 2% ripple. Ohmic heating is provided with
Copper air-core transformers that produce a loop voltage of about 2V for 0.4 seconds.
There are also both vertical and horizontal field coils used for positioning o f the plasma.
Figure 1.2 is a schematic o f the tokamak cross section and shows the position o f these
coils.
There are 18 access ports into the tokamak, six ports each on the top, bottom and
side of the machine. Note that there is no access to the inner edge of the plasma and that
the vertical views are obstructed by two or three strengthening ribs. The width of the
diagnostic port between toroidal field coils is very narrow in order to minimize toroidal
magnetic field ripples. Because of this limited port access, which is a common hindrance
in most tokamaks, diagnostics are required to be made as compact as possible to share port
space and be flexible enough to move to other ports as experiments change.
11
OH-1
OH-Z
IHI
CRYOSTAT
IHI
OH-Z
HF OH-3
-O N E METER
Figure 1.2:
A schematic of the M TX tokamak cross section. [R ic-92]
The fusion reaction is fueled by either pulsed gas or pellet injection. MTX used
either deuterium or hydrogen as its fuel and generated plasmas with densities >102° n r 3 by
passing a 100 - 350 kA electron current through the low gas pressure fuel in the toroidal
vacuum chamber. Using 140 GHz, electron-cyclotron heating (ECH) is achieved at the
midplane, at a toroidal field o f 5 Telsa. A typical plasma current of 350 kA gives an ohmic
power o f 700 kW. The plasma is spatially limited by a pair o f limiters (molybdenum rings)
that set the minor radius to 16.5 cm and the major radius to 64 cm. Basic MTX tokamak
parameters are listed in Table 1.1.
The control and diagnostics room for this experiment is located on the second floor
just north of the vault area which houses the tokamak. Terminals, desktop computers and
12
CAMAC hardware are located in this area with the main data acquisition, VAX computers,
located elsewhere.
The free-electron laser was developed at LLNL. It is located in an adjacent building
but connects to the tokamak by a 30 m, windowless, quasi-optical transmission system. It
generates short pulses o f gigawatt-level, millimeter-wavelength radiation that interacts
resonantly with the electrons in the plasma at their cyclotron frequency. Linear induction
accelerator modules are used to accelerate electrons up to energies o f 5 - 1 0 MeV. This
beam is injected into an alternating magnetic field that "wiggles" the beam in resonance with
the wave to be amplified. This FEL technology provides high microwave power on the
order of several GW at 140 GHz for short pulses of 20 - 50 ns. Although a high average
power o f up to 2 MW can be obtained with a continuous pulse train, only single-pulse
experiments have been performed.
A 140 GHz gyration, built by Van an, was used as a driver for the FEL or as a
direct long-pulse heating source for MTX. The microwave transmission line was
configured to accommodate either option. The design parameters for the gyrotron are 400
kW output for pulse lengths up to 0.5 second, however mode conversion losses limit the
power injected into the tokamak to 100 - 200 kW for pulse lengths o f 10 -1 0 0 ms.
PA RA M ETERS
VALUES
Major Radius
R
0.64 m
Minor Radius
a
0.165 m
Toroidal Magnetic Field
Bt
5 - 1 2 Tesla
Plasma Current
Id
150 - 400 kA
Density
0 .7 - 5 .0 x 102°m -3
Pulse Length
0.5 sec
Electron Temperature
T?
0.5 - 2.0 keV
Ion Temperature
Ti
'tE
0.5 - 1.5 keV
Confinement Time
Table 1.1:
5 - 2 5 msec
Range of operating parameters for MTX. [Ric-92]
13
Computer consoles
In control room
Beamline of
microwave
system
Mirrors
MFTF
vault
Mirrors
Shield
wall
Wiggler
Experimental Test
Accelerator II
Microwave Tokamak
Experiment (MTX)
A ccess ports
Incoming
beam
Plasma
Tokamak
Figure 1.3:
A drawing of the overall MTX facility. [Ric-92]
14
1.2.2 Turbulence in Tokamaks
Macroscopic magnetohydrodynamic (MHD) instabilities are long wavelength
modes (^~a) driven by destabilizing forces arising from current gradients and pressure
gradients in the plasma. Shorter wavelength (velocity space driven) instabilities are called
microinstabilities and readers interested in this topic are referred to [Lew-85]. At least 5
types o f large scale instabilities have been observed in tokamaks though there is an infinite
spectrum of possible unstable modes, each member being characterized by its mode
number. In the case of a circular, large aspect ratio tokamak, modes take the form
exp[i(m9 - n<|>)] where m and n are the poloidal and toroidal mode numbers.
Early tokamak experiments had problems with the plasma spontaneously pinching
itself off, called the m = 0 sausage instability. However the m = 0 sausage, and m = 1
kink, instabilities were found to be suppressed by a strong toroidal magnetic field (B^. A
modest longitudinal magnetic field, comparable to poloidal magnetic field (Bp) around the
plasma column, reduced the m = 0 instability but not the kink instability which twists the
plasma column into a helical shape like a corkscrew. Figure 1.4 illustrates these two
instabilities. When any part o f the plasma column is bent, Bp, on the inner edge of the
plasma bend, becomes stronger than Bp on the outer edge resulting in an increase in the
magnetic pressure that further bends the column and drives the plasma to the wall. To
stabilize the m = 1 instability, "the toroidal magnetic field must be made strong and plasma
column fat so no part o f the magnetic field between the plasma and the wall closes upon
itself along the length of the plasma column"; this is known as the Kruskal-Shafranov
condition [Bat-78]. But even with this large Bt, there are three principal instabilities called
Mimov oscillations, sawteeth oscillations, and disruptions which beset tokamaks today.
Wesson [Wes-87] and Bateman [Bat-78] describe possible mechanisms behind these
instabilities. The causes for Mimov oscillations are linked to magnetic fluctuations.
Sawteeth oscillations, visible from soft x-rays, are believed to be an m = 1 instability
occurring in the central region o f the plasma. Disruptions are thought to be associated with
15
Figure 1.4:
Illustrations of an (a) m=0 sausage instability, (b) m=l
kink instability and (c) m=2 instability on a straight
circular cylindrical plasma are shown without magnetic
field lines from Bateman, Instabilities, page 6.
a sequence o f MHD instabilities, however, the disruption event is only partially
understood.
Resistive instabilities and particularly tearing modes are generally associated with
the formation o f magnetic islands which change the magnetic topology at surfaces with
rational values o f q. Original work in this area was done by Furth, Killen, and Rosenbluth
[Fur-63]. Since the plasma is not perfectly conducting, island formation will occur to
some extent in all MHD instabilities. When the simple nesting o f the toroidal surfaces are
broken, magnetic islands appear in the plasma usually in a nonlinear fashion and change
the magnetic fields substantially. Tearing mode growth is limited by resistive diffusion at
the resonant surface and thus the width of the magnetic island is proportional to B T1^ . A
key parameter in tearing mode theory is the jum p in the radial magnetic field, A, across the
resistive layer. The growth rate o f the magnetic island is proportional to this parameter,
16
A4/5 [Fur-63], When islands o f different modes interact, magnetic surfaces are destroyed.
The magnetic field lines no longer map out a surface but instead follow a space-filling
trajectory. Such fields are said to be ergodic, clearly changing the confinement properties
o f the magnetic field. The strongest instabilities usually occur for the m = 2 mode.
General operating boundaries of tokamaks include the Kruskal-Shafranov,
Hugill/Greenwald and the Grantz MHD limits. A typical plot of the MTX operating regime
is shown in figure 1.5. The Kruskal-Shafranov limit for stability, introduced previously,
is defined as qa < 1. This is a fundamental limit for the maximum plasma current at a given
toroidal field to avoid kink instabilities. In practice modem tokamaks rarely operate at qa <
2.5 (q at the limiter). The Hugill limit is found by plotting the Murakami number (neR/Bt)
versus 1/q. Operating limits determined from the boundaries o f the Hugill plot in [Gre-88]
indicate, (1) there is a density limit proportional to the plasma current and (2) there is the
superposition o f a limit on q, q > 2. For the MTX tokamak, the Hugill limit is ne=1.6B/qR
xlO20 n r 3, with R in meters and B in Telsa. Granetz in 1982 while operating Alcator-C,
0 .5
O G k fueled
★ Pellet fueled
0
0
2
3
4
5
6
n e R /B
F ig u re 1.5:
A H ugill p lo t show ing th e n o n d isru p tiv e o p e ra tin g regim e
fo r A lcato r-C . [Tho-86]
17
published evidence for a density limit at which MHD activity occurs and predicted
disruptions at a 40% higher density [Gra-82], However on MTX, Makowski [Hoo-90]
found this activity observed by Grantez only occurs on the inside major radius o f the
discharge, and thus is unlikely to predict MHD activity.
A few o f the instabilities or disturbances which will be referred to later in this thesis
are listed in more detail below. However as a general comment; it is commonly thought
that through proper magnetic field line curvature and shaping of pressure and current
profiles, macroscopic instabilities can be controlled.
Disruptions
Disruptions are identified by a rapid decrease in ohmic current and are generally
agreed to be the most dangerous instability in tokamaks. A major disruption terminates the
plasma. "As early as 1963, disruption instabilities were observed as an abrupt and
generally unpredictable expansion of the plasma column accompanied by a large negative
voltage spike kicking back against the transformer." [Bat-78]
Disruptions occur over a wide range of conditions and are a complex phenomenon
most likely involving a sequence o f only partially understood events. Generally it is
thought m = 2 tearing modes are substantially involved. Observations and possible
explanations drawn from [Bat-78] and [Wes-87] are listed below,
•
"Helical distortions of the plasma column are observed to build up and lock
together just before each disruption, however this cannot be used as a
warning since the same rough pattern frequently occurs without a
disruption". [Bat-78]
•
"Along the q > 2 (Hugill) disruption limit, it is believed that as the q = 2
surface gets pushed outward in radius, the m = 2 island begins to interact
with the limiter, or the cold edge plasma thus causing the disruption."
[Ric-92] and rWes-87]
18
•
"The overlap of the m = 2 with the m = 1 or m = 3 islands could be
involved in causing the disruption. Even a modest impurity increase at the
plasma center which could alter the resistivity profile producing flat or
hollow current density profiles may be a possible mechanism." [Ric-92] and
[Wes-87]
Other phenomenon noted in Bateman coiresponding to disruptions include its effect
on hard x-rays which abruptly disappear (probably due to runaway electron losses) and
there is some evidence that impurities are suddenly lost. The electron temperature and
plasma current are observed to suddenly expand in minor radius, and the plasma column
suddenly shifts inward in major radius.
The following information on MTX disruption events is from a report by Bick
Hooper and Mike Makowski [H00-90). During normal MTX operations it was observed
that most of the disruptions occur away from the density limit boundaries, little MHD
activity was observed, and some disruptions appeared to be associated with bursts of
metallic impurities . There was data indicating that brief bursts of metallic impurities are the
cause of some disruptions. It is plausible that a number o f the disruptions are due to
impurities presumably arising from spades or other limiter effects. The disruptive process
was generally independent o f the tokamak operating parameters and MHD activity before
disruptions had various forms. The strongest MHD activity was seen at low q (< 3.5) but
disruptions without precursor activity were seen at all values of q. Disruptive shots
generally show no significant MHD when the disruption occurred during the steady state
part of the discharge, though it is often observed during the buildup. The Hugill (density)
limit was generally not disruptive but rather behaved so as to reduce confinement.
Following an initial disruption, the current channel usually reforms at a reduced major
radius and the plasma reheats, implying that the flux surfaces have closed. The new
configuration is unstable, however, and the channel once more disrupts, sometimes leading
to a plasma loss.
19
Plasma Oscillations
Two specific examples of plasma oscillations in the MTX tokamak arise from
MARFES and bursts. A MARFE, an acronym far multifaceted asymmetric radiation from
the edge, is a tokamak edge phenomenon first noted on Alcator-C in 1984 [Lip-84]. It is
characterized by a large amount of poloidally asymmetric radiation, an increase in density
and density fluctuations, and a decrease in temperature. The MARFE is a cool high density
region located at the smaller major radius periphery of the plasma. The affected region is
typically above the midplane, extending poloidally for about 30* and toroidally 360*. A
simple transport model in [Lip-84] was used to show the marfe may be the manifestation of
a thermal instability.
Bursts presumably arise from sparks or flakes from the limiters or from the walls of
the vacuum chamber. The burst is visible horn soft x-rays and metal line radiation
measurements, and sometimes from visible bremsstrahlung. Impurity radiation, bursts of
impurities, are measured also by the SPRED (Spectrometer Recording Extended Domain)
diagnostic. After a burst, the discharge recovers unaffected, however, a subset o f the
bursts are likely associated with disruptive discharges.
Sawteeth Oscillations
Oscillations of the electron temperature inside the q =1 surface are what is described
by the term "sawteeth". They are observed during normal tokamak operations and
considered benign since they simply redistribute heat along the q =1 surface, flatten the
electron temperature and plasma current profiles, but are not detrimental to overall plasma
confinement. Soft x-ray emission from the center of the plasma during sawteeth
oscillations show a gradual rise and subsequent crash of the electron temperature inside the
q =1 surface. Outside the q =1 surface sawteeth are inverted. This means that a sudden
fall in temperature around the center of the plasma is associated with an increase in
temperature in the outer regions. The original sawtooth model is the so called "magnetic
20
reconnection” model proposed by Kadomtsev [Kad-75]. In this model the cycle begins
with q > 1 on axis, then the temperature on axis increases due to ohmic heating and q0
drops below one which triggers the m =1 mode. Growth o f an m =1 island is given to be
responsible for the sawtooth crash.
1.2.3 Other Diagnostics on MTX
There are over 20 diagnostics installed on the MTX tokamak in order to measure
plasma parameters during the discharge. Some diagnostic techniques which are relevant to
this work are discussed below. Two instruments in this group are the far-infrared (FIR)
interferometer which measures the radial plasma density profile, and the position loops
which measure the bulk motion o f the plasma. These are primarily referenced in this work
to verify reflectometry measurements. The other diagnostic that will be mentioned
measures radiation emitted from the plasma. It will be used in Chapter 4 to confirm the
existence of disturbances noted by the reflectometer. The reflectometer, the principal
diagnostic used in this thesis, will be described in Chapter 3.
FIR Interferometer
The Far-Infrared Interferometer was built in collaboration with the plasma physics
division o f UCLA [Cha-70]. It uses a CC>2 pumped dual-barrel FIR heterodyne laser
custom built for LLNL by the United Technologies Research Center (UTRC). A special
effort was made by the manufacturer to provide reliable power and frequency locking
electronics. The laser gas, usually difloro me thane, is pumped by the CO 2 laser, tuned in
the cavity to generate a 1 MHz beat frequency, and operates at 184 micrometers. Quite
stringent criteria were used in the choice of the comer-cube GaAs Schottky detectors. They
were chosen for their good noise to power ratio (NEP) o f 10*10 W/Hz*1/2, excellent signal
amplitude from intermediate frequencies (IF) into the MHz range, and because of their
21
ability to be packed into an array. The only problem encountered with this setup is beam
refraction, however this is only an issue for densities above 3 x 1020 m '3.
The FIR interferometer has 15 channels with chord spacing o f 1.5 cm. In terms of
the minor radius, the chord positions in centimeters are listed in the following array,
[16.75, 15.25, 13.75, 12.25, 10.75, 9.25, 4.75, 3.25, 1.75, 0.25, -1.25, -2.75, -8.75,
-10.25, -11.75]. These chords transverse the plasma vertically and therefore produce a
horizontal plasma density profile. The quantity measured by the interferometer is phase
change which corresponds to a line-integrated density. The optical path length o f the
waves change in response to traveling through the plasma. The magnitude of this change is
a measure of the plasma density along that line. Each chord measures a line density or
phase shift and an Abel inversion routine is then used to determine the plasma profile.
Azimuthal symmetry is assumed. The signal denoted, "FIR_NBAR", which will be
referred to in this work, is the center line chord, at r = 0.25 cm, scaled to give a line
averaged density assuming a parabolic profile. The acquisition speed of the FIR
interferometer was set at 10 kHz.
Position Loops
MTX is equipped with cosine and saddle loops that can be used to obtain the
plasma position. These loops are part of the original MIT Alcator -C tokamak. They are
constructed using motor wire wound on a thin G-10 form that is wrapped around the
outside o f the vacuum vessel (but inside the TF coils) at a radius o f approximately 20 cm as
shown in figure 1.6. The signals from these loops are processed in analog circuitry to
provide a plasma position feedback signal as discussed in [Pri-83].
The cosine and saddle loop voltage are equal to the time rate of change of the
magnetic flux passing through the loop, Vioop= d<p/dt. Combining the flux equations for
each loop, cosine and saddle, eliminates unwanted terms and provides an expression
22
Saddle c o ll
(on edges, c ro s s e s a t c e n te r)
Figure 1.6:
A diagram of the position loops. [Pri-83]
for the plasma shift, 5x
8x = —
Zip
COS
'C O S
1 —“ 'T
b
_
F $ad , a
1 + -TT
b“
sad
where a is the plasma radius, b is the loop radius,
b2 - a 2
+■
2R
ln( t )
and
4R
(1.2.a)
are the flux through the
cosine and saddle loops and Q os ar|d Q ad are geometric constants defined as
.
Ceos =
005
V3H0NA
nb
and
jcb
(1.2.b)
Here N equals the turn s/c m , A die area per turn for the cosine coil, and t equals the loop
width o f the saddle coil. The terms on the right of equation (1.2.a) equal a constant of
about one cm for MTX. The displacement 8x represents the offset of the center of the
outermost flux surface (surface in contact with the limiter) relative to the center of the
limiter ring. Positive 5x is in the direction of R.
There are several signal loop measurements which can be plotted. LOOP_POS
_HORZ and LOOP_POS_VERT are signals acquired in the vault, digitized directly, then
integrated and processed in software. CNTLP_POS_HORJZ, where CNTLP refers to
"control” room, is the output of a hardware integrator. This signal from the vault is
23
transmitted over analog fiber-optic links into a crate in the control room and fed into a
hardware integrator for real-time position control of the plasma and displayed as
CNTLP_POS_HORIZ.
Visible Bremsstrahlung
Tokamak plasmas usually contain various impurity ions with much higher atomic
numbers, Z, than the fuel. In a hot plasma, electron-ion collisions give rise to
electromagnetic emission called bremsstrahlung radiation. Typical electron-hydrogen
collisions, where temperatures in a tokamak are in the keV range, result in bremsstrahlung
radiation power in the soft x-ray region. In the visible region, approximately 4000 to 7000
A, electromagnetic emission most likely corresponds to forbidden transitions o f highly
charged ions in their ground state configuration and from impurity influxes.
