close

Вход

Забыли?

вход по аккаунту

?

Microwave imaging diagnostics for plasma fluctuation studies

код для вставкиСкачать
Microwave Imaging Diagnostics for Plasma
Fluctuation Studies
By
Jian Wang
B.S. (University o f Science and Technology o f China) 1999
M.S. (University o f California at Davis) 2004
DISSERTATION
Submitted in partial satisfaction o f the requirements for the degree o f
DOCTOR OF PHILOSOPHY
In
Electrical and Computer Engineering
in the
OFFICE OF GRADUATE STUDIES
o f the
UNIVERSITY OF CALIFORNIA
DAVIS
Approved:
Anh-Vu H. Pham
^.-'Vyt/vA-Vc* Ay
A hi
H
/ 7 JUUAygjC/
Jonathan P. Heritage
fj
N eville C. Luhmann. Jr. (Committee Chair)
2005
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: 3212889
INFORMATION TO USERS
The quality of this reproduction is dependent upon the quality of the copy
submitted. Broken or indistinct print, colored or poor quality illustrations and
photographs, print bleed-through, substandard margins, and improper
alignment can adversely affect reproduction.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if unauthorized
copyright material had to be removed, a note will indicate the deletion.
®
UMI
UMI Microform 3212889
Copyright 2006 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, Ml 48106-1346
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
To
My Parents
ii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Acknowledgements
First and foremost, I would like to express m y deepest thanks to m y advisor,
Professor N eville C. Luhmann, Jr., for having given me the opportunity to be a member
o f his Millimeter Wave Technology Group.
In addition, I would like to thank the members o f m y Doctor committee, Professor
Johnathan Heritage and Professor for their valuable time and advice.
Furthermore, I also appreciate Dr. Bihe D eng and Dr. Calvin Domier for their
valuable advice and assistance during this work. I am thankful to Mike, thank for his
assistance in fabricating mechanical components; and m y colleague Lu Yang and
Zhengang Xia for their help and some advice. I would also like to thank all the members
o f this research group for their friendship and support.
I am also thankful to m y colleagues, Princeton Plasma Physics Laboratory (PPPL)
researchers, Drs. E. Mazzucato, H.K. Park and T. Munsat, as w ell as researchers from the
FOM-Instituut voor Plasmafysica Rijnhuizen,the Netherlands.
Ill
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Microwave Imaging Diagnostics for Plasma
Fluctuation Studies
Abstract
by
Jian Wang
Doctor o f Philosophy - Electrical and Computer Engineering
University o f California, Davis, 2005
Professor N eville C. Luhmann, Jr., Chair
Electron
Cyclotron
Emission
Imaging
(ECEI)
and
M icrowave
Imaging
Reflectometry (MIR) combined systems are being investigated by the UC Davis Plasma
Diagnostic Group (PDG), in collaboration with Princeton Plasma Physics Laboratory
(PPPL) researchers, Drs. E. Mazzucato, H.K. Park and T. Munsat, as w ell as researchers
from the FOM-Instituut voor Plasmafysica Rijnhuizen,the Netherlands. The goal is to
develop the plasma diagnostic systems based on the imaging technology developed in the
UC Davis PDG group, for the study o f plasma micro-turbulence, w hich is extremely
important for the understanding o f anomalous transport behavior o f magnetically
confined plasmas such as in tokamaks.
This dissertation work provides the design o f the optical systems, the design o f
the electronics, the testing o f the antenna array and the data analysis o f TEXTOR
ECEEMIR combined systems.