The layout o f the visible bremsstrahlung diagnostic on MTX includes 15 vertically
viewing chords extending in minor radius from -12.6 to 16.8 cm, with uniform spacing of
2.1 cm. The actual geometry is somewhat complicated. Simply put, the 15 channels are
divided into 3 fan-shaped groups of 5. Each group is established in a separate port to view
vertically.
What is measured by the visible bremsstrahlung diagnostic is the following,
Vbrem = J ng^gfC dl
(1.3)
where Zeff is the effective atomic number, X(niZj2)/£(njZj), aud ne and Tc the electron
density and temperature. This measurement can then be used in various ways, to measure
impurity information through Zeff or to measure temperature or density fluctuations.
The visible bremsstrahlung measurement can be used to estimate the amount of
metal impurities entering the discharge by assuming the temperature and density are
constant and using the following formula,
24
AZcfl/Zeff = AVbrem/Vbrem
(1.4)
where AZefr= nzZ2(L/a)/nc, with LVa being the fractional chord length over which the high
ionization states occur ( - 0.5), and nz and Z are the density and charge of the impurity, and
AVbrem is the change in the visible bremsstrahlung measurement.
In using the visible bremsstrahlung information for density fluctuations, the
application is more difficult In measuring density perturbations, first the deviation, or
change, in the Vbrem measurement is determined.
Then assuming initial terms are known and rearranged (1.5.a) to determine the density
perturbation, (Site), as a function o f radius the following equation was derived,
meas. + jT e ( r)
where
(1.5.b)
Z rff-1
SZeffyZeff is small at high densities and assumed negligible
5Te/Te° is obtained from the polychromator
ne° is obtained from the interferometer
and I terms are the visible bremsstrahlung integral.
It can be seen from this equation, this means o f measuring density perturbation is only an
estimate. It is dependent on knowing information from the polychromator, and
interferometer and draws on several assumptions.
CHAPTER II
THEORY OF WAVE PROPAGATION IN A
PLASMA
Reflectometry is based on the principles of electromagnetic wave propagation and
reflection in a plasma. In our case, microwaves launched into a tokamak plasma are
reflected at a cutoff density, and retrace their path to a receiving horn. Figure 2.1 is a
drawing of the entire path traveled by the reflected microwaves. With the use o f optics the
signal travels over IS meters. As the radial position of the cutoff density varies, there is a
variation in the length and time traveled by the reflected microwave signal. Fluctuation
7m.
Mirror
o - . j a a
i
Receive
Transm it
Lens
Top B
Port
1. m
Slot
▼
Plasma
Figure 2.1:
A drawing of the reflectometer optical relay path. The
signal is shown entering vertically through the top B port.
The axis shown represents the electromagnetic field
directions of the propagating signal.
25
26
measurements of about one centimeter result in a rime variation on the order of 1(H 1
seconds, however one centimeter motion is several 2 jc radians in phase difference, which is
easy to measure with reflectometry. Therefore reflectometry measures the phase variation
of waves transversing the plasma.
The following sections will discuss the propagation of microwaves in a tokamak
and the measurement of phase change. The system of units used in this chapter are
gaussian-cgs.
2.1
Wave Equations
Maxwell's equations and the equations o f motion, including a Lorentz force,
describe the propagation o f electromagnetic waves in any medium. Applying the Vx
operator to Faraday's law o f induction, and substituting Amp&re's law plus assuming a
harmonic time dependence (e'°*) leads to the following wave equation,
Vx(VxE) -
- “ “ jj = 0 .
(2.1)
A tokamak plasma can be described as inhomogeneous, and magnetoactive
(anisotropic). In this medium, the temperature of the electrons, on the order of ten million
Kelvin (1 keV), are considered "cold" electrons since the electron-ion collision frequency is
much lower than the frequency o f the launched (probing) microwaves. In a typical MTX
plasma this collision frequency is approximately 100 kHz1, much less than the 75 to 110
GHz frequency of the launched microwaves. Therefore applying the MHD fluid model for
a cold, magnetized, inhomogeneous plasma to equation (2.1) gives
2
V x(V xE)
c
£ e :E = 0
(2.2)
27
'S
e = iD
where
2
*»>*
S = 1----- P V -
and
- iD
O'
S
0
0
P,
(2.2b)
2
D
(0
© I.
= - R ) ^ r ,
“ o 0 )S -0 3 ^
2
0)1.
P=l-- £
0>o
(2 .2c )
and €0b is the frequency o f the propagating electromagnetic waves. These equations are
f*
4jinee 2V/2
functions of the electron plasma frequency, oa^ =
, and electron cyclotron
me j
eg
frequency, co^ = —
where both the election plasma density, ne, and toroidal magnetic
m ec
field, Bt, are functions o f position. Another assumption typically made is that the solutions
to the wave equation are linear. This is the case when considering small amplitude
electromagnetic waves as in our experiments.
In MTX, the microwaves were launched perpendicularly to the magnetic fields lines
in the tokamak so that the electric field vectors of the waves were parallel with the magnetic
field, exciting ordinary mode (O-mode, E//B) waves. Cartesian coordinates can be used to
describe our system as follows: the propagation (k , propagation vector) is in the iz
direction, the electric field (E(z)) is in the ix direction, and magnetic induction (B(y,z)) is in
the iy direction. Another wave that is widely used is the extraordinary mode where the
electric field vector o f the propagating wave is perpendicular to the magnetic field (X-mode,
E-LB). The differences, advantages, and disadvantages of each mode will be discussed in
section 2.3.
Thus, it follows for O-mode that the Vx (Vx E) term in equation (2.2) can be
simplified to,
Vx (Vx E) = a 2E(z)/9z2 ix ,
and equation (2.2) can be written as,
28
ir(z )E (z ) = 0
(2.3)
where
(2.4)
and tope2 « n^z). Note that the index of refraction, % in O-mode reduces to zero when
C0pe2 = coo2, and there are two frequency regions in O-mode as follows,
I.
ti2 >
0, where the launched microwave frequency is greater than the plasma
frequency, (Oo> OJpe, and the critical density layer has not yet been reached.
In this region the microwaves will continue to propagate in the plasma with
a phase velocity (v<d) greater than the speed of light (c), but group velocity
(do^/dk) smaller than c.
II.
T|2 < 0, or cUo< tOpc, in this region the launched microwaves cannot
propagate further through the medium but will be reflected at cope = (tip.
The waves can, however, penetrate a small distance into the overdense
medium. These are called evanescent waves and penetrate a few
wavelengths in distance into the plasm a.
It is important to keep in mind that the microwave signal propagates only until it
reaches a critical density, and the density in the tokamak is radially varying. The
expression for the critical density is simply,
ricnt = (me/4rte2) aj02 = 3.14 xlO-I0 0)o2
(cm'3)
(2.5)
and the radial variation in plasma density (expressed in terms o f z) is usually modeled in a
parabolic form,
( 2 .6 )
where np is the peak density, a = ao - 18x1, the minor radius o f the tokamak minus an offset,
and a is a shaping parameter.
29
2 .2
Phase Comparison
The path followed by the launched microwaves is quite complicated. There are
phase changes through each lens, window, and slot. However, we are interested in the
phase variation of the plasma alone. In practice, we measure the change in the phase
difference, O&ff = <I>inc - <Drefj, between the incident signal and reflected signal during
plasma onset. During plasma excitation, all the other phase change mediums are constant;
the only phase-altering medium which varies is the plasma medium.
An analytical equation describing the phase variation in the plasma is obtained by
dividing the plasma medium into two regions and solving the wave equation, equation
(2.3), independently in each region [Gin-70]. Assuming the cutoff is at z = 0, the wave
equation in the region away from the cutoff, z > 0, is solved using geometrical optics or the
WKB (Wenzel Kramers Brillouin) approximation. The wave equation at the cutoff or near
the reflection layer, z £ 0, can be solved by a full-wave calculation using an index of
refraction varying linearly with position. These two solutions are then matched at the
boundary to obtain a phase difference equation throughout the plasma medium. The
following derivation is o f this phase change equation, and is presented to draw attention to
the relationship between phase change and density.
The electric field can be obtained from equation (2.3) using the method of
geometrical optics by first expanding the electric field, E(z), as follows,
/
E(z) -
E(0j + — E(i) +
(2.7)
where <Uo is the frequency of the microwaves or propagating waves and y , E(0 ), E(j), E(2 ),
etc. are unknown functions of z. Substituting (2.7) into (2.3) leads to the following
expression,
30
cr
+ B— + C + D ~ + F -^ j+ . . . = 0
C
to 0
( 2 .8 )
co‘
where A, B, C, etc. are expressions containing E(j),
and their derivatives. Since this
equality should be true for all values of oJq/ c, it should hold true when A = B = C = . . . = 0.
Thus the expansion terms in (2.8) can be determined as follows,
A = [n 2 - ( v ' ) 2]E (0) = 0
B _ E (O )+ 2 v 7E(0)_O
'< 0)
2y'
(1)
2hj/'
_
=
0
etc.
giving the values o f E(i)
A:
ti2 = (V ')2,
B:
E(0) = 4S 2. = - i S 2 i _ .
W
‘(z)
C:
E
=
<1}
(2.9)
y = ±fT[r\\z)dz
(2. 10)
i
z t:"
1 f E? - dz = __________
.
f
dz
V v 7 z; o 2 i V v
V ^ z ) z7Ja 2iVTi(z)
( 2 . 11)
where a(0 ) is an integration constant.
The first approximation of geometrical optics assumes that E(0 ) is the only
significant term. Using (2.9) and (2.10) in equation (2.7) gives,
E(z) =
—
a +.
V ^(z)
+i— /Vrl2(z) dz
-i^2 l^T\2(z)dz
c .*0+
..
+ _ J b = e c ‘V ^z)
assuming a forward (+) and backward (-) wave, and constants a± and
(2.12)
zq.
approximation of the electric field the following must therefore be true.
For this first
31
tE(ijl«IE < 0jl
and
higher E(j) terms < E(i)
(2-13)
where Ao is the vacuum wavelength of the launched microwaves. Substituting the
expressions for E(o), (2.10), and E(i), (2.11), into (2.13) and assuming n(z) is a
monotonic function through the interval
( zq ,z ),
and there is no absorption, equation (2.13)
is satisfied by the following inequality,
dtt
h s. dzl
l
(2.14)
?TT
In „2
ty ^
Therefore a sufficient condition for the applicability of the geometrical optics
approximation is given by equation (2.14). This solution is valid as long as the gradient of
the index of refraction over one wavelength is small. Away from the reflective region,
therefore, a solution to the wave equation, is given by equation (2.12). The phase change,
that is the change in the exponential o f equation (2.12), from a position Zq to z (round trip)
is clearly seen in this region to be
(2.15)
The full-wave solution to equation (2.3) using a linear expression for the index of
refraction and assuming no absorption is obtained in the following manner. First there is a
change in variables
(2.16)
where the index o f refraction is expressed as
(2.17)
32
fi)>
04 =
geometrical
optics
region
far from
reflective
layer
z>0
mm
mm
z -0
Figure 2.2:
A picture of the boundary conditions used for the full-wave
solution to the wave equation.
The boundary conditions are set so the region of interest is defined as z i 0 as
shown in figure 2.2. There is a fixed boundary condition for an incident wave at z = 0, the
reflective layer, and z > 0, the penetration region . Also note the derivative dn/dz has a
discontinuity at z = 0. At this interface there will be reflection of the waves coming from
the region z < 0. Equation (2.3), using the change in variables noted in (2.16) can now be
rewritten as
d2E
y + J ;E = 0
(2.18)
which reduces to a Bessel equation and has solutions o f Bessel functions of the 1/3 order
or equivalently, integral Airy functions,
E(^) = ^ - J c o s
dx .
(2.19)
Simplifying this solution, for large \ ( l ^ |» l ) , it is possible to use an asymptotic
representation of the Airy integral,
E($) ~ ^ r 1/4cos(|!;3'2 -
l§ l» 1 .
Using MTX parameters, £ is calculated to be of the order 102. Therefore, this is an
acceptable approach. An analytical form of the large £ approximation using,
(2.20)
33
zr
.
and
0) 2ic
— = -—
c
d if(z )
dz
takes the form,
2 /3
5 = ( f * , ) 2,V ( Z) =
2n
(2 .2 1 )
n (z)» i
d V (z )
*■0
dz
This expression is similar to the condition for the first geometrical optics
approximation. Equation (2.20) is itself a solution in the geometrical optics method.
Equating this solution, equation (2.20), to the geometrical optics solution, equation (2.12),
and equating the exponential variation and amplitude terms imply
3
c J
and
=
^ q (z )
Assuming that the beginning of the reflective layer is at z = 0+, and the incident wave has
an amplitude of unity, eitot, A is determined as
and
. , 4<0
-i(—
z,—I t,)
E = E+ + E_ = l + e 3c 2
( 2 . 22 )
With a bit o f rearranging, the phase shift between the incident and reflected waves is seen
to equal
* = 2 “ ] T l( z ') d z '- ^
/* J
c 0
2
(2.23)
What is interesting to note from this integral is the link between the electron plasma
density and phase change. One can insert the index of refraction into (2.23) knowing the
34
density profile at a particular instant and obtain a phase measurement from the cutoff
density. This calculation repeated throughout the shot would predict the information we
measure with the reflectometer, that is, density layer motion or fluctuations, This
calculation would be quite tedious. Recall the density profile of our model depends on 3
parameters, peak density, offset, and alpha (shaping parameter). A peaking of the density
would narrow the profile, thus move the cutoff layer in, and produce steeper density
gradients. The offset would be a direct motion horizontally. If the shaping factor alpha
increases, the density peaks more and a decreasing alpha produces a flatter plasma shape.
Comparisons between the density profile diagnostic, the interferometer, and the
reflectometer are thus very informative and a comparison between these diagnostics will be
made in section 4.1.
Lastly, in practice, equation (2.23) cannot be used to measure density layer motion
because o f the complexities involved. Instead a simple estimate o f phase change is useful.
If one could assume long wavelength perturbations in the plasma, a rough prediction of the
phase change measurements would simply be,
= 2ko 8z
(2.24)
where 8z is the change in location o f the cutoff as a result o f the perturbation and ko = cOq/ c.
However as other authors have noted, the change in phase is an integral and does not
necessarily imply a local change at the cutoff. The integral is a measure of the variation in
the index o f refraction over the plasma length specified. Some other concerns or potential
difficulties in obtaining a localized measurement were mentioned by Sips [Sip-90] and are
listed in the following points.
1.
The existence of evanescent waves creates a problem because it infers the
launched microwaves do not necessarily reflect at the cutoff and this adds an
uncertainty to the location of reflection. The problem is most severe when
the local density gradient about the cutoff, (Vn), approaches zero. Those
35
working with JET, [Sip-90], found about a 5% uncertainty in position and
estimated the chance o f probing a region with a flat density profile as slim.
Therefore the presence of evanescent waves may not be significant.
2.
In tokamaks there are helical magnetic field lines which in O-mode
reflectometry implies an X-mode component. This component will not be
reflected at the critical density for O-mode but penetrate further. This
component may be negligible in MTX due to our operation at a high toroidal
magnetic field and moderate plasma current A rough estimate of the ratio,
B(/Bp, is approximately 40. Also, estimated returns from the dispersion
relation predict a X-mode component to be highly unlikely.
3.
Another problem due to the geometry in a tokamak is the added curvature of
the reflective layer. However by minimizing the spot size o f the launched
microwaves at the estimated point of reflection this difficulty could also be
dismissed.
2 .3
Uses of O-mode and X-mode Waves in Reflectometry
Reflectometry can use O or X waves. Much of the work comparing O-mode and
X-mode reflectometry has been done by the TFTR group. First recall the dispersion
relation and cutoff frequency, Cn2 = 0), for O-mode and X-mode propagation.
C02=O)pe2
O-mode:
cor
= l/2[oice+ (tote2 + 4(Ope2)i/2] right-hand cutoff
oil
= l/2[-aic*+ (uice2 + doipe2)1/2] left-hand cutoff
where "right-hand" means that the electric field rotates in the direction o f the electron
rotation in the magnetic Held.
36
Reflectometry in X-mode leads to determining two quantities which vary with
position in the tokamak, tOpe** n^z) and
B(z). Either the density profile or the
magnetic field profile must be known to obtain information on the other. This coupling
requires more experimental measurements and the accuracy o f the reflectometer
measurement will depend upon the accuracy o f the other diagnostic, measuring either
magnetic field or density throughout the shot
O-mode reflectometry is much simpler since the cutoff is only a function o f the
electron plasma density. This simplifies the procedure of looking at plasma density
fluctuations.
There are additional advantages and disadvantages of each mode of operation as
discussed by Nazikian, fNaz-90], and Bigelow, [Big-92] in Table 2.1.
O-mode
+
Simple view of density motion
X-mode
+
Probes the high field side of the plasma
and has a wider density range
+
Potentially better localization of the
measurement to the reflecting layer
+
Advantages in small angle reflectometry
+ Lower frequency operation
* The shorter the probing X the more
localized the measurement to the
reflecting layer
More complicated data inversion
Higher frequency operation at higher
field
Table 2.1
O -m ode and X-mode characteristics compiled fro m
Nazikian and Bigelow.
Since X-mode reflectometry has a right and left cutoff frequency, the reflection of
microwaves can take place on either the high or low magnetic field side of the plasma,
resulting in a wider region of the plasma which can be probed. The right hand frequency,
37
G)r , is the higher frequency and is reflected at greater magnetic field strengths whereas col
is a lower frequency. Extraordinary mode reflectometry requires higher frequency
operation which has both advantages and disadvantages. Higher fiequency, shorter
wavelength, reflectometry means a better localized measurement Therefore, since X-mode
operates at higher frequencies, there is the advantage of better localization to the reflective
layer and for many groups this has been their reason for choosing X-mode over O-mode.
However, higher frequency operation is more expensive, and this is a significant
disadvantage.
38
Notes to Chapter II
^This collision frequency was calculated by a formula in Introduction to Plasma
Physics and Controlled Fusion, by Chen, page 179, using an value of InA of page
181 for a fusion reactor operating at 1 keV.
CHAPTER IH
DESIGN AND SUPPORTING RESEARCH
The JAERI microwave reflectometer was installed in June 1991. A prototype
using a signal frequency o f 94 GHz and the product of an existing FIR interferometer
system was used beforehand to get a sense of the performance that could be expected from
the actual reflectometer. From its operation, we noted that either a waveguide or some type
o f transport system would be necessary since a signal at the power level being considered
only travels about 10 cm before dispersing and losing its ability to be reflected back or to
track the phase. A full waveguide system was considered, however, fundamental
waveguide losses due to finite conductivity resulted in too large a dB loss per unit length at
these high frequencies.
The first prototype dual lens and waveguide reflectometry system transported the
signal using optics about 2.8 meter (one way), the second lens of which focused the signal
into the vacuum chamber. This set up is shown in figure 3.1(a). However, the near
proximity o f the microwave hardware caused problems. In January 1991, the prototype
reflectometer encountered problems with an isolator made o f a ferrite material. There was
a strong effect on its performance due to the high magnetic fields in the region just above
the tokamak. Even after shielding, an increase in cross-talk between the transmit and
receive signals was noticeable. Therefore a long quasi-optical system was adopted. The
reflectometer is unique in its use of this quasi-optical system. Another noted problem,
during initial experiments, were spurious reflection from lenses, the vacuum window and
39
40
port flange. These were easily corrected by adding microwave absorber over the flange
and tilting the lenses and window so as to scatter the spurious signals.
Section 3.1 will continue this survey of the reflectometer setup and present a
detailed description o f the final design. Testing and modeling of the reflectometer are
described in sections 3.2 and 3.3. Then in section 3.4, the general operation of the
reflectometer will be discussed.
^5° 'Quartz glass
Trans.
(a)
Absorber 'lined tube
Lens
Duct
Propagating distances 2.8 m (one way)
Date: 12^0 Beginning at shot # 10120
Plasma
(b )
Rec.
Trans.
Optical coupler
Mirror
Propagating distances 8.1 m (one way)
Date: 6/91 Beginning at shot #11413
Plasma
(c)
.................
Rec.
Trans.
Optical coupler
Propagating distance^ 8.1 m (one way)
Date: 4/92 Beginning at shot #13070
Plasma
Figure 3.1:
Duct
Mirror
The progression of the microwave reflectometer setup.
41
3 .1
Design o f the JAERI Reflectometer
The final design o f the reflectometer allowed for top or side entry into the tokamak.
Microwave hardware and the optical relay system found in the vault are described in
section 3.1.1, while the acquisition and phase comparison mechanism in the control room
are detailed in section 3.1.2. Details pertaining to hardware and electronic assemblies were
provided by R. Stever who was the microwave diagnostic engineer for this project.
3. 1.1 Hardware and Setup in the Vault
Two assemblies, shown in figures 3.2 and 3.3, contain the electronic components
which makeup the microwave reflectometer signal. The hardware involved in producing
the microwave signal is in two sections: an upconverter/downconverter front end and an
intermediate frequency (IF) unit. The IF assembly contains two sources, local oscillators
LO l (2-18 GHz) and L 0 2 (1.8-18.3 GHz), which are phase locked using a phase lock
loop module with L 0 2 locked 30 MHz below L O l. Couplers C l through C7 are used to
provide power from the local oscillators to voltage tuned YIG (Yttrium Iron Garnet)
bandpass filters, VTF1, VTF2 and VTF3. These filters automatically track the oscillator
signals to filter out harmonics and spurious signals. C2, C3 and C7 provide power from
LO l to YIG filter VTF1 and VTF3 which filter the LO l signal. VTF2 is used to filter
harmonics and spurious signals from L 02. The filtered L 0 2 signal is used to
downconvert the 2 -1 8 GHz IF signal from the front end assembly to 30 MHz via mixer
M l. A 30 MHz reference signal is also generated using LO l and L 0 2 in mixer M2. This
signal is phase compatible with the 2 - 18 GHz reference signal used in the upconverter.
The 30 MHz IF signals generated by M l and M2 are then filtered and amplified using
amplifiers AMP1 and AMP2 which are limiting amplifiers providing +3 dBm output for
input signals between
42
vTP I
MX
our
«
IB* SR ftg .
Cf
OLTT
cs
Figure 3.2:
The JAERI reflectometer intermediate frequency (IF)
assembly for frequencies 75 to 107 GHz. (from R. Stcvcr)
-60 dBm and -10 dBm. After amplification and filtering, these signals are then transmitted
to the control room and fed into a phase detector. Therefore the IF assembly produces a
reference out, 2 - 1 8 GHz signal, to the upconverter/downconverter assembly and receives
from it a plasma in, 2 - 1 8 GHz signal. It also yields plasma and reference output signals
at a frequency o f 30 MHz which are used in the phase comparator. Also it should be noted
43
RPUCTEDSIM.
TSTO
»r
TWfrMTTSIOA.
?i to iro^i
F ig u re 3.3:
LO
ir
T h e J A E R I reflecto m eter fro n t end assem bly fo r an
o p e ra tin g freq u en cy of 75 to 107 G H z. (from R. Stever)
that there is a tuning control module in the IF assembly which controls SW1, SW2 and
SW3 in the front end assembly. These switches are used to set the frequency band.
The front end unit, upconverter/downconverter assembly, produces the transmit
signal and accepts the receive (plasma) signal which has traveled through the optical relay
system reflecting somewhere in the tokamak vessel. The frequency range o f the
microwave signal is designed to be 75 to 107 GHz. This range is subdivided into two
bands, low band 75 - 91 GHz and high band 91 - 107 GHz. Common modules used in
creating the transmit signal and upconverting and downconverting that signal are two Gunn
oscillators, GUNN1 at 73 GHz and GUNN2 at 89 GHz, C l , and SW 1. In the
44
upconverting process, the 2 - 18 GHz reference signal from the IF assembly is input into
mixer U 1 where it is mixed with GUNN1 for low band transmission or GUNN2 for high
band transmission. SW1 is used to select either GUNN1 or GUNN2 and that signal
travels through a coupler, C l, and is sent to U1 and D l. The output o f U1 than goes to
SW3 which selects BPF1 (bandpass filter for frequencies 75-91 GHz) or BPF2 (bandpass
filter for frequencies 91-107 GHz). The output o f BPF1 or BPF2 then goes to SW2 which
routes BPF1 or BPF2 to the transmit waveguide. The oulput signal at SW2 is 1 mW ± 3
dB. The transmit signal is launched from a circular gold plated horn 1 cm in diameter. In
the down-conversion process, the reflected signal enters a second identical horn and is sent
to mixer D l where it is mixed with either GUNN 1 (low band) or GUNN2 (high band)
depending on the setting o f SW1. The IF output o f D l is again a 2 - 18 GHz signal which
is amplified in AMP1 by 20 dB and then sent to the IF assembly for further downconversion and filtering.
The transmit and receive circular homs are mounted on the optical coupler tray, a
small system used to split the return signal then direct and focus it into the receiving horn.
The optical coupler is shown in figure 3.4 along with a directivity study. The transmit
signal, after being launched from the hom, passes through a lens and quartz splitter. The
focal point o f the small lenses is 12 cm focusing the transmit signal at the splitter in one
direction and in the return path, focusing the plasma signal at the horn. The transmit signal
is focused at the splitter to decrease reflections. The splitter is essentially a thin flat piece of
quartz 1.4 mm in width. A fraction o f the transmit signal is scattered at the splitter and to
avoid spurious signals in this assembly there is an adjustable absorber block which can be
positioned to minimize internal reflections. The transmit signal propagates from the optical
coupler about one meter to the first transport lens. The returning signal at the splitter is also
partially reflected or split The component of the plasma signal which scatters 90* is
bounced towards another 90* reflector which directs the signal towards the small lens
which focuses it into the receiving hom. This optical coupler works quite well, resulting in
45
Lens,
Splitter
Transmit
12.5
Lens
Reflector
Receive
12.5
Lenses
f=11.9cm
Hom
RCH010
74GH>
90
A:
B:
c
F ig u re 3.4:
Splitter
Reflector
1.4 mm Quartz, flat 2.5 mm Al, flat
94G H z
110
Transmit/Receive short circuited.
E
B
0
coupler
lens
l< 0 1
0
coupler
lens
reflector
absorber
A schem atic o f the optical co u p ler used to sp lit th e reflected
signal is show n above a lo n g w ith sidelab te sts o f its
directivity. D istances on th e coupler d ia g ra m a r e in cm .
46
losses o f only 7 dB. Using this coupler, the entire transmit/receive (T/R) unit demonstrates
a sensitivity of about 40 dB. This is a worthwhile option to the traditional setup of using a
standard waveguide directional-coupler. A waveguide directi onal-coupler was initially
used but had serious problems with internal interference and cross-talk.
To protect valuable components in the front end and IF assemblies, the front end
was encased in a mu-metal box and a long optical relay system was adopted. During the
last two operational runs, the reflectometer was set up with an optical relay path of about 8
meters entering the tokamak by either the top or side B ports. The spacing between
transport lenses was about two meters and a special lens was used at the port entrance to
focus the transmitted signal into the plasma. The diameter of the microwave signal varied
from about 15 cm at a lens to 4 cm at the waist. The port lens narrowed the signal to a spot
size of about 2 cm in diameter. A tubular support beam was used to hold optics between
the far wall and the tokamak. All the lenses were fabricated using clear polystyrene with a
dielectric value of 1.5. The transport lenses were 15.24 cm (6") in diameter and about 1
cm thick with spherical surfaces and a focal length of approximately 84 cm. The top port
lens was a drop lens suspended about 6 cm above the tokamak vacuum window. It also
had a diameter of 15.24 cm but a focal length of 52.54 cm. This port lens positioned the
waist o f the signal at a minor radius o f about 10 cm. In the side entrance arrangement the
port lens replaced the vacuum window. In this position the port lens was required to be
smaller, having a diameter o f 11.5 cm (> 5"), however, window losses could be neglected.
A problem using the port lens in this position was that the lens material tended to outgas.
Therefore using this arrangement, a micropump had to be installed to keep vacuum
conditions in the tokamak. The focal length o f the side port lens was about 75 cm,
positioning the waist o f the microwave signal in the port slot. Power losses from the
lenses were experimentally measured to be about 1 to 2 dB/lens. The lenses were all
angled to about 10* to minimize reflected power through the transport system.
47
A serious problem encountered in the transport path, which will be discussed in
depth in section 3.2 and 3.3, is the difficulty of propagating the microwave signal through
the skinny MTX ports. The top B port which was initially accessed, has dimensions of 2.5
cm wide x 9.2 cm high x 23 cm long. The narrow width of the port reduced the power
return of the microwave signal and created quite a few challenges.
Also in the vault was the reflectometer rack containing a Camac crate, a GPIB crate
controller, and a LeCroy 8210 recorder and a 3063 IGOR (16-bit input gate/output register)
module. The 8210 recorder set at 10 kHz was used to acquire the reflected IF power
throughout the shot. A lowpass filter on this signal prohibited frequencies above 8.6 kHz.
Also by using an HPIB extended computer hook up and the IGOR module, frequency
setting of the reflectometer could be executed from the control room. This system to fix the
reflectometer frequency by regulating the IF section (though not between bands) used 12
bit tuning, 4096 steps o f 3.906 MHz/bit, for either high band (91-107 GHz) or low band
(75 - 91 GHz) setting. Transmitted signals to the control room included a 30 MHz
reflected plasma signal, 30 MHz reference signal and the IF reflected power.
3. 1.2 Control Room Processing and Acquisition
Initial operations of the prototype reflectometer were also helpful in debugging
acquisition subroutines and testing the phase comparator in the control room. Recall the
signals transported from the vault to the control room are the plasma (reflected) signal, the
reference signal, and the reflected power. The plasma and reference signals are fed into a
phase detector, sometimes first requiring amplification.
The output signal of the digital phase comparator is a direct measurement of the
phase difference between the two input signals. These phase detectors, also used in the
interferometry system, were modified for reflectometry measurements by eliminating an
existing design frequency limit o f less than 200 kHz maximum observable fluctuations.
The bandwidth o f phase detection was extended for reflectometry to track fluctuation
48
frequency up to 500 kHz. These detectors have a wide dynamic range of phase detection
due to the use of prescaling. Using the prescale option, the phase comparator can handle
up to ± 32 fringes, therefore ± 32 wavelengths o f motion. However the prescaling circuit
constitutes a zero-crossing detector and this imposes a condition requiring a relatively high
signal-to-noise ratio. Extraneous zero crossings, when experienced, result in step changes
o f 360 degrees and can only be removed if they occur infrequently. A calibration of the
phase comparator gave 400 mV/rad which must then be multiplied by the prescale value.
The phase comparator has an excellent resolution of less than 5* error and accepts an rf
input between 1 - 100 MHz. A 5* error corresponds to 0.035 volts with the prescale option
set at 1 or, when considering a frequency of 100 GHz, 0.04 mm motion. The equation for
converting between volts and position changes is
Distance (cm) -
0 .4 (v / rad)
2jc(rad)
2
There are two output junctions from the phase comparator that differ in their use of
filtering. The front output o f the phase comparator was usually set to 10 kHz filtering,
while the back junction had no filtering and provides signal information up to 500 kHz.
The rear signal was fed into fast LeCroy 8818 recorders and front into the slower LeCroy
8210 recorder. The 8818 recorder has a memory size of 32k which can be expanded by
attaching (grouping) memory modules, and signal voltage range of ± 0.5 V. The
acquisition rate o f this recorder can be as high as 100 MHz but in this experiment was set
between 200 kHz and 1 MHz; it can be delayed from dtO (zero time trigger) to any point
during the shot using a model ETC 2202 digital delay generator. The slower recorder
monitors the whole shot. The 8210 recorder can receive a signal in the range o f ± 5.0
volts, has 4 channels, and a memory of 32k. It was set at an acquisition rate between 10
and 20 kHz.
The phase measurements were then acquired on a HP UNIX system using an
interactive code developed by W. Meyer and then transferred for storage onto the VAX
49
transport lens
coupler
TransTRcc,
Pellet
Injection
Tokamak
s*N
Equipment Setup
n i i 11
jd
upler
HP computer
U-melal box
Front
end
T |
1
reflected signal
transmit signal
to IF assembly in rack
On optical railing
in vault region
RFL rack
Keceiver
IF stage
reflected signal
transmit signal
to phase detector
in control room
Recorders
>«t t t «
Spectrum
analyzer
Phase
comparator
Amplifiers
RFL rack in MTX
control room
RFL rack in vault
region
Acquisition Hardware Setup
Figure 3.5:
The JAERI reflectometer vault and control room setup.
50
computers. I customized the acquisition subroutines for data acquisition specific to the
reflectometer. The recorded data was read into files, plotted, and stored.
3 .2
Side-Lab Tests
Sidelab tests confirmed the need to use some type of transport system to propagate
the microwave signal. From a reflector plate 10 cm away from the transmit hom, small
incremental changes of the reflection point gave incorrect (jumpy) phase information due to
signal losses. The following is a list of tests performed on the quasi-optical reflectometer
setup. They were used in the examination process o f new equipment and to determine the
sensitivity or directivity o f the reflectometer system. Also, they verified or pointed out
troublesome areas that were encountered in the actual MTX setup.
1.
By incrementing the reflection point, the phase change was verified.
This produced fixed phase measurements by which the probing
wavelength, prescale option, calibration, and power return could be
monitored or verified.
2.
Reflection off vibrating and rotating targets.
3.
Tests 1 and 2 through a mock port.
4.
Field scanning of the signal through the port setup. The scanner was also
used to verify the focal point of lenses.
This discussion will start with test 3 which incorporates tests 1 and 2, a picture of
which is shown in figure 3.6. This mock port setup usually included the optical coupler,
one or two transport lenses, the port lens, a quartz window and a duct, all positioned in the
same relative manner as they would be on MTX. Absorber was placed around the slot
having dimensions of 3 cm x 12 cm x 14 cm (sidelab only) and lenses were tilted as in the
actual experiment. The microwave source used in phase and reflective power experiments
51
was the actual IF assembly and front end of the JAERI reflectometer. Tests verifying the
full operating range o f the reflectometer were also conducted with this setup. Reflected
power, (dB), was measured in sensitivity studies, and for testing the phase comparator or
tracking phase change measurements, the output phase difference from the phase
comparator was measured via an oscilloscope.
x4
CouDler
ipier
A
■4)
O
Distances (cm)
Spectrum
Analyzer
Figure 3.6:
Oscilloscope
d
|" Slot /| Target
Window
with absorber
Phase Comparator
©
x5 x6
xl:
x2:
x3:
x4:
113
214
207
20
x5:
18
Targets
x6: 14
d : variable
Power and phase tracking sidelab experimental setup.
A flat reflector was placed at the waist between lenses and behind the entire setup to
obtain the following power losses listed in Table 3.1. Transport lenses typically showed
losses o f 1 to 2 dB, and the port lens, in Table 3.1, produced a loss o f 5 dB. Through the
slot another 4 dB was lost and with the addition of the window, another -7 dB. This setup
therefore predicted on the actual experiment about a 20 dB loss in the propagation of the
microwave signal into the tokamak if the reflection occurred off a flat surface. Other
experiments comparing flat and curved (radius 9.5 and 6.5 cm) reflectors indicted that
curved surfaces could add another 2 dB or more in losses. Note, also, that the measured
port lens loss of 5 dB was not at the focal point of the port lens in the actual setup on MTX
at the time. Losses from the port lens should be lower. Also, from other power
52
P o s itio n
Sensitivity:
Return Power/Absorber
date: 10/25/91,
11/13/91
Focal point of L I
-15/-66
Focal point o f L2
-16/-66
Behind Lp (70 cm)
-24/-58
"
(above)
-28/58
"
(above)
Table 3.1:
" with duct
" with window
-21/-60
-35/58
Power returns in the sidelab setup.
measurements, it was noted that without absorber around the window, the flange had a
power return of up to 8 dB. This produced an interfering signal to that o f the plasma
signal. This problem was suspected in early reflectometer shots and thus verified in the
sidelab and corrected on the actual experiment
Incremental motion of a flat and curved surface with a similar setup yielded good
results, verifying the signal wavelength and the prescaling option, and estimating power
return on the actual setup. Phase measurements and power return at various prescale
settings and all integral reflectometer frequencies were checked in the sidelab. Wavelength
verification was done for several frequencies. The transmit power from the reflectometer
varied with frequency between 0.4 and 0.8 mW.
By replacing the reflective targets mentioned above with a moving or vibrating
reflective target not only reflected power and sensitivity experiments could be conducted
but also phase tracking. These targets included an aluminum rotating hexagon wheel (1" x
1" faces) or aluminum covered vibrating speaker positioned behind the slot and used to
mimic an oscillating plasma cutoff layer. Placing the hexagon wheel behind the slot in
figure 3.6, measured power values o f -45/-S6, showing 11 dB sensitivity, and for the
speaker, these values were -4C/-48, therefore producing 8 dB power return above
background. Background in these studies is the power measured with absorber in front of
the target. Oscillating targets produced traces like those shown in figure 3.7. The study
53
(b) Prescale, +«
(a) Prescale, +4
(c) Prescale, +16
Plot
AVolts on differing faces
(a )+4
2 volts, 3.8 volts
(b)+8
0.9 volts, 1.8 volts
(c) +16
0.4 volts, 0.6 volts
*+16 became insensitive to altered
face as would be expected.