iv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Contents
Acknowledgments......................................................................................a
Abstract............................................................................................. ................................................................iii
Chapter 1 Introduction and Motivation
1.1 Controlled Thermonuclear F u sio n .................................................................................................... 1
1.2 Tokamak Confinement and Instabilities.......................................................................................... 3
1.3 Introduction of Electron Cyclotron Emission Imaging (ECEI)..................................................... 10
1.4 Introduction o f Microwave Imaging Reflectometry (M IR)........................................................... 12
1.5 Overview of the D issertation............................................................................................................ 14
Chapter 2 Theoretical Basis of Electron Cyclotron Emission Imaging
(ECEI) and Microwave Imaging Reflectometry (MIR) Diagnostics
2.1 ECE Imaging....................................................................................................................................... 25
2.1.1
Introduction ....................................................................................................................25
2.1.2
Electron Cyclotron Emission (E C E )............................................................................ 25
2.1.3
Principles of ECE radiom etry....................................................................................... 29
2.1.4
Spatial Resolution of ECE D iagnostics....................................................................... 33
2.1.5
Temperature Resolution of the R adiom eters.............................................................. 34
2.1.6
The ECE Imaging D iagnostic....................................................................................... 34
2.2 Microwave Imaging Reflectometry................................................................................................. 37
2.2.1
Theoretical basis of Conventional Reflectometry....................................................... 37
2.2.2
Microwave Imaging Reflectometry.............................................................................. 41
v
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 3 Optical Design
3.1
General Optical System Design Considerations............................................................................. 49
3.1.1 Imaging A rra y .........................................................................................................................49
3.1.2 ECEI Design Considerations................................................................................................52
3.1.3 MIR Design Considerations.................................................................................................56
3.1.4 Combined ECEI/MIR S ystem ............................................................................................... 60
3.2
Optical System Design of the TEXTOR ECEI System ............................................................... 63
3.2.1
Introduction o f CODEV ....................................................................................................63
3.2.1.1 System Data Window...................................................................................................64
3.2.1.2 Lens Data Manager Window ....................................................................................66
3.2.1.3 View Lens Window...................................................................................................... 67
3.2.1.4 A nalysis........................................................................................................................ 69
3.3
3.2.2
Optical Design Parameters .................................................................................................71
3.2.3
Gaussian Beam Trace ........................................................................................................ 73
3.2.4
Real Ray T ra c e ..................................................................................................................... 76
3.2.5
Modulation transfer function (M TF)...................................................................................77
3.2.6
Point Spread Function......................................................................................................... 78
Optical System Design of the TEXTOR MIR System .................................................................79
3.3.1
Original Optical D esign ....................................................................................................... 79
3.3.2
Gaussian Beam T ra c e ...........................................................................................................82
3.3.3
Real Ray Trace...................................................................................................................... 85
3.3.4
Modulation transfer function (MTF)..................................................................................86
3.3.5
Point Spread F u n ctio n ......................................................................................................... 87
3.3.6
Tobin M unsat’s Optical D esig n ......................................................................................... 88
Chapter 4 ECEI and MIRElectronics Systems
4.1
TEXTOR ECEI E lectronics.............................................................................................................92
vi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.1.1
Power Divider Design...................................................................................................... 95
4.1.2
Testing the Power D ivider................................................................................................99
4.1.3
Printed Circuit Local Oscillator (LO) M odules........................................................... 102
4.1.4
Printed Circuit Power Divider and Mixer Modules......................................................106
4.1.5
Printed Circuit IF Amp/Detector/Video Amp M odules............................................. 107
4.2
Antenna Array B o x ..........................................................................................................................109
4.3
TEXTOR ECEI Antenna Array T estin g...................................................................................... I l l
4.4
TEXTOR MIR E lectronics.............................................................................................................116
Chapter 5 TEXTOR ECEI/MIR Data Analysis
5.1
5.2
ECEI S ystem .................................................................................................................................... 120
5.1.1
Sawteeth O scillations......................................................................................................120
5.1.2
MHD O scillations........................................................................................................... 128
MIR S ystem ......................................................................................................................................131
Chapter 6 ECEI/MIR Optical Designs forother Tokamaks
6.1
6.2
DIII-D ECEI Optical System Design............................................................................................. 138
6.1.1
Optical System Considerations.....................................................................................138
6.1.2
Optical System D esign...................................................................................................139
6.1.3
Gaussian Beam T race..................................................................................................... 140
6.1.4
Ray Trace Calculation..................................................................................................... 143
6.1.5
Modulation transfer function (M T F )............................................................................. 143
6.1.6
Point Spread Function..................................................................................................... 144
NSTX MIR Optical System D esig n ............................................................................................... 144
6.2.1
Optical System Considerations........................................................................................144
6.2.2
One-Dimension MIR Optical System D esign ................................................................. 145
vii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6.2.3
Two-Dimensional MIR Optical System D esig n ........................................................ 150
6.3
KSTAR Tokamak ECEI Optical System D esig n .......................................................................154
6.4
JT-60 Tokamak ECEI Optical System D esig n ........................................................................... 159
Chapter 7 Summary and Future Developments
7.1
Summary........................................................................................................................................... 164
7.2
Future D evelopm ents.......................................................................................................................165
7.2.1
ECEI diagnostic upgrades for TE X T O R .......................................................................165
7.2.2
MIR upgrades for TEX TO R .......................................................................................... 168
List of Figures:
Figure 1.1 The required values o f n tE to obtain ignition plotted as a function o f
temperature T.