Setup:
|< 0 [
coupler
Figure 3.7:
0
0
trans.
port
lens
lens
<? I absorber
hexagon
wheel, every
other face altered.
Testing the prescale option of the phase comparator by
tracking phase off a hexagon wheel.
54
being conducted in these particular photographs, figure 3.7, is a test o f the phase
comparator prescaling option. The target in use was a hexagon wheel which could be set to
rotate at frequencies up to 50 Hz and in this study, had every other face altered by adding
aluminum strips. From the pictures it can be seen that the phase comparator's prescale
option was working since the voltage measurement of motion decreased proportionally
with the increasing prescale value. The motion detected in this test was about 0.5 cm.
Most phase tracking sidelab tests, using oscilloscope traces, were at very modest oscillation
frequencies (0.1-1 kHz) and measured small magnitude motion. The lack o f symmetry
seen in some traces is due to poor alignment. Exact alignment was essential for good
power return, however in the sidelab was difficult and very tedious. Overall phase tracking
experiments showed the phase comparator and reflectometer system could analyze and
receive data at these low frequencies reflected off moving objects.
In test 4 an x-y scanner is used to measure the radiation pattern or electromagnetic
field profile of the transmit signal exiting the duct. The configuration of these tests was
similar to that of figure 3.6 where the slot was 3 cm wide by 12 cm high by 14 cm in
length. For these particular experiments, a modulated 94 GHz source signal was used to
propagate through the mock port setup. This source produced a gaussian waveform which
was measured by an automated antenna sensor. Computer controlled scans were taken
along the x-axis and y-axis with the z position set manually. The sensor was linked
directly to the computer which generated plots and mechanically controlled the x-y stepping
motors. The geometry used in this experiment placed the E-plane in the x direction
(horizontal), H-plane in the y direction (vertical), and propagation in the z direction.
Therefore the duct limited x to 3 cm and y to 12 cm. An evolving E-field profile at the slot
exit is shown in figure 3.8. In free space propagation, this profile would still be gaussian;
however, the E-field radiation pattern is significantly influenced by the duct. The field
patterns shown are located at z = 2 ,4 and 12 cm behind the duct. The H-plane is not
shown since the vertical plane is non-limiting and shows little change in the field profile.
55
BERM S I Z E
(a)
2 N CM
E-PLRNE BEPH PATTERN
positioned 2 cm
positioned 4 cm
behind the duct
(b)
•It
-.iter m
positioned 12 cm
behind the duct
DISTANCE IN CH
Figure 3-8:
Electric field radiation patterns as measured by the x-y
scanner in the sidelab. The plots shown are behind a slot (3
cm x 12 cm x 14 cm) at distances of (a) 2 cm, (b) 4 cm and
(c) 12 cm.
56
These tests were performed to study waveguide effects created by the duct and survey the
propagating signal and power losses incurred. More results follow in section 3.3.3, which
compares sidelab field scans behind the duct and those hom the MTH code.
Also measured by the x-y scanner are points of maximum power return which
correspond to the focal point o f lenses. By this means new optics could quickly be tested.
3 .3
MTH Code Analysis
The MTH code is a numerical code which models the transmission of
electromagnetic waves making use of the Huygens’ principle. Field profiles of a
propagating electromagnetic source signal are generated by the code. The MTH code
provides a computational method for modeling microwave power launching and
propagation. It was used at Lawrence Livermore National Laboratory (LLNL) to model
and analyze experiments of the free-electron laser (FEL) that transmitted a 140 GHz signal
into a high density plasma in MTX. The MTH code modeled the path o f the microwave
signal consisting o f 4 concave mirrors, and up to, and through the MTX port, predicting
the performance o f this transmission. The original code was given to Jack Byers at LLNL
by Tom Samec of TRW; however at LLNL numerous additions and modifications were
added by J. Byers, M. Makowski and B. Stallard. In preparation for the implementation of
the reflectometry system, this code was used to study the propagation of the reflectometer
microwave signal into the tokamak vessel through a narrow MTX port.
MTH is a Huygens’ code and therefore determines the effect at the instant t = ti o f a
wave phenomenon caused by a given disturbance at the initial instant t = to using an
intermediate step at t = t'. The input file for the MTH code consists of 3 parameter lists,
one for each stage o f the propagation. The structure of the code is such that it propagates
the electromagnetic field profiles from a source mirror mO (initial parameters) through a
57
transitional stage m l, and finally to a detector m inor m2. This code is first used to create a
source by setting the initial parameters equal to the dimensions o f the actual hom or
launching device and specifying a null intermediate stage so the signal can propagate to its
far-field past the Rayleigh length,
zr = tcw02A .
During this propagation the signal also
expands. The waist expansion for a gaussian signal can simply be modeled by the
following equation,
= wr
(3.1)
where w0 is the waist o f the signal at z = 0, \ is the wavelength o f the beam, and z is the
propagated distance. [Mar-82] The detector or final m inor is then used as the source
mirror for the next stage o f the sequence. The MTH code is run N tunes for N different
regions o f propagation; N turning mirrors, N ducts, or whatever is defined in the
intermediate stage.
At LLNL various models for possible sources or intermediate stages were used to
study the propagation o f the FEL signal and incorporated into the original code. Those
which will be used in the reflectometer study are a gaussian source and variable length duct
which behaves as a waveguide and generates modes. Unfortunately, the code did not
model lenses which would have aided in the study o f reflectometer profiles.
The coordinate system in the MTH code used a primary, secondary and propagation
direction. For the reflectometer the propagation direction was z, the electric field was in the
primary or x direction, and the magnetic field was in the secondary or y direction.
Therefore, the electromagnetic field transverses the x and y coordinates and the signal
propagates in the z direction. The electromagnetic field components have the form \y(x,y,z)
= u(x,y,z) exp(ikz).
A specific study using the MTH code with applications to the reflectometer was the
examination of transport schemes to propagate the microwave signal efficiently through the
58
narrow MTX p o rt Figure 3.9 depicts this study centered around the port slot. These case
studies represent two extreme illumination schemes. If the port lens focuses the microwave
signal in the plasma, the duct would be fully illuminated and the beam would be severely
truncated at the window and port Truncation o f the signal would result in a large power
loss, however, if the waves showed good reflection at the plasma cutoff layer, less
scattering losses in that plasma region would be encountered as well as the advantage of a
clear return signal. Conversely, if the port lens focuses the microwaves at the slot
entrance, more signal would enter through the slot but the resulting microwaves would exit
unfocused which might result in poor reflection from the plasma. This study therefore
weighs signal power return, and signal reflection at the plasma layer which directly
corresponds to the signal having a flat phase front. The MTH code for reflectometry
studies looked solely at propagating the microwave signal through the slot to a fictitious
reflective layer around 8 cm from the exit. Dimensions for the top B port on MTX were
used for this study and are 2.5 cm in width (x, primary direction), 9.2 cm in height (y,
(a) Large Illumination, Case A
TE01
sourci
duct, 2.5x9.6x23 cm
(0.0)
[0 . 1)
-35 cm
0 cm
(U)
23 cm
31 cm
(b) Small Illumination, Case B
duct, 2.5x9.6x23 cm
~ p T
-10 cm
|flU)
Ocm
Figure 3.9: The study using the MTH code modeled the transmission of
the reflectometer microwave signal though the top B port of
MTX.
59
secondary direction) and 23 cm in length (z, propagation direction). Smith describes the
modeling o f the signal through the slot as "the field impinging onto the entrance o f the duct
is represented as a set o f duct waveguide modes, which are then transported to the end of
the duct with the phase shift appropriate for each mode. This calculation shows that a
mixture o f modes are launched from the duct which interfere in the plasma". [Smi-901
Readers interested in mote details about the MTH code may refer to the appendix
which contains a detailed discussion on how to use this code and further references.
3. 3.1 Test Cases A and B
Case A and B are similar in that they both used a 94 GHz source (X = 0.3 cm) and
the same stage sequence. The stages were set to render electromagnetic fields profiles at
(1) the hom, (2) the entrance to the port, (3) the exit o f the port, and (4) various positions
in the vacuum vessel. In stage 1 an imaginary hom is carefully chosen to have the proper
dimensions so that upon propagating in stage 2 it will reach the duct having the appropriate
size (waist) which is known from sidelab scans or estimated from lens calculations. In
stage 2, the signal from the hom is allowed to propagate far enough so as to neglect near­
field effects when used as the input file in the next stage through the slot. This distance is
equivalent to z r . Therefore, the first 2 stages place an electromagnetic signal having the
appropriate field profile at the entrance to the duct. In stage 3 the signal is truncated,
chopped in the xy plane, and then transmitted through the duct where modes are formed
and alter the field profile. Then in stage 4, the microwaves are propagated into the vacuum
vessel. These tests were specifically performed for the top B port and unfortunately minus
the effects of focusing.
Large Illumination
Case A studies the fully illuminated duct which corresponds to the port lens
positioning the focal point o f the microwaves in the plasma region of the tokamak. A TEqi
60
source, a 2.5 cm square, modeled the hom. The Rayleigh length was calculated to be
about 38 cm; therefore in stage 2, the initial signal was allowed to propagate 35 cm to the
duct entrance. The duct or slot was input to be 23 cm long as in the actual experim ent The
electromagnetic field profile o f all stages in case A are shown in figure 3.10. The plot
corresponding to stage (2,3) o f figure 3.10 shows a xy profile at a minor radius in the
tokamak o f 8 cm. This means propagating an equivalent length o f 8.5 cm into the vacuum
chamber. This profile can be compared to the gaussian profile in stage (0,1) to illustrate the
definite effects o f propagating through the p o rt In figure 3.11, a vertical exit and a
horizontal exit view o f the signal along with its phase contour are illustrated. These
diagrams also show dramatically the waveguide effects. Upon exiting the slot, the E-field
(vertical view) is seen to furiously expand, and the H-field (horizontal view) forms peaks
and nodes. The phase front appears as a wake in which the ripples elongate with
propagation distance. The signal leaving the duct is definitely not well-behaved, but
evolves to a fairly clean signal at about 8 cm. Figure 3.12 shows an enlarged view of the
phase front for case A and B at the minor radius of 8 cm. From this diagram, figure
3 .12(a), the phase front of the signal is seen to be flat and 1.2 cm wide. A flat phase front
is desirable because then the signal returns in unison from the reflective plasma. If this
front is somewhat curved, different parts o f the phase front would return from differing
radial position and give a jumbled phase measurem ent The power entering and leaving the
slot were calculated to be 0.208 mW and 0.135 m W using an initial source power o f 1
mW. The entering power value is determined purely by geometrical considerations.
Therefore, the large illumination study indicted a transmitted power into the plasma region
of 13.5% the source power and a phase from which is ’’flat" for 1.2 cm.
Small Illumination
Case B upholds the view that if more of the transmit signal propagates through the
duct, more will reflect from the plasma. This is accomplished by the port lens focusing the
61
microwaves at the duct entrance. Therefore, this focusing yields small illumination of the
duct. This study has sequence stages identical to those in case A and starts with a TEoi
source, an imaginary hom, having the dimensions o f a 1 cm square. The Rayleigh length
using this hom dimension is about 6 cm. The propagating region in stage 2 was set to 10
cm. Figure 3.13 displays the field profiles produced with this setup. It can be seen in
stage (0,1) that more of the beam enters the duct however in stages (1,2) and (2,3) more
nodes and peaks have formed than in case A. In this case study, the H-plane appears to be
more disturbed in case B. In figure 3.12(b), the phase front displayed at a minor radius of
8 cm shows a slightly convex phase front 1 to 1.2 cm wide with larger side-lobes than in
case A. Truncation losses at the slot entrance and transmission through the slot in case B
brought the signal power down to about 0.858 mW. Therefore to summarize, the power
transmitted through the duct is 86% of the source power and the phase front is "slightly
convex" and about 1.2 cm wide.
3.3.2 Results from Case A and B Studies
The results of the large and small illumination study were critical in setting the focal
length parameter of the port lens. Considering the phase front was flatter in case A (large
illumination) and because it was thought that the reflected power would still be at a
workable level, the large illumination setup was initially chosen, and installed in the top B
port was a port lens with a focal length of 65 cm.
A general trend, however, shown in the MTH results indicated that the larger
illuminating setup had an initially flatter phase front but at positions further into the vacuum
region the small illumination became flatter. This was derived from measurements at minor
radii of 6.5, 8, and 10.5 cm. At a radial position of 6.5 cm, case A was slightly concave
and case B convex and at 10.5 cm, case A produced a rounded (convex) phase front and
case B a fairly flat phase. Therefore, when closer to the duct exit, case A is a better choice,
but for longer propagation into the plasma, case B may work better.
62
The phase front and power return were the competing factors of this study. In
terms o f power transmitted into the system small illumination was certainly more attractive
than large illumination. Case B transmitted 8 times more power into the duct than case A.
However, recall the MTH code did not calculate return power but transmitted power, so
this value may be deceiving when scattering at the reflective layer is considered.
3. 3. 3 Side-Lab Results of MTH Study
Case studies A and B were also the subject of sidelab experiments using the x-y
scanner to measure field profiles at the exit of the duct. In the sidelab, the setup was
similar to figure 3.6, however, using one transport lens and no window. Also note, the
sidelab slot had dimensions 3 cm x 12 cm x 14 cm, therefore, had a larger cross section
and was shorter than the actual MTX port duct. Figure 3.14 compares case A (large
illumination) and case B (small illumination) at (a) 4 cm, and (b) 8 cm behind the duct. In
figure 3.14(a), case A and B profiles have a dip at the center o f the signal. In case B, the
dip measures about -4 dB and in case A, -2 dB. In figure 3 .14(b), the profiles have calmed
down and it appears that case B may be misaligned. The profile in case A by 8 cm is well
defined.
63
f ie ld
m a g n itu d e
f ie ld
•
J b S lp ll
m a g n itu d e
• M l* -
1 1 .0 4 4 1
field magnitude contours
•col*- S.0612
c o n to u rs
(0 , 0 )
•c o l* - 10.5000
c o n to u rs
f ie ld
(1,2)
8
J * 51p l t
m a g n itu d e
M o l * - B.6 0 9 0
(0,1)
c o n to u rs
(2,3)
2 l.-j j .u .— t :
»
-m u n
-o jts x
o jjx o o
o.m
Figure 3.10: The radiative contours from the MTH code for the large
illumination case A study. Refer to figure 3.9 for position
of stage numbers (0,0), (0,1), (1,2) and (2,3). Stage (2,3)
is at a minor radius of 8.5 cm
64
f i e l d m agnitude co n to u rs
>51*11
•caiv 9.3621
vcrl. d-^i j
Ve»-Vic<xl
V<e*uJ
§:
phase contours
RrtlpU
gj
fieLd mognutude contours
>SlpU
tcoir 9.3621
Kor i
{t
£> *'
^
ObS
4.H
.113
M
Figure 3.11: Vertical and horizontal planes exiting the duct for case A.
65
JbStpLt
ot j -
0.030
field phase
Case A
.
44
0*01
J b S lp U
ot * *
0.0 3 0
f ie ld
phase
Case B
■O.OJ
Figure 3.12: A comparison study of the phase front in case A and B.
Results are from the MTH code.
66
field magnitude contours
•ml.*' 10.5000
f ie ld
(0,0)
m a g n itu d e
c o n to u rs
• o o l v 14.0744
(0,1)
9
[VS
9
f i e l d
> 5 1 pit.
m a g n itu d e
•eat*-* 24.1788
c o n to u rs
f ie ld
Jb 5 1 p lt
m a g n itu d e
c o n to u rs
H9oL«- 20.8068
Figure 3.13: The radiative contours from the MTH code for the small
illumination case B study. Refer to figure 3.9 for position
of stage numbers (0,0), (0,1), (1,2) and (2,3). Stage (2,3)
is at a minor radius of 8.5 cm
67
BERM S I Z E IN CM
F - P L R N E BERM PRTTERN
CA S? A
(a)
x>
*o
I
O'
Ul
X
o
1.1111 I I I I I
Ul
i i >| m i | i * r i |
i-gi i
- io
i j i I i i i l l .1 i i i
IT 1 1 1 1 1 1 1 1 1
-s.e e
-4 .M
-3 .0 0
-e .e e
-i.e e
-v e.ee
fi.e e
+ 3 .00
-» e.ee
-K .e e
* e .e e
DISTANCE. IN CM
BERM S I Z E IN CM
E - P L R N E BERM PRTTERN
1 1 1 1 r 11
n
111 1 r
i I 11 1 1 1 1 1 1 1 11 1 i r i i i i i
r n
O t> E A
(b )
.0
-o
Ul
X
o
a
ui
>
<r -5.ee
■iitiiitt
-4 .e e
-e .e e
-r.e e
-i.e e
fe .e e
|
d
o:
fi.e e
11 1 1
I
-fr.e e
11 1 1
-* 3 .ee
| - 11
1
<j
f5 .e e
-K .e e
1 111
-io
-re
■■
-s.e e
*./TT 1 1 1 1 1 1 1 1 1
—
—»
-4 .e e
-
3.00
-r.e e
-i.e e
-*e.ee
-fi.e e
fz .e e
f3 .e e
f4 .e e
f5 .e e
DISTANCE IN CM
Figure 3.14: A comparison of case A and B using the x-y scanner. The
h^hinrf
.” !? duct.
P05"10"*11 al <a> 4 cm and (b) 8 cm
behind K
the° sidelab
68
3 .4
The Reflectometer on MTX (no plasma)
An overall diagram of the MTX setup was presented in section 3.1. General
comments regarding the operation of the reflectometer, and additional information in
regards to its setup in the vault are presented in this section. Section 3.4.1 will detail a
sensitivity study o f the system and note how it is aligned. Then section 3.4.2 will close
this chapter by displaying non-plasma operation o f the reflectometer system on MTX.
3. 4.1 Sensitivity of the Reflectometer Set-up on MTX
Section 3.1.1 presented an overview of the losses which were encountered by
transporting the reflectometer microwave signal through the quasi-optical relay path on
MTX. This section is intended to give further detail on that discussion. Table 3.2 lists the
power return at specific points in the setup of the reflectometer shown in figure 3.5. These
measurements indicate where losses appear through the transport system.
At the focal point of the first transport lens, the power return, considering the
values dated 7/91 measured from a flat reflector, was -12 dB, +38 dB above the
background value o f -50 dB. Between lens 2 and 3, a signal of +30 to +36 dB above
background was reflected. Note, using the measurements from 4/92, die power return
could increase when focusing the signal more tightly, as from the second transport lens,
and produce a larger signal return. Between lens 3 and the port lens fewer measurements
Point of Measurement
dB (6/91)
Focal point of lens 1
dB (7/91)
Volts (4/92)
-12
1.25
1.36
Focal point o f lens 2
-7
-14
Behind lens 3
-14
-18
Clear transport (off tokamak wall)
-33
-28
0.7
Background (off absorber)
-37
-50
0.22
Table 3.2:
Power return through the reflectometer setup.
69
were taken because this focal point was not easily accessed. The measurements listed as
behind lens 3 were after the first turning mirror in the top B port layout. This was not at
the focal point. It can be noted, however, that the value at the focal point would yield less
than 4 to 7 dB in losses. Through the entire system into the port, the reflected power from
the inner tokamak wall plus spurious signals, ranged from zero to +22 dB above
background; a common IF power return being less than half a volt. At different transmit
frequencies, the power o f the transmit signal would vary. This variation was from about
0.8 to 0.4 mW. Along with the initial variation in power, the propagation of the signal
through the system, losses in the duct and through the lens, and its ability to reflect from
the inner tokamak wall also varied.
Alignment of die transport system on the MTX tokamak was done using a small
HeNe laser placed on the railing in front of the optical coupler. The laser beam was
positioned to be at the center point of the microwave signal. Pinhole targets replaced lenses
in the lens holders, and by using the laser, midpoint positioning of the lens was checked.
The beam traveled through the pinholes and turned at the appropriate m inor or minors to
the vacuum window where a reflector was placed. Good alignment meant the laser beam
was able to retrace itself through the pinholes towards its source. Also, the positioning of
the laser beam was checked to be located at the center of the vacuum window. If this was
not the case, the turning mirrors were adjusted and the alignment rechecked. In coming
through the top port, the centerline of the tokamak is 1 degree offset from the centerline of
the entrance. This also was taken into account when aligning the reflectometer system.
3.4.2 Non-Plasma MTX Operations
The intent o f showing non-plasma reflectometry data is to display what would be
detected if the return plasma signal were solely the product o f reflecting from stationary
objects like a flange, or from spurious signals from lenses and the window. The two shots
displayed in figure 3.15 pertain to non-plasma motion during a regular MTX shot Plots
70
(a) and (b) were taken using a flat reflector in the path o f the microwave signal In (a) it is
mounted behind lens 2 on the railing between the wall and the tokamak, and in (b), the
reflector was laid over the port entrance. The motion seen in these plots would then
correspond to tokamak induced motion horizontally in (a) and vertically in (b). The
transport lenses are placed horizontal with respect to motion o f the tokam ak, so if the phase
measurement were locked on a spurious signal from these, it would note motion similar to
that o f plot (a). If the return signal was actually from the port flange from the top B port,
vertical with respective to the tokamak, it would yield motion like that seen in plot (b).
Chapter 4 will show that this was not the case.
(<X )
r f I C21
SHOT
1 1 4 9 6 mtmrt t t r n *
im 0
-3 t
-5
Q
S
10
13
rflC 10J
rFlC Sl
SHOT
20
23
seconds
30
33
40
45
30
40
43
30
X 1 0 ^ -2
11499 • i s r t
*.i
-7
-e-
-3
0
3
10
15
rf1C l0]
20
25
seconds
X 10~ -2
Figure 3.15: Non-plasma reflectometry data obtained during normal
MTX operations.
CHAPTER IV
EXPERIMENTAL RESULTS
Despite its short utilization, the reflectometer observed some interesting plasma
effects where operation and plasma disturbances induced modem. Results represented in
this chapter include shots taken while operating the reflectometer during several MTX
experimental physics runs. Chapter 4 is divided into three sections. Section 4.1 describes
shots which illustrate the reflectomcter's ability to accurately probe the plasma. Tests o f
plasm a sensitivity in this section include detection of the plasma cutoff density, an FIR
interferometer and reflectometer comparison, and detection o f large plasma motion.
Section 4.2 analyzes shots containing plasma disturbances, specifically plasma oscillations
and disruptions. Then section 4.3 will discuss conclusions drawn in the previous sections.
For a description o f other diagnostics mentioned in this chapter, refer to section 1.2.3.
4 .1
Validity o f the Reflectom eter
Many tests o f the reflectometef’s general performance have already been detailed in
Chapter 3, however in the following section o f Chapter 4, these tests pertain to the
reflectomcter's ability to monitor plasmas. Chapter 3 concluded that the reflectometer setup
could produce accurate measurements o f phase from which the position o f the cutoff
density could be inferred. In this section the use of the re flee tome try system on the
tokamak will be discussed. Recall that the possible limitations noted in Chapter 3 were low
71
72
power return and curvature of the phase front. These need to be avoided in order to receive
a reliable phase measurement. Also, hazards such as large magnetic field effects on
instrumentation, spurious signals, and poor alignment needed to be quickly detected and
then carefully corrected.
4 .1 .1 Sensitivity to Cutoff Density
A reasonable test of the reflectomcter's performance is to analyze its sensitivity to
the cutoff density. Recall the value o f the cutoff density is set by the incident microwave
frequency in ordinary mode. Before the plasma reaches this critical density, the incident
microwaves reflect off the inner wall o f the tokamak. Upon reaching the critical density,
the reflectometer signal then begins to monitor motion at the cutoff density layer.
An ideal case picturing the phase difference measured by the reflectometer
throughout a shot is displayed in figure 4.1. This drawing shows a density profile, the
return power of the reflectometer plasma signal, and a phase measurement detected by the
Density
n CO
Reflected Power
'A y '
!
Phase
a: off wall
---- b: refraction
c: build up
j
d: equilibrium
a 1 1>| V|-------------------- d______________
Figure 4.1:
Displayed is an ideal profile of the reflectometer phase
measurement throughout the shot.
73
reflectometer. The regions listed in the figure are described below,
a.
The reflectometer signal is reflecting from the inner wall o f the tokamak and
in this interval, the plasma density is much lower than the cutoff density.
b.
The plasma density has increased and strong refraction o f the microwave
signal is observed. The refraction causes a loss of reflected power plus
fringing of the reflectometer phase measurement
c.
The critical density layer is present in this region and the microwave signal
is reflecting from this cutoff density. The plasma is in the build-up or in
the decay stage, therefore, the reflected power and phase measurement are
changing.
d.
The reflective plasma layer is in an equilibrium position and fluctuations, if
present, are observable.
Considering the onset of the cutoff density layer, regions a through c, figure 4.2
displays two shots, 12353 and 13732, which detail the two types o f onset noted by the
reflectometer. Shot 12353, which will be further analyzed in section 4.2, shows an almost
immediate change in the reflectometer signal while shot 13732 clearly illustrates the onset
o f signal variation when the density reaches the critical density value. In shot 12353 the
critical density is 1.15 xlO20 m '3 corresponding to a frequency setting o f 96.7 GHz. The
FIR interferometry line data can be used to determine the presence o f the cutoff density
layer by plotting the line densities at a specific time, then obtaining a radial density plot and
deteimining if the peak density equals the critical density. Using this method, a critical
density value o f 1.16 xlO20 m '3 is reached at 0.067 seconds in shot 12353. The density
profile determined by the interferometer noted a well centered profile with a alpha of about
0.2. At 0.067 seconds in shot 12353, shown in figure 4.2(a), the phase data develops
larger oscillations corresponding to the presence of a cutoff density layer.
With the delayed onset in shot 13732, from the reflectometry data in figure 4.2(a),
the critical density o f 1.19 xlO20 m '3 corresponding to 98 GHz operation is reached at
approximately 0.046 seconds. This value can be verified using the FIR interferometer line
74
(a )
PHASE,
SHOT = 1 23 5 3 , 1 3 7 3 2
13732
r
-1
-2
o.oo
0.02
0.04
0.06
0.08
0 .1 0
0.08
0.10
TIME (SEC)
CENTER LINE DENSITY
20
5.0x10
0.00
0.02
0.04
0.06
TIME (SEC)
Figure 4.2:
The onset time of the critical density is shown in (a) the
reflectometer plot and (b) the FIR interferometer plot for
shots 12353 and 13732 (dashed line in plot b). The phase
data in 13732 is offset by +1.2 volt so as not to
overlay with 12353.
densities to determine when the peak density matches to critical density.
11118
time
was calculated to be 0.041 seconds. Figure 4.2(b) displays the line averaged density
during these shots at a minor radius near zero. This center line density is a chord
positioned near the geometrical axis which is scaled to give the peak density if the density
profile is parabolic and the plasma is not offset radially. In the shots displayed, 13732 is
offset about 4.0 cm and in 12353 by 0.1 cm. Therefore, the center line density does not
exhibit the appropriate peak density for shot 13732 because of the large offset.
An explanation for the immediate phase change in the reflectometry data at the onset
of the plasma, can partially be drawn from theory that was discussed in Chapter 2, and by
considering refraction o f the microwave signal. Recall in theory, the following equation
75
for the phase shift (O),
0> = 2 ^ - J i l ( r ) d r
(2.15)
induced by a change in the index o f refraction (T|(r)),
1tfr) = - ^ l - b ( l - ( r / a ) 2)*
(4.1)
where the density is modeled by equation 2.6 and b is a product o f constants, at some
specified time. As soon as the index of refraction changes with the presence of a plasma, a
phase shift is induced as the microwave signal transverses the plasma, reflecting from the
inner tokamak wall. The index of refraction through which the probing microwaves travel
changes as the plasma is developing. This change is in the b term which includes the value
of the peak plasma density. These microwaves are damped in the plasma and sense
immediate changes in the index o f refraction. This corresponds to a change in phase, thus
explaining shots which respond immediately to the plasma.
The interferometric measurement just described, however, is only valid at much
lower densities than the cutoff density. Recall, from the ideal case, that refraction o f the
microwave signal is also a possible explanation for immediate onset The plasma acts as a
defocusing lens, and the microwave signal is scatter when transversing the plasma. This
effect would induce fringing o f the phase measurement and should easily be seen in the
reflected power. However, if the return signal is not from the inner tokamak wall
transversing the plasma, but a spurious signal, the power may remain approximately
constant. This was observed in some reflectometer shots. Some shots showed an initial
decrease in power which indicates refraction, but in other cases, the power return would
remain constant or increase immediately to a power level approximately equal to that seen
later from the cutoff density layer.
76
Comparing the delayed onset shot 13732 to 12353, they initially differ in that
13732 is set at the least sensitive prescale option (+32), while 12353 is at the most sensitive
setting (+1). The divide-by 32 prescale option renders a less sensitive measurement of
phase variation and this begin to indicate why the onsets differ. The following statements
are based on a general survey o f shots used to determine any particularity that may explain
why there are two types of onset for the reflectometer.
1.
Quickly ramping densities, those greater than 1020 m '3 at 0.05 seconds into
the shot, resulted in an immediate onseL Shots with slower ramping
displayed both delayed and immediate onsets.
2.
Shots from the top B port showed solely immediate onset. This could be
due to higher density operations.
3.
Some shots display something in-between, that is a jumpy delayed onset
4.
Consecutive shots which switch between the immediate and delayed onset
were usually consecutive shots in which the frequency of the probing
microwaves were changed. The density profiles often remained unchanged,
and the return signal power also may or may not have changed.
5.
One possible explanation for delayed onset is that spurious signals lock the
phase measurement until a larger reflected plasma signal from the cutoff
layer appears. The phase would then abruptly change to measuring plasma
motion.
Statements 1 and 2 most likely are the result of differences in the plasma growth,
peaking of the density profile, which is dependent on OH current ramping. Statement 5
can be identified with the power return of the signal, and in analyzing this statement, it was
found shots with delayed onset increased or decreased in power at the beginning of the
shot. However, the IF returned power, like that in shot 13732 displayed in figure 4.3, also
reveals a second increase in power simultaneous with plasma oscillation. In figure 4.3, the
power jum ps about 0.2 volts at the beginning o f the shot and then, at about 0.045 seconds,
the power increases a little more. This second increase coincides with the oscillating phase
77
IF REFLECTED POWER (R F L f3 l),
Shot = 13732
0 .6 0
0 .5 0
0 .4 0
0 .3 0
0.20
0 .1 0 0.00 _
-0 .0 5
0 .0 0
0 .0 5
0 .1 0
0 .1 5
0 .2 0
TIME {SEC)
Figure 4.3:
The IF power return of a delayed onset shot 13732.
measurement from the plasma. Therefore, in this case, the return signal increases in power
at the initiation of the plasma, however, this is a saturated signal that is not monitoring
plasma motion. The presence of a return plasma signal from the cutoff layer also increases
the power return, superseding any spurious signals, and monitors the plasma motion.
In either case, the reflectometer does monitor the critical density layer in all cases,
illustrating clearly when the density falls below the cutoff. Shot 13982, shown in figure
4.4, is a typical example of a case where the center line density levels off to a value below
the cutoff density of the reflectometer and the phase measurement resulting in a flat signal.
Table 4.1 lists information corresponding to figure 4.4. In Table 4.1, the FIR
interferometer peak density values are listed as well as the position o f the critical density
layer determined from a radial density plot at the time specified.
78
1 .5 x 1 0
cn
E
i—
t
,20
CENTER LINE DENSITY (FIR_NBAR)
SHOT= 1 3 9 8 2
1.0x10 20
- 5 .0 X 1 0
o.oo
o.io
0.20
0 .3 0
0 .4 0
0 .5 0
0 .4 0
0 .5 0
TIME (SEC)
PHASE (RF1 8 2 1 0 )
0.00
0.10
0 .2 0
0 .3 0
TIME (SEC)
Figure 4.4:
Displayed is shot 13982 in which the critical density layer
is only present for an intermediate time between 0.033 to
0.217 sec.
Shot 13982
Time (sec)
n o t l ^ m * 3)
nco Position (cm)
(1)
0.02
0.28
not present
(2)
0.033
0.75
4 (offset, 4 cm)
(3)
0.05
1.56
10
(4)
0.10
2.15
11
(5)
0.15
1.11
9
(6)
0.217
0.75
-1.5 (offset, -1.5 cm)
(7)
0.25
0.70
not present
Table 4.1:
A list of values pertaining to figure 4.4 for shot 13982.
The cutoff density, nco, is equal to 0.75X1020 m*3.
79
4 . 1 . 2 Sm ooth P lasm a M otion
A brief study which compared the radial motion as measured by the FIR
interferometer and the reflectometer is shown in figure 4.5. The FIR interferometry data
was obtained as follows:
1.
The FIR interferometry data was corrected for single fringe jumps.
2.
Multiple fringe chords which upset the inversion process were deleted.
3.
A full time history analysis was then performed. This is where single time
slices of the data are consecutively taken, resulting in time plots of the peak
density (np), shaping parameter (a), offset (5x), and the standard deviation.
4.
Rearranging the density profile, equation (2.6), to
(4.2)
where a(t) = 16.5 - I6x(t)l, and nc0 is the cutoff density, resulted in a time
plot of the radial motion o f the cutoff density layer in cm.
In shot 11864, shown in figure 4.5, plot (a) shows the radial motion o f die density
layer, 0.81 xlO20 n r 3, calculated using the FIR interferometry data. This plot is smooth
and reveals less than one centimeter motion throughout the steady-state region of the shot
The reflectometer plot, 4.5 (b), shows less than two millimeters motion and at this
magnitude the information may actually be noise on a smooth measurement However, it
was expected that the reflectometer measurement o f relative motion should be less than the
interferometer due to geometrical reasons. The reflectometer is probing vertical motion of
the plasma and the interferometer probes horizontal motion. Vertical motion is expected to
be less than horizontal motion.
With this study, only smooth shots could be analyzed due to multiple fringe shifts
encountered in the interferometry data. Shifted line density data had to be deleted from the
inversion and in shots where there were plasma oscillations, too many chords had to be
thrown out and the inversion became unreliable.
80
FIR Cutoff P osition
( n=
0.813 5 6 4 ( x « 2 0 m-3) , Shot=
11664
18
c
16
m
14
12l_
0 .0
0 .4
0 .2
0 .6
Time (seconds)
RFL Radi s i Motion ( » d i v i d e - b y )
- 0 . IOC
- 0 .1 2 -
-0 .1
0 .0
0 .2
0 .4
0 .6
Time (seconds)
Figure 4.5:
Shot 11864, comparison of radial motion as measured by
the (a) FIR interferometer and (b) the reflectometer.
4 .1 .3 Large Scale Plasma Motion
Due to a vacuum leak on July 9, 1991 plasma operations where affected for the next
few days. The leak resulted in higher than norma] levels of water vapor in the tokamak and
residual wall contamination. The poor wall conditions affected operation o f the tokamak
both on the 10th and somewhat less on the 11th o f July. As a routine clean up operation,
the tokamak was operated with a toroidal field of 6.5 Telsa and worked down to the more
difficult 5 Telsa operation. The resulting plasmas were often ill-behaved, but these resulted
in interesting shots and gave the reflectometer a good tokamak test
Three back-to-back shots, 11858,11859 and 11860 are shown in the figures 4.64.8. These are high density "clean-up" shots. In 11858, the first plasma shot of the day,
81
the feedback control of the positioning of the plasma was having difficulty centering the
plasma. With these conditions, the normal feedback gain was overcompensating for
plasma oscillations which pushed the plasma into the limiters which resulted in plasma
generation o f wall impurities. This condition is often typical of operations while the walls
are cleaning up. In shot 11859 the feedback chassis gain had been adjusted but because the
density was lowered again in 11860 the same problem as in 11858 was encountered.
Figures 4.6 • 4.8 each display four data plots from, (a) the reflectometer, (b) the
horizontal and (d) the vertical position loops, and (c) the FIR interferometer. The position
loops were described in section 1.2.3 and plots (b) and (d) differ in the direction in which
they monitor position and also in the method by which their data is analyzed. Recall
CNTLP refers to "control" loops which are control room signals that are integrated by a
hardware integrator and LOOP refers to data acquired in the vault and later software
integrated. The CNTLP data is usually more reliable since it is uses in the feedback system
to position the plasma. Considering these points, a comparison o f the reflectometry data to
that o f the positions loops can be presented.
Shots 11858 and 11860 show large position oscillations at a frequency varying
between 50 and 100 Hz. Shot 11859 is fairly smooth. The reflectometer was set at 81
GHz and to view vertical plasma motion. The reflection point occurred roughly at a density
layer o f 0.8 xlO20 m '3 corresponding to the outside edge o f the plasma. The reflectometer
signal matches the shape of the horizontal position loop motion and the FIR outside line
density exactly. However, in magnitude, the motion measured by the horizontal loops
roughly indicate position changes on the order o f one centimeter. The reflectometer shows
about 0.5 volts phase change which would correspond with a fraction of a millimeter
motion. The magnitude o f motion shown by the reflectometer matches the vertical position
loops. The reflectometer, therefore, is very sensitivity to density profile perturbations
induced by large horizontal oscillations within the magnitude expected of vertical motion.