Figure 1.2 Schematic o f a tokamak illustrating the principles o f operation.
Figure 1.3 The helical magnetic fields wrap around the torus toroidally and
poloidally, forming the nested magnetic surfaces.
Figure 1.4 Classical fluid imaging.
Figure 1.5 Sample Volum es and Sensitive Wave number Ranges o f Typical
Fluctuation Diagnostics.
Figure 1 .6 Comparison between Conventional ECE radiometer.
Figure 1.7 Left picture shows that the ideal 1-D reflectometry only considers
phase fluctuation. Right picture shows in the case o f 2-D fluctuations, the reflectometer
receives a complicated, m ixed signal containing both amplitude and phase fluctuations.
viii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2.1 (a) shows O-mode. (b) shows X-mode.
Figure 2.2 Electron cyclotron radiation frequencies o f the two low est harmonics
in TEXTOR with a central magnetic field o f 2.25 T.
Figure 2.3 The LO frequency ( f LQ ), IF frequency ( f j p ) , and IF bandwidth
( B jF ) determine the frequency range o f ECE radiation to be detected.
Figure 2.4 Schematic o f a double-side-band heterodyne ECE radiometer for a
tokamak.
Figure 2.5 Schematic o f a single-side-band heterodyne ECE receiver.
Figure 2.6 Conceptual picture o f an ECE imaging diagnostic system.
Figure 2.7 Schematic representation o f microwave reflectometry.
Figure 2.8 Computer simulation o f the cutoff surface o f plasma.
Figure 2.9 Comparison o f 1-D (a) and 2-D (b) reflectometry.
Figure 2.10 Schematic representation o f beam trajectories in the vicinity o f the
cutoff layer.
Figure 2.11 Isometric surface plot o f the normalized field amplitude o f the
reflected wave, from the numerical simulations in Ref. 26.
Figure 2.12 Imaging optics is used to map the virtual cutoff layer onto the
detector plane.
Figure 2.13 Comparison o f Conventional 1-D m icrowave reflectometry and
M icrowave Imaging Reflectometry.
Figure 2.14 Conceptual picture o f Receiving System o f MIR (Lenses Based).
Figure 3.1 The structure o f a planar dual dipole antenna.
ix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.2 16-channel Imaging array for MIR is fabricated on printed circuit
board.
Figure 3.3 Side view o f an imaging array, showing the attached hyperhemispheric
lens and the antenna pattern.
Figure 3.4 Left photograph is the back view o f the 16-channel MIR Imaging
Array. Right photograph is the assembly o f the array box.
Figure 3.5 Conceptual picture o f ECE imaging diagnostic system (based on
lenses).
Figure 3.6 The conceptual picture o f the beam spot o f the system (one
dimension).
Figure 3.7 Conceptual picture o f MIR System (based on lenses).
Figure 3.8 Large diameter imaging optics image the plasma cutoff layer onto the
mixer array; hence, the sample volumes coincide with the focal plane o f the imaging
optics.
Figure 3.9 Conceptual picture o f the beam spot o f the transmitting system and
receiving system (one dimension).
Figure 3.10 Conceptual picture o f the sight lines o f receiving system.
Figure 3.11 Conceptual picture o f Combined ECEI/MIR systems.
Figure 3.12 Screen Shot o f CODEV.
Figure 3.13 System data window. Set wavelength w hose units are mn and
fields/vignetting.
Figure 3.14 System data window. Set system settings.
Figure 3.15 Screen shot o f Lens Data Manager Window. It is the final design o f
ECEI.
X
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.16 V iew Lens Window. D ecide which cross-section w ill be shown in the
plot window.
Figure 3.17 Fan o f Rays. It means the number o f the traces from one field point
on the object surface.
Figure 3.18 Picture o f a complete optical system. The example is the ECEI optical
system.
Figure 3.19 Real Ray Trace window. Choose output form and give appropriate
settings.