82
This excellent correlation between the position loops and the reflectometer demonstrates
that the reflectometer can accurately diagnose plasma oscillations.
The vertical perturbations sensed by the reflectometer are possibly the result o f the
limiters scraping off plasma. As the plasma is pushed towards the wall, fuel is deposited
into the limiters which then alters the plasma profile producing plasma variations.
Analyzing the density oscillations shown in the interferometer line densities for shots
11858 and 11860, the line densities in each shot simultaneously exhibit increases and
decreases in density, therefore, demonstrate shape variations. The horizontal motion could
thus be resulting in the scrape off of plasma which changes the density profile producing a
poloidal perturbation which is measured by the reflectometer. The density is rattling up and
down due to plasma scrape off and re-ionization. Therefore, this would imply the
reflectometer senses not just motion but also profile changes.
83
PHASE (R F L J 3 2 1 0 ),
SHOT = 1 1 8 5 8
-1 .4
-1.6
-2.2
-2 .4 ?
-2.6 E
0 .0 0
0 .1 0
0 .2 0
0 .3 0
0 .4 0
0 .5 0
TIME (S E C )
HORIZONTAL POSITION (C N TLP-PO S-H O R IZ)
-21 —
0.00
0 .10
0.20
0 .3 0
tim e
0 .4 0
0 .5 0
(s e c )
LINE DENSITY ( f ir [ 2 ] )
(M
0.0
0.00
0. 10
0.20
0 .3 0
0 .4 0
0 .5 0
TIME (S E C )
VERTICAL POSITION (LO O P-PO S-V ERT)
0.6
0 .4
0.2
0.0
-0.2
- 0 .4
-0.6
0.00
0.10
0.20
0 .3 0
0 .4 0
0 .5 0
TIME (S E C )
Figure 4.6:
A comparison of (a) reflectometry, (b) and (d) position
loop, and (c) line density data for shot 11858. This
comparison of large plasma oscillations favorably shows
the reflectomcter's sensitivity to plasma motion.
84
PHASE (R F L _ 8 2 1 0 ),
SH 0T = 11 8 5 9
- 1 .4
-1.6
-1.8
in
p**
6 -2-0
>
-2.2
0 .0 0
0 .1 0
0 .2 0
0 .3 0
0 .4 0
0 .5 0
TIME (SE C )
HORIZONTAL POSITION (CN TLP-PO S-H O RIZ)
-2
0 .0 0
0 .1 0
0 .2 0
0 .3 0
0 .4 0
0 .5 0
0 .4 0
0 .5 0
* 4 , 6 4 6 9 6 0 e + 19)1 / m
TIME (SEC)
LINE D ENSITY ( f i r f 4 p
2.0
1.0
0.5
0.0
0 .0 0
0 .1 0
0 .2 0
0 .3 0
TIME (SEC )
VERTICAL POSITION (LOOP_POS_VERT)
0.6
0 .4
0.2
0.0
-0.2
-0 .4
-
-0.6 L
0 .0 0
0 .1 0
0 .2 0
0 .3 0
0 .4 0
0 .5 0
TIME (SEC)
Figure 4.7:
A comparison of (a) reflectometry, (b) and (d) position
loop, and (c) interferometer line density data for shot
11859.
85
PHASE (RFI
8 2 1 0 ),
SHOT= 1 1 8 6 0
- 1 .4
-1.6
-2.2
- 2 .4 V
-2 .eL .
0.00
0.10
0.20
0 .3 0
0 .4 0
0 .5 0
TIME (SE C )
HORIZONTAL POSITION (CNTLP_POS_HORIZ)
-2
0 .0 0
0 .1 0
0 .2 0
0 .3 0
0 .4 0
0 .5 0
0 .4 0
0 .5 0
TIME (SE C )
LINE DENSITY ( f i r ^ l )
3.9509J4e+19)1/
"e
1.0
0.6
0.6
0 .4
0.2
* 0.0
0 .0 0
0 .1 0
0 .2 0
0 .3 0
TIME (SE C )
0.6
VERTICAL POSITION (LOOP_POS_VERT)
0 .4
0.2
0.0
-0.2
-0 .4
-0.6
0.00
0.10
0.20
0 .3 0
0 .4 0
0 .5 0
TIME (SE C )
Figure 4.8:
A comparison of (a) reflectometry, (b) and (d) position
loop, and (c) interferometer line density data for shot
1I860.
86
4 .2
Disturbances in the MTX Tokamak
A multi-chard interferometer monitors the plasma profile but it does not detect
localized oscillations, nor is it customaiily used to study turbulence. In the study of
turbulence, many established diagnostics monitor temperature oscillations, such as the soft
x-ray diagnostic and ECE (electron cyclotron emission) polychromator, but few are
established to study oscillations in plasma density. This has resulted in a better
understanding of energy transport than particle transport. The intent of reflectometry is to
detect and measure density fluctuation, thus emulating the use of the polychromator with
respect to temperature. Results from the reflectometer shown in this section comprise
information that could be extracted from several other diagnostics. Observed will be
oscillations most likely due to impurities affecting the plasma profile and disruptions.
Therefore, the reflectometer will be displayed with a host of other diagnostics. At the end
o f Chapter 4, there ate shot reviews (a full time display o f eight distinct plasma parameters
of a particular shot) for shots analyzed in sections 4.2.1 and 4.2.2, to detail the condition
o f the discharge during the entire shot and for purpose of comparison.
4. 2. 1 The Detection of Plasma Oscillations
Perturbations in the plasma density were detected by the reflectometer in all stages
o f the discharge. They were observed in the first 100 msec during the ramp-up stage,
during the steady-state or flat top region, and near the end of the discharge. Bursts of
impurities or some type of density perturbation were observed in reflectometry data as an
oscillatory change. Shots 12416 and 12353, which will be analyzed in this section, note
changes in oscillation at the middle (12416) and the end (12353) o f the shot. These
particular shots were taken on the 12th and 11th of September 1991 during a plasma
cunent-ramp experiment. The reflectometer at this time was aligned to observe vertical
87
plasma oscillations, entering the tokamak from the top B port. On both days the operating
microwave frequency was 96.7 GHz; therefore the cutoff layer corresponds to a density
layer of 1.15 x 10^0 nr-*.
A specific comparison of data plots for shot 12416 is shown in figure 4.9. FIR
interferometer line densities were first used to obtain the radial position of the cutoff layer.
PHASE (RFI
8 2 1 0 ),
SHOT= 1 2 4 1 6
- 0 .5
-1.0
§
-2.0
- 2 .5
0 .1 0
0 .2 0
0 .3 0
0 .4 0
TIME (SEC)
VISIBLE BREMS. (BREM_VBREM__2)
600
400
200
<
-2 0 0
0.10
0.20
0 .3 0
0 .4 0
TIME (SEC)
LINE DENSITY (F IR fl3 l^
to
X o.o
w
0 .1 0
0 .2 0
0 30
0 .4 0
TIME (SEC)
Figure 4.9:
A comparison of the (a) reflectometer, (b) visible
bremsstrahlung and (c) an interferometer line density for
shot 12416. The signal VBREM_2 and FIR[13] are at a
minor radius of 10.5 and 10.25 cm, positioned on the
inside region of the tokamak.
88
This radius is needed to determine which chords of diagnostics like the soft x-ray and
visible bremsstrahlung to p lo t Figure 4.9 displays the reflectometer, visible
bremsstrahlung and FIR interferometer data from 0.1 to 0.4 sec into the shot. The region
o f interest is between 0.22 and 0.28 sec. During this 60 msec interval, the reflectometer
data swells and large oscillations of differing frequency. H ie reflectometer was at its most
sensitive setting, therefore, this motion is very small in magnitude. The visible
bremsstrahlung matched the reflectometry data well. The visible bremsstrahlung inside
chord (VBREM_2) at -10.5 cm shows an increase in radiation during this interval. The
outside chord (VBREM_12) at +10.5 cm (not shown), however, shows no resemblance to
the reflectometry data or the inside chord. The FIR interferometer line densities for shot
12416, shown in figure 4.10, display fringing and oscillations during this time interval on
both the inside and outside chords. At a minor radius near 10 cm, the outside line densities
either decrease or experience a fringe shift, while the inside chords, such as chord 13
displayed in figure 4.9(c), appear to increase in density. Therefore, the bremsstrahlung
radiation and density are increasing on the inside, and no radiation and a density decrease
appear on the outside region of the tokamak during this interval. From the SPRED
(Spectrometer Recording Extended Domain) data in this interval, there appears to be no
increase in impurities. The visible radiation would then have to come from the plasma
itself, possibly a cold packet o f plasma centered on the inside o f the tokamak. The
description of this perturbation matches that of a MARFE discussed in section 1.2.2 where
there is a large amount o f asymmetric radiation, an increase in density, and decrease in
temperature, all centered in the upper inside region of the tokamak. It makes sense that a
poloidally symmetric plasma ring would be affected, and because the cutoff layer of the
reflectometer is positioned at around 11 cm and in this ring, the reflectometer is measuring
this disturbance. Also from the full diagnostics display, figure 4.15, during this interval
the soft x-rays disappear and no MHD activity is seen. The x-rays are noticeable between
0.05 and 0,23 sec and fall off right before the increase invisible bremsstrahlung.
0.187500
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Figure 4.10: A display of FIR interferom eter line densities data for shot 12416.
oo
VO
90
In shot 12416 only the slow recorder acquired the disturbance being analyzed.
However, in shot 12353, shown in figure 4.11, data acquisition on both reflectometer
recorders was obtained with the faster recorder operating at 200 kHz. Figure 4.11 of shot
12353 shows distinct multi-frequency oscillations, less than 2 kHz, between 0.42 and
0.435 sec about 0.020 sec before the end of the shot. This is a precursor o f the oscillatory
ending that this shot exhibits. A minor radius o f 7 cm for the position of the cutoff layer
was determined at 0.4 sec. At this time the density profile was offset toward a smaller
major radius by -1.38 cm. Nearer to the end o f the shot, the plasma was further offset
inward to about -3 cm at 0.44 sec. The reflectometer was operating at 96.7 GHz, cutoff
density of 1.15 xlO20 n r 3. Using this information, an inside soft x-ray chord was chosen
at a minor radius o f -5.01 cm and visible bremsstrahlung chord at a radius of -6.4 cm, to be
plotted alongside the reflectometer data in figure 4.11. Again, in this shot, the
reflectometer data compares well with the visible bremsstrahlung plot. The match,
however, is not exact, but the visible bremsstrahlung lags the reflectometer in time. In
these plots the reflectometer oscillation commences prior to an increase in visible
bremsstrahlung radiation and dies down as the visible bremsstrahlung peaks. No match is
noticeable with the FIR interferometer data because at late times in a shot the interferometer
tends to fringe and lose track o f the density. In this particular shot, the FIR interferometer
shows no signal after 0.41 sec. Thus, the FIR interferometer data does not carry this
ending information, and neither does the SPRED diagnostic which measures impurity
concentrations. The SPRED diagnostic was set to view a 400 msec shot. The x-rays are
included in this comparison because, as in shot 12416 and other shots showing
disturbances, they died out in a timely fashion just before the reflectometer oscillations.
The JAERI soft x-rays (not shown) displayed large irregular sawteeth between 0.2 and
0.38 sec, just 0.04 seconds before the reflectometer oscillations. This marks a sequence of
events for these disturbances, the soft x-rays go to zero, the reflectometer oscillates and
simultaneously or adjoiningly the visible radiation increases and peaks. Soft x-rays
91
measure oscillations in the temperature, therefore, this sequence first shows temperature
oscillations and then plasma oscillations along with an outburst in radiation. This sequence
o f events verifies results of transport studies which show that a temperature disturbance is
or can be followed by a density fluctuation. [Sip-90]
^ 0.008
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0 .0 0 6
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0 .0 0 4
SOFT X-RAY (SFX R _2^B ).
SHQT= 1 2 3 5 3
V)
UJ
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<g o.ooo ILI
0 .3 0
0 .3 5
0 .4 0
0 .4 5
0 .5 0
TIME (S E C )
PHASE (RFI 8 8 1 8 )
0 .3 0
0 .3 5
0 .4 0
0 .4 5
0 .5 0
TIME (S E C )
200
VISIBLE BREMS. {BREM_VBREM_4
150
50
0 .3 0
0 .3 5
0 .4 0
0 .4 5
0 .5 0
TIME (SE C )
Figure 4.11: Shot 12353 shows a burst 20 ms before the plasma
terminates. Shown is data from (a) the soft x-ray, (b) the
reflectometer and (c) the visible bremsstrahlung
diagnostics. Reflectometry data was acquired at 200 kHz.
92
4. 2.2 The Detection of Minor Disruptions
Disruptions, which are described in more detail in section 1.2.2, are a phenomenon
in tokamaks that is not well understood. Several hypotheses in regard to what provokes
this event and its formation have been postulated, however there is only modest evidence
supporting any one claim. Characteristics of a disruptive event include: a rapid decrease in
ohmic current, an expansion in minor radius of the electron temperature and plasma
current, hard x-rays disappear, impurities are lost, and the plasma column suddenly shifts
inward in major radius. Precursor MHD activity is not essential though it sometimes
appears.
Disruptions are very noticeable, since they terminate the plasma, thus, it is no
surprise the reflectometer clearly recognizes these events. Three shots analyzed in this
section are 11885, 11873 and 13694 shown in figures 4.12,4.13 and 4.14. Shots 11873
and 11885 are companion shots to those in section 4.1.3, since they were taken on the
same day when the reflectometer was operating at 81 GHz and observing vertical plasma
motion. This frequency corresponds to a cutoff density of 0.81 x lO ^ m '3 . In shot 13694,
the microwave frequency was set at 100 GHz corresponding to a cutoff density of 1.23
xlO20 m '3. The reflectometer setup in this last shot is through the side B port, therefore, it
detects horizontal motion of the plasma.
Shot 11885 in figure 4.12 contains an excellent example o f multiple disruptions.
Recall Hooper's description o f such an event, "Following an initial disruption, current
channel usually reforms at a reduced major radius, and plasma reheats implying that the
flux surfaces have closed. The new configuration is unstable, however, and the channel
disrupts at least once more as the plasma is lost." [Hoo-90] This MTX report on disruption
events postulates impurities play a major role in disruptions. In the case o f shot 11873 and
11885, this is highly possible since the tokamak had experienced a recent leakage problem
and thus had high impurity levels. Figure 4.12 of shot 11885 presents data from the soft
x-ray, reflectometer, visible bremsstrahlung and FIR interferometer diagnostics. Since the
93
reflectometer was operating at such a low frequency at 0.15 sec into the shot its reflective
layer was estimated to be at a minor radius o f about 13 cm. Therefore, V B R E M 13 at 12.6
cm and channel 10 (the outermost chord) o f the soft x-ray diagnostic at 9.42 cm are
illustrated. The reflectometry data in this array o f diagnostics, figure 4 .12(b), clearly
displays a disruption near 0.2 sec, a second dip at 0.27 sec, and consecutive dips or slow
oscillations between 0.295 to 0.33 sec at which time the discharge terminates. H ie soft xray data, figure 4.12(a), shows small but rapid dips early in the shot before 0.07 sec and
these are also seen as small spikes in the visible bremsstrahlung plot. These early
oscillations are not sensed by the reflectometer because o f the large plasma offset (44 cm)
and flat density profile at this time. It is highly possible the reflectometer was not probing
the same region and therefore wasinsensitive to these oscillations. However, the detail
seen by the reflectometer near the first large disruption and afterwards concurs with what is
seen in the interferometer and visible bremsstrahlung plots. The magnitude of vertical
motion sensed by the reflectometer is 1 to 2 mm at a prescale setting of divide-by 8. From
the shot review, figure 4.17, one notable difference from the previously mentioned
disruption characteristics is that little bumps are seen in the plasma current profile,
coinciding with the disruptions. The disruption characteristic, mentioned previously, noted
an increase in minor radius of the plasma current which should correspond to a dip in the
plasma current profile.
Shot 11873 shown in figure 4.13 illustrates the same simultaneous occurrence in
the reflectometer, the interferometer and visible bremsstrahlung results as in shot 11885. A
disruption is clearly visible in figure 4.13 at about 0.2 sec in all the data plots. What is
unique about this shot is that one disruption does not lead to further disruption and the
termination o f the discharge. Instead following the disruption, the plasma stabilizes. Xrays increased showing reheating and the visible bremsstrahlung remains level. The
reflectometer also gives a level signal and an interferometer chord, which appears
reasonable after multi-fringes, shows a stable plasma.
94
A reflectometer setup to monitor horizontal motion of the plasma through the side B
port was installed around shot 13070. Upon moving to the side port much larger motion
was detected along with constant fringe jumping in the phase comparator and mote signal
noise. The major disruption shown in shot 13694, figure 4.14, occurs near 0.22 sec in a
shot that initially appeared quite well-behaved. A shot review comparison, figure 4.19,
showed that up to the point o f the disruption, little activity was seen. In figure 4.14, the
reflectometry data was from the faster recorder operating at 1 MHz which acquired a signal
during the middle o f the shot, thus capturing this disruption. The other diagnostics shown
alongside the reflectometer data in this figure are the soft x-ray (at 9.42 cm), the visible
bremsstrahlung (at 10.5 cm) and the MHD loops positioned at the D-port. The reflective
region of the reflectometer at 0.15 sec was estimated at 10 cm and at this point the density
was well centered in the tokamak. One interesting note is the MHD activity that is seen as a
precursor 3.5 msec before the disruption in the interval between 0.22 and 0.224 sec. The
soft x-rays ceased at the beginning of this MHD activity and a small increase appeared in
the visible bremsstrahlung. The reflectometer in this region ceases fringe jumping and
appears flat. The IF power (from the returned plasma signal) remains high during this
interval and the FIR interferometer verifies the existence of the reflective layer, indicating
that the reflective layer is still present. The flat reflectometer measurement indicates the
cutoff layer is not moving or, perhaps as discussed in section 4.1.1, the plasma signal is
being scattered and a spurious signal is producing this phase measurement. The visible
bremsstrahlung ends the shot with a large burst of radiation.
95
SOFT X-RAY (SFX R _10_B ),
SHOT= 1 1 8 8 5
o .o a
o.oo
o.io
0.20
O.JO
0 .4 0
TIME (SEC )
- 1 .9 0
-
2.00
-2.10
=j - 2 . 2 0
-2 .3 0
- 2 .4 0
-2 ,5 0
0.00
0.10
0.20
0 .3 0
0 .4 0
TIME (S E C )
VISIBLE BREMS. (BREM_VBREM_1 3 )
400
300
i
2 00
100
0.00
0 .1 0
0.20
0 .3 0
0 .4 0
TIME (SE C )
CENTER LINE DENSITY (FIR_NBAR)
2 .5 x 1 0
2-0x10
1 .5 x 1 0
<
1.0x10
r
5 - O x lO 19 —
- 5 .0 x 1 0
0.00
0.10
0.20
0 .3 0
0 .4 0
TIME (S E C )
Figure 4.12: Shot 11885 displays multiple disruption in a shot the lasts
330 ms. For comparison plotted are (a) the soft x-ray,
(b) the reflectometer, (c) the visible bremsstrahlung and (d)
a FIR interferometer line density.
96
SOFT X -R A Y (SFXR—IO—B),
0 .0 0
0 .1 0
0 .2 0
SHOT= 1 1 8 7 3
0 .3 0
0 .4 0
0 .5 0
TIME (SE C )
-1.8
-2.0
- 2 .4
-2.6
0 .0 0
0 .1 0
0 .2 0
0 .3 0
0 .4 0
0 .5 0
TIME (SE C )
VISIBLE BREMS. (BREM_.VBREM._13)
500
400
.
300
200
100
0.00
0.10
0.20
0 .5 0
0 .3 0
TIME (SE C )
LINE DENSITY (FIRf2])
- 0.8
K 0.0 E
0 .0 0
0 .1 0
0 .2 0
0 .3 0
0 .4 0
0 .5 0
TIME (SE C )
Figure 4.13: Shot 11873 detects a disruption at 190 ms which stabilizes
the plasma. Shown are (a) the soft x-ray, (b) the
reflectometer, (c) the visible bremsstrahlung and (d) an
FIR interferometer line density.
97
(a)
^
SOFT X-RA Y (S F X R „1 0 _ B ),
SHOT= 1 3 6 9 4
0 .0 4 0
%
g
0 .0 3 0
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0.020
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111
t
0.010
& 0.000
0 .2 1 6
0 -2 1 4
0 .2 1 6
0.220
0.222
0 .2 2 4
0 .2 2 6
TIME (SE C )
PHASE (RFI 8 8 1 8 )
J*
0.05
- 0 .0 5
0 .2 1 4
0 .2 1 6
0 .2 1 8
0 .2 2 0
0 .2 2 2
0 .2 2 4
0 .2 2 6
0 .2 2 4
0 .2 2 6
TIME (S E C )
VI5IBLE BREMS. (BREM_VBREM,1 2 )
2500
2000
.
1500
1000
500
0 .2 1 4
0 .2 1 6
0 .2 1 8
0.220
0.222
TIME (S E C )
(PULP-MHD-POLOID-ty
(M w #
-2
0 .2 1 4
0 .2 1 6
0 .2 1 8
0.220
0.222
0 .2 2 4
0 .2 2 6
TIME (SE C )
Figure 4.14:
Shot 13694 displays a major disruption which terminates
the plasma at approximately 220 ms. Plotted are (a) the soft
x-ray, (b) the reflectometer, (c) the visible bremsstrahlung
and (d) the MHD position loops.
98
4 .3
Discussion of Results
Chapter 4 was divided into two sections, one demonstrating the capability o f the
reflectometer and the second, illustrating its use in detecting the physical condition o f the
plasma. In section 4.1, the reflectometer data was analyzed for accuracy and sensitivity to
the plasma. Three different tests were discussed and the following observations were
detailed,
The reflectometer illustrated two types of onset when probing the plasma.
One was an immediate onset which is expected from theory, and the second
was a delayed onset which could be explained experimentally. In the delayed
onset, changes in the phase measurements began to appear when the cutoff
layer was established If the return plasma signal was initially the result of
spurious signals before the cutoff layer was present, it could be that not until
the plasma signal reflects from the cutoff layer and increases in power does
the plasma signal supersede this initial spurious signal. At that point, it would
start to monitor plasma motion.
The reflectometer appears to be very sensitive to motion of the cutoff layer.
Large horizontal oscillations in the position of the plasma, most likely due to a
problem with the position feedback gain, were precisely tracked by the
reflectometer. Positioning of the reflectometer in this run was vertical,
however, so the magnitude of motion was very small.
Similarly, from section 4.2, the reflectometer performed well in diagnosing
oscillation in the plasma. In shot 12416, figure 4.9, the reflectometer detected a
disturbance in the plasma which other diagnostics identified to be positioned in an inside
region of the tokamak. The phase difference from the reflectometer indicated small motion,
but it was plainly visible in the phase information. Indentified by the reflectometer and
other diagnostics in this shot was a MARFE [Lip-84]. In shot 12353, figure 4.11, the
reflectometer displayed oscillations before the end of the discharge. Oscillations is 12353
were at frequencies less than 2 kHz and because the SPRED diagnostic, which determines
99
impurity concentrations, does not monitor this late into the shot, the cause of the
oscillations was uncertain. However, the oscillations presented a precursor to the
oscillatory ending which followed 0.02 sec later in shot 12353. In shots 11885 and
11873, figure 4.12 and 4.13, disruptions were monitored by the reflectometer. In both
cases the phase measurements were small in magnitude but clearly detailed the disruption
event. Then in shot 13694, figure 4.14, the reflectometer, set to acquire phase changes at a
rate o f 1 MHz, observes a major disruption. MHD activity was present and the
reflectometer either showed a scattered plasma signal, where the return signal was actually
fixed on a spurious signal, or showed the horizontal motion of its cutoff layer was zero
during this activity. A list o f general comments from section 4.2 are included below.
1.
Oscillations in the phase measurement acquired by the reflectometer compare
well with oscillations in other instruments such as the visible bremsstrahlung
diagnostic and FIR interferometer.
2.
The reflectometer, during high density operations, usually probed the plasma
edge. In this region, it was quite sensitive to bursts and oscillations.
3.
Oscillations noted by the reflectometer, in the shots presented, ranged in
frequency from Hz to kHz.
4.
The reflectometer continues to monitor the cutoff plasma layer through
multiple disruption in a shot.
5.
Motion, while viewing the plasma vertically, was always in the mm or less
range. In the horizontal direction, the phase difference measurement appeared
quite jumpy. It was unclear if this was fringe jumping. However, the
measured phase difference in the horizontal direction produced larger voltage
changes than in the vertical direction, indicating larger motion.
6.
In noting disruptions, faster acquisition of the phase was helpful. To
accomplish this a delay signal to the recorder is necessary, however, it is only
by chance that a disruption falls in the time interval being recorded.
- o s f ---------------
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CENTER UNE DENSITY (FWUI6AB)
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020
OJO
SOFT X-RAY (SFX RJLB)
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OJO
OJO
0.10
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OJO
PLASMA CURRENT fLOOP_ROC_CejNT)
OJO
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OJO
OJO
PEAK TEMP. (ECE—TEPEAK)
1J
1J
OJ
SM
04
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OJO
OJO
1WC (SEC)
090
OJ
OJ
OJO
010
020
OJO
THE (SEC)
Figure 4.15: A shot review of shot 12416.
0.40
OJO
PHASE fRFL-8210). SHOT- 12333
OXO
0.10
OJO
030
[PULP-MHO-POLOIPJrt
0.40
0X0
OJO
CENTER UNE DENSITY (TlR_NBAR)
1 0 * 10* °
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0.30
0.40
0.30
0.40
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0.40
OJO
VISIBLE BREMS. fBREM.VBREM-4)
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130
•X*10*°
100
-SX »10
0X0
0.10
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0X0
0X0
0.10
OJO
HORIZONTAL POSTON (CNTIP.
OJO
SOFT XftAY (STX R _2J0l
x
o
0X04
OJO
4 J.1 0 5
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OJO
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PLASMA CURRENT (LDOP_ROGJ>EJNn
OJO
OJO
IOC (SCC)
OJO
0.30
PEAK TEMP. (ECE.TEPEAK)
OJO
0.10
Figure 4.16: A shot review of shot 12353.
•we (see)
0.40
-t.to
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- 2.10 m
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400
010
0.40
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VISIBLE BREMS. (BREM.VBREM.13)
300
^200
100
OJO
090
010
HORIZONTAL po sitio n (CNTLP_POS_HORIZ)
020
OJO
040
030
040
030
SOFT X-RAY (SFXR_1Cl B)
jjrf r —
ooo
aio
020
OJO
PLASMA CURRENT
040
(LOO
030
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OJO
OJO
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TUCtSEC)
020
PEAK TEMP. (ECE.TEPEAK)
1
020
010
030
OOO
OIO
Figure 4.17: A shot review of shot 11885.
OJO
TMC (SCC)
03 0
-u r
PHASE
(Rn_B21<».
SHOT-
11873
i
-u
030
030
040
OJO
CENTER UNE DENSITY (ElR-NBAR)
I/m *
VISIBLE BREMS- (BREMJ/BRENLI3)
AM
090
010
020
HORIZONTAL POSITION (CNIU>_P0S-H0R1Z)
0.30
090
SOTT X-RAY (SFXR_1Q_B)
V
OJO
PLASMA CURRENT (LOOPJ Q C -D tL J N il
OOO
OJ
010
030
0.30
0.40
090
PEAK TEMP. (ECE-TEPEAK)
OJ
I W
03
OjOO
030
OOO
020
TMC(SCt)
OJO
TM£(SCC)
Figure 4.18: A shot review o f shot 11873.
OJO
PHASE (RR—S210), SHOT- 13694
(to
0.1
OJ
0.0
OJ
OJ
0.1
OJ
VISIBLE BREMS. (BREM_V8 REM_12 )
CENTER UNE QENSfTY fFlR_NBAR)
j
<900
* 1000
900
(to
OJ
0.1
ai
OJ
HORIZONTAL. PQSII10N (C KIU »JO SLH O R IZ)
• au
f an
J aio
OJ
SOFT X-RAY (SFXR_9_Bl
& OJO
ao
at
OJ
PLASUA CURRENT tLOOPJTOCJOEJNQ
•10
PEAK TEMP. (ECE-TEPEAK)
1J
14
■10
OJ
■10
■10
ao
nut (see)
a«
oj
ao
ao
0.1
Figure 4*19: A shot review of shot 13694.
tnc (see)
OJ
CHAPTER V
DISCUSSION AND CONCLUSIONS
Reflectometry may be used to investigate various aspects o f the plasma density. It
can provide density profiles like an interferometer, and also, being a localized
measurement, it can yield information on density layer fluctuations, aid in the study of
particle transport theory, and provide correlation measurements between density layers.
The reflectometer is one o f the few diagnostics that monitors changes in the density. It is
not a new diagnostic, but only recently has interest been renewed in reflectometry because
of its usefulness in the study o f tokamak plasmas.
The JAERI reflectometer was operational in the Microwave Tokamak Experiment
(MTX) at Lawrence Livermore National Laboratory (LLNL) which made use of the
Alcator-C tokamak. The reflectometer operated in O-mode with a variable frequency range
of 75 - 110 GHz. This corresponds to tracking information from density layers in the
range o f 0.7 to 1.5 xlO2®nr-*, Alcator-C provided high density plasmas reaching
approximately 5.0 xlO20 n r 3, in a vacuum chamber 16.5 cm in minor radius and 64 cm in
major radius. The design o f the reflectometer was unique in its use of a quasi-optical relay
system to transport the microwave signal over 15 m from a low magnetic field region near
the building wall to inside the tokamak vessel. Losses in the path were minimal, 1 to 2 dB
per lens and about 7 dB through the coupler. An optical coupler was used in this relay
system to split and redirect the returning plasma signal to the receiving horn. Through this
entire arrangement the sensitivity was about 40 dB. However, an overwhelming loss in
signal was encountered through the MTX port. A narrow duct in the port, 2.5 cm in
105
106
width, proved to be quite troublesome. In the reflectometer system it brought down the
returned IF power signal to about 0.5 volts, and the sensitivity o f the system to about 12
dB.
The objective the JAER1 reflectometer was to detect plasma fluctuation. A literature
review pertaining to plasma oscillations noted the following.
1.
High frequency fluctuations
50 kHz) have been observed.
2.
Regular MHD activity would be indicated by low frequency
oscillations (< 1 0 kHz).
3.
Oscillations in the plasma had been detected to be lower in frequencies toward
the plasma center.
4.
Perturbation o f the electron density evolved much slower than a perturbation
of the electron temperature.
Also, conflicting information was present in the literature on the sensitivity of the
reflectometer measurement. This simple reflection is anticipated to be highly dependent on
the density gradient scale length, Ln=nc/(dne/dr). For density perturbations with
wavelengths near the density gradient scale length, it was stated the change in phase could
be interpreted near the cutoff layer. However, if the perturbation wavelength was near the
free space wavelength o f the probing beam, the density perturbations were considered to be
unresolvable.
The first study performed on the JAERI reflectometer system touched on our major
concern of propagating enough signal into the vacuum chamber and having a flat phase
front at the reflective layer. For this purpose the MTH code was used to model the
propagation o f the reflectometer signal into the tokamak vacuum chamber through the
narrow MTX port. Two methods of focusing the propagating signal were examined.
Large illumination o f the MTX duct where the microwave signal was focused in the plasma
and small illumination o f the duct where the signal was focused at the duct entrance. The
results of the study showed that full illumination o f the duct produced an initially flatter
107
phase front (< 10 cm into the vacuum vessel) but at further distances into the vacuum
region, a flatter phase front was seen with the small illumination. Small illumination was
about 6 times greater in transmitted power into the vacuum chamber than the full
illumination case. These two methods were also studied in the sidelab, using an x-y field
scanner, which similarly indicated that the larger illumination of the duct appeared to yield a
more well defined signal than smaller illumination near the exit of the ducL Therefore, in
our use of optics through the top B port, the waist of the port lens was placed 10 to 8 cm
into the vacuum chamber or plasma, therefore using large illumination o f the duct
Results verifying the reflectometer’s ability to track the motion of the plasma
density layer were quite easily acquired. The reflectometer measured the presence o f the
cutoff density layer exacdy. Also, upon returning from a vacuum leak, large oscillations
were induced by the feedback control system of the tokamak, therefore giving the
reflectometer a good tokamak test. The reflectometry data precisely matched the large
oscillations also noted in the horizontal position loops and the FIR interferometer. The
only questionable details o f these measurements were the magnitude o f the oscillations
sensed by the reflectometer. The horizontal position loops showed bulk plasma motion
during the oscillations of about one cm. The vertical position loops appeared insensitive to
the horizontal oscillations and show only little glitches of motion on the order of one mm or
a fractions o f mm. The reflectometer, which was aligned vertically, showed the same
oscillations seen in the horizontal position loops, with the magnitude exhibited by the
vertical loops, i.e. showing fraction o f mm motion. O f course, bulk plasma motion and
individual plasma layer motion are not identical measurements and it would seem likely that
the density layer motion could be larger, but that is not what was detected. A possible
explanation o f the vertical oscillations detected by the reflectometer follow when
considering plasma scrape off by the limiter. As the plasma is pushed horizontally into the
limiter, scrape off of the plasma occurs inducing a density profile variation which produces
a poloidal perturbation. Therefore, the reflectometer system is accurately measuring phase
108
variations corresponding to less than millimeter motion due to plasma profile variations
resulting from of the slow horizontal plasma oscillation induced by the feedback control
system of the tokamak.
In addition, the reflectometer during these experimental runs detected plasma
disturbances in MTX, particularly plasma oscillations and disruptions. From a ledger on
disruptions in MTX, they occurred mostly away from density limits, when little MHD
activity was observed, and some disruptions appear to be associated with bursts o f metallic
impurities. Reflectometry data added nothing new to the observance o f disruptions. It,
however, gave the same information as seen in the FIR interferometer and visible
bremsstrahlung diagnostics. The phase difference shows jumps or fringes, during the
disruption, and continues to observe density layer motion if subsequent disruptions occur.
When acquiring fast reflectometry data (> 200 kHz acquisition rate) about a disruption,
possibly more information can be deciphered, however, in the operation of the JAERI
reflectometer this data was very limited. Plasma oscillations detected by the reflectometer
were MARFE's and possibly bursts, which in MTX were attributed to sparks or flakes
from the limiter or from the walls of the tokamak vacuum chamber. The detection of a
MARFE by the reflectometer, in shot 12416, was a sensitive measurement o f a poloidal
density perturbation. Bursts in the discharge were noted by the reflectometer, visible
bremsstrahlung and certain FIR interferometer line densities. Reflectometry data usually
compared best with information from the visible bremsstrahlung diagnostic which is
proportional to the plasma density squared. The interferometer did not observe density
oscillations near the end of the shot. It sometimes fringe-shifted or died out before this
ending region. The reflectometer appeared quite sensitive to plasma oscillations and bursts,
most likely due to the positioning o f its cutoff density layer near the outer edge of the
plasma in high density operation. The fast data of the reflectometer even senses precursor
oscillations to the burst. In a few shots, the reflectometer measured oscillations, in the kHz
range, just prior to an oscillatory termination of the plasma. The visible bremsstrahlung
109
followed the reflectometer with bursts of radiation, and then the reflectometer displayed a
growing oscillation which terminates with the sh o t Therefore, the reflectometer, unlike
other diagnostics, gives a description o f the ending of the discharge, and it should be
emphasized, appears quite sensitive to the plasma edge.
For the limited time the reflectometer was installed, it ran so as to transmit as much
power as possible into the tokamak without compromising a flat phase fro n t Also,
interpretations o f the phase measurements assumed long wavelength perturbations in the
plasma, therefore estimating a change in the phase difference to be roughly equivalent to a
position change, 8 0 = 2koSz, where Sz is the change in location and ko - (Hq/ c. The
operation o f the reflectometer was setup to detect fluctuations vertically, through the top B
port, and horizontally, through the side B port. The side measurements, however, were
never truly resolved. The M TX group had expected the reflectometer to show larger-scale
density layer motion and this definitely should have been the case when coming through the
side B port. Phase change measurements did drastically change in this move from top to
side, but the side seemed to give too much motion. Phase differences o f several volts were
very common and along with that, frequent fringe shifting. Even at the most insensitive
prescale option of the reflectometer (+ 32), oscillations were present Therefore future
work on the reflectometer could be in optimizing and looking for problems in side port
operations. It was brought to my attention that the port lens focused the microwave beam
in the port. Perhaps using a longer focal length would have corrected the problem.
Therefore testing and adjusting the reflectometer on the side port to receive more
information on horizontal oscillations would have made this thesis more complete. The
vertical motion detected by the reflectometer, however, showed great sensitivity and
exhibited excellent resolution o f tokamak plasmas.
110
APPENDIX
Ill
APPENDIX A
DESCRIPTION OF THE MTH CODE
This further description of the MTH code is presented to assist those at Lawrence
Livermore National Laboratory interested in using this code for the first time. Hiis
appendix includes a discussion on how to run the code, sample input files and output plots,
and a few hints on "logic" or program organization. Recall from Chapter 3, the MTH code
is essentially used to model the transmission of an electromagnetic signal through free
space, a waveguide, or as it is reflected by a mirror. The MTH code is a huygen's code
therefore has 3 stages. It utilizes a source file, input file depicting the stages, and a post
processor (code) for plotting results. These codes were forwarded to J. Byers who along
with M. Makowski and B. Stallard have modified the MTH code for specific applications at
LLNL.
Additions to the MTH code and some other details outlined in this appendix are
listed in the first 1000 lines of the code itself. A summary of the modifications made by
those at LLNL is outlined below.
•
Shaped mirrors: The addition of mirror shapes included counterbore,
spherical, flat cone, and a twist reflector. Parabolic focusing was also
being tested.
•
Field rotation: Added was a rotation angle to the primary vector.
This also is described as arbitrary rotation about the z axis.
•
Waveguide: Incorporated were additional modes and a variable duct length.
Also added was the ability to model a corrugated waveguide.
•
Sources: Added were an annulus and a circular waveguide source.
•
Illumination: Uniform illumination was approximated by the addition o f a
simple vlasov term.
112
In addition to the modifications listed, the execution o f the MTH code was also changed.
The code was revised to run on the cft77. The input file was modified to include new
physics being modeled and the post processor for larger more useful plots. A typical MTH
calculation on the Cray takes less than 8 min cpu time. Only the revised code is discussed
in the following presentation.
Running the MTH code
The commands to compile and run the MTH code and the post processor on the
Cray machines are listed below.
Compiling MTH code:
reft p=smthjb l=lsmthjb on=m lib=(imsl,imsl$fun) x=xsmthjb / 12 18
Running the MTH code:
xsmthjb
o=****o p=****p rs=***p /12 18
Compiling the post processor code (sjbmSlp):
reft i=sjbm51p I=ljb51p on=m lib=(disspla) x=xjb51p / 12 18
Running the post processor:
xjbSlp p=****p ps=****ps i=pspecs r=****r / 12 18
where **** means optional wording.
Table A.l:
Compile and run commands.
Recall the structure of the MTH code. It propagates an electromagnetic field from a
source mirror mO through an intermediate mirror or stage m l (this could be a duct, mirror
or free space) and finally to a detector m inor m2. Usually mO and m2 are flat planes
normal to the beam, but m l, when reflecting from an actual mirror, is oriented at an angle
o f 45 degrees to the beam so as to achieve a 90 degree reflection. Also, m l can be modeled
to posses some curvature for focusing. The typical resolution o f the mO and m2 stage is
113
51x51 and m l, usually being a more complex stage, is sometimes set to 151x151 point
resolution. The field orientation is set by specifying a primary, secondary and normal (or
propagation) direction.
To propagate the fields from a given source through a series o f N steps requires
running the code N times, once for each intermediate stage. The detector plane, m2,
resulting from the previous step becomes the source mO for the present step. The input file
and files created by the MTH code can be denoted in the following fashion,
'i': input file
'p': output file
'rs': restart file
'o': not used
Both i and rs are used as input files,
Both o and p files are output files.
The p-file is frequently used as the rs-file for the next step and is the input file to the post
processor. The o-file is rarely used.
A list o f the read statements in the MTH code furnish the structure of the i-file and
are presented in the next table. Recall, 'p' refers to the primary, 's' the secondary and 'n'
the normal axis. A specific description o f terms follows:
(1)
There is no set notion for the file names read in line 1165, but it is
recommended that one use names ending w ith,
i,
o, a n d
p.
(2)
istp: If istp.eq. 1, the program stops at m l and the m2 namelist variables are
equated to m l. If istp.eq.2, the program skips writing the m l namelist and
proceeds to m2 calculations. If istp is anything else the program quits,
isrc: If isrc.ne.2, it uses a mO source and skips reading m2 in line 1196. If
isrc.eq.2, source data is read from earlier output in line 1732.
(3)
m u : Is the frequency of the electromagnetic signal.
im dsrc: If imdsrc.ne. 1, it skips the vlasov collection and generating a
rectangular waveguide source in line 1419.
(4)
mOxO
mlxO ... and m2x0 ... indicate the (x,y,z) position of the plane in
the specified stage. These are relative to an overall geometry.
(5)
i#p, r#s: Indicate the curvature of the primary and secondary direction of the
p la n e . A value such as e20 implies a fiat plane.
n#p, n#s: Sets the point resolution. The resolution can be set at 51x51 or
151x151.
(6)
mOpx ..., m lp y ..., m2py ... are lengths, 1/2 the measured length in the
direction (p,s,n) specified. These values set the boundaries when
propagating through a duct, or specify the region of interest for plotting
and calculations.
114
Line
Read statement and format
1165
1166 901
read(4,901) contr,cifil,cofil,csfil
format (4a 10)
1182
1184 906
read(4,906) istp.isrc
format (214)
1188
read(4,inpt)
namelist /inpt/ mu imdsrc
1193
read(4,mirror0)
namelist /mirroiO/ mOxO mOyO mOzO
rOp iOs nOp nOs
mOpx mOpy mOpz
mOsx mOsy mOsz
mOnx mOny mOnz
acborc ajl51 ajl52 a jl5 3 ajr ajth amO ani2 am4
annulus azlin azlin2 azsq azsq2 bOql bend 190
bend290 c lcub c2cub coneO conel cone2 corrug
counterb cublinl cublin2 cubsql cubsq2 doane
dphase21 dphase41 ductlm efgauss ephionly
filter fourier imtheta kpmax ksmax lcirc
lcirclS lduct lteandth ltm 1x024 newpfi
paroff phshift rOcurv rlcu rv rlrip rann rannl
rbb rctm rho rippll rippl2 rlsrc rsm l45
rwaist sphere 1 tw istl twistr va v f vlasov
x2off xoff xyann xyannO xyannl xyann2 y2off
yoff zeqn 1 zeqn2 zmin
1194
read(4,m irrorl)
namelist /m irro rl/m lx l m ly l m lz l
r ip r ls n ip n ls
m lp x m lp y m lpz
m lsx m lsy m lsz
m inx m ln y m ln z
Ipsi lcross fh fe delta
1238
read(4,mirTor2)
namelist /mirror2/ m2x2 m2y2 m2z2
r2p r2s n2p n2s
m2px m2py m2pz
m2sx m2sy ni2sz
m2nx m2ny m2nz
1239
read(4,m ircubl)
n am e list/m ircu b l/b lq l b lq 3 b lq p h b2q2 b2q3 lrotm ls
lrotm lp lrotm2s lrotm2p lrotm l4z thetals
thetalp theta2s theta2p thetal4z
1377
1372 972
read(4,972) n lpx,n 1sx,n2px,n2sx
format (4i5)
Table A.2:
Read statements in the MTH code for the i-file.
115
(7)
nlpx, nlsx,n2px,n2sx are output grid scale factors.
Logic term, such as those set at the end of the mO namelist, will be discussed in the
program organization section and example input files are show in the along with figures.
Sample input and output files
The output of the MTH code, p-file, is the input to SJBM51P, a post processor
which produces plots of the field profiles. Changes to the plotting program acquired by J.
Byers include the phase slope calculation, eliminating the 1/(271) in the dpsi/dx plot, and in
size and scaling adjustments o f the plots. The post processor runs with a second input file
which I renamed ispecs. It sets plotting parameters such as the size and axis notion. The
plots are in terms o f a log scale, and distances are in meters both in the input and output
files. The amplitude range and plot height of the output can be modified by adjusting wlp
and wcy.
The files displayed as reference files in this appendix are, in figure A .l, an i-file for
(a) the creation of a rectangular waveguide source and (b) the propagation of the source,
and in figure A.2, (a) the propagation of the electromagnetic source through a duct and (b)
the ispecs file for the post processor. Typical output plots resulting from running the post
processor are then displayed. This output corresponds to the i-file in fig.A,2(a).
In terms of the ispecs file, the following are general comments.
Line 1; Gives the plot name and is arbitrary.
Line 4: Specifies the axis notion.
Note, the ispecs file displayed is not the one used for the output shown.
Line 10: Are the terms isk, isf and isv read in line 514 o f SJBM51P and like most
terms listed are used in sizing and grouping the output figures.
116
(a)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
26
29
30
31
(b)
Figure A .l:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
+mth
1
1
tbm0011
obm001 1
oldp
r n u * 9 . 4 e l 0 . tmdarc*!
S
m 0 x 0 - 0 , m 0 y 0 " 0 . m0z0~-0. 10
r0p > l.e20 r 0 s - l.e 2 0
n0p-51 n0s-51
m0px"0.01 m0py>0. m0pz-0.
m 0 s x > 0 . m 0 s y * 0 . 0 1 m 0 * x «0 .
n i 0 n x - 0 . « 0 t > y - 0 . m0nza l .
n ew pf1> .tru e.
f 1 1 t e r " .fa l s o .
p h sh fft" .fa lse.
S
m l x 0 * 0 . m l y 0 “0 . m l z 0 B0 .
rlp * l.e2 0 r ls* l.e 2 0
n l p a 51 n l « “ 51
m lpx«0.0127 m lpy-0. m lpz-0.
m l s x * 0 . m l s y > 0 . 0 4 6 0 m l s z “0 .
mlrtxa 0 . m l n y - 0 . m l n z M .
I p s t* .fa ls e . f*«4. fh-2. d e lta -0 .
S
m 2x0-0. i»2y0-0. m 2x0-0.0I
r 2 p -l.e 2 0 r2*«l.e20
r>2p-51 n Z s - 5 1
m 2 p x -0 .0 1 2 7 m 2py-0. m2pz-0.
m 2sx-0. m 2 sy-0 .0 4 6 0 m2sz-0.
nt 2nx>0. m 2 n y - 0 . m 2 n z - l .
S
$
1
1
1
1
+mth
tb0111
ob0in
pb0011
1
2
r r t u - 9 . 4 e l 0 . tmdsrc-1
S
m 0 x 0 - 0 . m 0 x 0 " 0 . m0y0~-0,40
r0 p -l.e2 0 r0 s-l.e 2 0
n0p-51 n0s"5I
m 0 p x - 0 . 0 1 m 0py-0. m0pz-0.
m 0 s x « 0 . m 0 s y - 0 . 0 1 m0sz»0.
ni0nxa 0 . m 0 n y - 0 . n i 0 n z - l .
n ew p fl" .false.
ft Iter-.fa lse.
p h sh lft-.fa lse.
$
m l x 0 a>0 . m l y 0 » 0 . s i l z 0 - 0 .
rlp -l.e2 0 r ls-l.e 2 0
nlp-51 n ls-51
m lp x -0 .0 1 2 7 m lpy-0.
m lpz-0.
nlsx*ff. m lsy -0 .0 4 6 0 m Isz-0.
m lnx-0. n ln y -0 . n ln z -1 .
l p s l - . f a l s e . f e - 4 . fh-2. d e lta -0 .
$
m 2 x 0 -0 . m 2y0-0. m2z0«0.01
r2 p -l.e2 0 r 2 s-l.e 2 0
n2p«51 n2s*51
m 2 p x -0 .0 1 2 7 m2py-0.
m2pz"0.
m 2 sx -0 . n 2 sy -0 .0 4 G 0 m2sz-0.
m2nx-0. n2ny*0. m 2nz-l.
S
S
1
1
1
1
These files are input, i-files, for the MTH code. The file
shown in (a) creates a rectangular waveguide source and (b)
propagating that source a specified distance.
117
1
2
3
4
5
6
7
8
S
Iff
11
12
13
14
15
16
17
If?
19
20
21
22
23
24
25
26
27
28
29
30
31
32
(b )
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Figure A.2:
+mth
fbl711
o b 1211
2
2
rni.r-9.4el0, ) n d s r c * 2
Pb0!11
S
riJffxff-MT. M 0 y 0 ™ 0 . nt0z0»0.
r B p = 1 . © 2 0 r 0 s - l ,©20
n 0 p - 5 1 n0:-“ 51
m&py. - 0 , 0 1 2 7 i n f p y ^ . m 0 p z ™ 0 .
m.0sx=0. Bi0sy»fJ . 0 4 S 0 n 0 s z = 0 .
litJ?nK"?f. n 0 n y *ff. n'.'nz* 1 .
nev/pf l-.ti ue.
four for™.truo.
f 1 1 t o r * .f 1 s o .
p h s h < f t “ .tru-r.
d u c t 1 n™iT. 2 3 kprnax^? k s m a x » 1 4
S
m l x 0 ' ’0. nfy0*-0. m ’ 2 0 - 0 . 0 0 1
rlpi=l.e20 r l s " l . c 2 0
n i p '■■51 n 1 s ” 31
m l p x r/T.01 27 r)lpy™0. m l p z - 0 .
in.Isx-.?, M ’ s y is0 . 0 4 6 0 n l s z = 0 .
minx-.1?. m l n y - 0 . nlnz«*l.
S
m2x~^0. m2y0=r. m2z0-0.23
r 2 p - 1 . © 2 0 r2-r 1 , e 2 0
n 2 p ^ S I n Z 5 “ 5i
m 2 p x :--0.0127 r*2py” 0. m2pz**0.
m 2 s x “0. n 3 s y = 0 . 0 4 G 0 m 2 s z « 0 .
ni2nx"..'. r»2ny-0. r.i2nz«l.
$
S
1
1
1
1
Jb 5 1p i t
S
$
y
$
(f»s»l
2
2
1
1
*z
wmt n- 0. 0j ff i
2
2
2
2 _
*
31
41
51
2G
pow«2.5e-V
rcrt*0.
$
x
*-y
yx
*'
Sy
Syx
Sz
Sz45
$
s,
s
S
The files shown are in (a) an i-file to propagate a plane
through a duct and in (b) an example ipsecs file for the
post processor.
f i e l d m ag n itu d e c o n to u r*
phoee contours
M.im
.mm
| * -a.au
field mognltude
JS IpU A j - -a.ow
OUTPUT
a
119
J6Ipil
r t , - Q,000
it j - 0*000
rv o ld ia g n iU d o
a B ^ ia r 'Biif a : "A
Is?
o
^OlpCt
it I • 0.000
>9I?U H
0.000
121
'p&lplt
at W-* D.QDQ
> 6 lplt
UU'm'£
M ■ - O.QOQ
L n L a g r o ta d p o w a r I r o n a a l a a l o n
1
1
r
r
it
3
i.i
to
BOX
USX
XJBS1P
F
T V S O L I B . M F E . CRAV
FRIO
OUTPUT...
0023
-
VERSION
13:17:11
J
O
03/10/91F
FRAMES PLO TT E D
USER NUMBER
•
0704S*
124
Program organization
The MTH program makes use o f many "logic" terms and goto statements,
therefore, is at times hard to follow. Included under this subheading is a list o f the logic
variables used in the MTH code and where they are located in the program. Therefore, by
using this list, searching for a particular option will be easier. Some general notes are also
added below.
If newpfl equals is true, the code regenerates (with irsc=2) or makes (with iscr=l)
a p-file with no explicit samec propagation, then accesses the fourier, corrugated
waveguide, and phshift (phase s h ift) options.
For a source without propagation newpfl =.true. and phshift =.false.
For waveguide propagation and phase shift over a duct of length ductlm, newpfl,
fo u rier, and phshift must all be true. However, due to geometrical constraints,
there are a maximum number of modes that can be set in the duct Kpmax and
ksmax, for the primary and secondary directs, should be set to these values. Check
lines near the phshift calculations for the use o f these terms.
The term doane controls field reconstruction following the Doane modified fourier
coefficient calculations. For accessing doane, fourier, newpfl and co rru g must
be set to true.
If rsm l4 5 =.true, the program propagates mO to m2 without using the m l stage.
This option does not use the rs-file as the source for the m l field and skips over the
mO to m l calculations.
Iteandtm is used for setting arbitrary modes.
125
Logic Variable
and (line location)
Default
annulus (1393,1640)
bendl90 (2151)
bend290 (2445)
coneO(1405)
cone I (2108)
P
co n e2 (2427)
com ig (1865,1924,1960)
counterb (2085)
d o an e(1857)
ephionly (1651)
filter (1787)
fourier (1856)
imtheta (1585)
F
F
F
F
F
F
F
Related Variables and
(default value)
bOql (0), rann (0.1), rwaist (0.03)
xoff (0), yoff (0), azlin2 (0), azsq (0)
x2off (0), y2off (0), azlin2 (0), azsq2 (0)
xyannO (0), rann (0.1), rOcurv (l.e20)
xyann 1 (0), xoff (0), yoff (0), rann 1,
rlcurv
x2off (0), y2off (0), xyann2 (0)
ductlm (0.22), kpmax (2), ksmax (2)
rlsrc (1), acbore (1)
F
F
T
F
F
lcirc (1531,1716)
lcirclS (1548,1716)
lcross (2032,2050)
lduct (1522)
F
F
F
F
lpsi (2032)
Irotm lp (1270)
liotm2p (1327)
lrotm2s (1309)
lrotm l4z (1289)
lrotm ls (1252)
lteandtm (1487)
ltm (1479)
newpfl (1831,2829)
paroff (2102)
phshift (1918)
rsm l45 (1199,1735,2204)
sphere 1 (2083)
twist 1 (2487)
twistr (1657)
vlasov (1462)
F
F
F
F
T
F
F
F
F
F
zeqnl (2147)
zeq n 2 (2441)
F
F
F
F
F
F
F
F
a j r ( l) ,a jth ( l) ,a jl5 1 ( l) ,a jl5 2 (0),
ajl53 (0)
♦same as imtheta
fh, fe, delta
amO (0.5), am2 (0.5), am4 (0), dphase21
(0), dphase41 (0)
fh, fe, delta
thetalp (0)
theta2p (0)
theta2s (0)
thetal4z (0)
thetals (0)
1x024 (0), rctm (0)
1x024 (0)
xoff (0), yoff (0)
xoff (0), yoff (0)
va (3.1226e-2), vf (9.66e-2), rho
(2.115e-2)
azlin (0), azsq (0), xoff (0), yoff (0)
azlin2 (0), azsq2 (0), x2off (0), y2off (0)
Extra set variables:
clight (3e8), cublinl (0), cublin2 (0), cubsql (0), cubsq2 (0), c2cub (0), clcub (0),
efgauss (4), rbb (0), m s (1), rippll (l.e-8), ripp!2 (l.e-8), rlrip (0), zmin (0)
General References:
SAMEC, T., et.al., Bull. Am. Phys. Soc. 32 (1987) 1872.
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