Figure 3.20 Gaussian Beam Trace window. Beam half width is computed from
the receiving angle o f half bandwidth o f 1/e electric field 15.5 degrees.
Figure 3.21 Side view o f ECEI optical System.
Figure 3.22 Detailed beam structure at the image plane, 20-channel beam is
shown.
Figure 3.23 Top view o f ECEI optical system.
Figure 3.24 Gaussian Beam calculation o f the central Channel.
Figure 3.25 Gaussian Beam calculation o f the bottom Channel.
Figure 3.26 Gaussian Beam calculation o f the top Channel.
Figure 3.27 Color output o f Gaussian Beam Trace: Side View.
Figure 3.28 Color output o f Gaussian Beam Trace: Top View.
Figure 3.29 3-D view o f the complete system.
Figure 3.30 Real Ray Trace o f the bottom channel.
Figure 3.31 Real Ray Trace o f the bottom channel.
Figure 3.32 MTF Analysis o f the design.
xi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.33 Point Spread Function o f the Center Channel.
Figure 3.34 fields/vignetting Window.
Figure 3.35 Screen shot o f Lens Data Manager W indow o f my optical design.
Figure 3.36 Side V iew o f MIR Optical System.
Figure 3.37 Top V iew o f MIR Optical System.
Figure 3.38 Gaussian Beam calculation o f the Center Channel.
Figure 3.39 Gaussian Beam calculation o f the top Channel.
Figure 3.40 Gaussian Beam calculation o f the bottom Channel.
Figure 3.41 Color output o f Gaussian Beam Trace: Side View.
Figure 3.42 Color output o f Gaussian Beam Trace: Top View.
Figure 3.43 3-D view ing o f the complete system.
Figure 3.44 Real Ray Tracing o f the top channel.
Figure 3.45 Real Ray Tracing o f the bottom channel.
Figure 3.46 MTF Analysis o f the design.
Figure 3.47 Point Spread Function o f the center point.
Figure 3.48 Screen shot o f Lens Data Manager W indow o f Dr. Munsat’s optical
design.
Figure 3.49 Side V iew o f Dr. Munsat’s MIR Optical System.
Figure 3.50 3-D view ing o f the complete system. Only the center channel and two
edge channels are shown.
Figure 3.51 Gaussian Beam calculation o f the center Channel.
Figure 4.1 Schematic diagram illustrating how 2-D electron temperature images
are obtained via ECEI.
xii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.2 Schematic diagram illustrating the arrangement o f the wideband IF
electronics for the 2-D ECEI system.
Figure 4.3 Conceptual Picture o f an Equal Power Divider.
Figure 4.4 Wilkinson Divider Module in AD S design. Center Frequency 4.5GHz.
Figure 4.5 Design Assistant (a) and layout (b) o f the W ilkinson Divider whose
center frequency is 4.5 GFIz.
Figure 4.6 Simulation Result o f one Wilkinson Divider. S21 and S 31 are shown.
Figure 4.7 W ilkinson ( 8 -Way) power divider D esign in A D S. GML-1000
(20mils) High Frequency Laminate is used.
Figure 4.8 Wilkinson ( 8 -way) Power Divider. 50 ohm loads are connected to the
ports when S-parameter measurements are performed.
Figure 4.9 S-parameter result o f A D S Simulation. From 3-7 GHz, the insertion
loss varies from 9.0 dB to 9.975 dB.
Figure 4.10 Test result o f the 8 -way power divider.
Figure 4.11 Diagram o f LO Module.
Figure 4.12 S-parameter Measurement o f the N B B-310.
Figure 4.13 Shown above is an LO module with an output frequency o f 4.3 GHz.
Figure 4.14 Diagram o f Mixer Module.
Figure 4.15 Photograph o f Printed Circuit Power Divider and Mixer Module.
Figure 4.16 One Mixer Module and one IF Am p/Detector/Video Amp Module are
installed inside a metal box.
Figure 4.17 Printed Circuit IF Amp/Detector/Video Amp Module.
Figure 4.18 Complete ECEI Electronics Box.
xiii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.19 Left Picture shows the dual dipole array placed on the substrate lens.
Right picture shows one dual dipole antenna.
Figure 4.20 These two pictures show the 20 channel dual dipole printed circuit
antenna/mixer imaging array (two view s), incorporating wideband baluns and low noise
microwave preamplifiers.
Figure 4.21 Metal plate with a tightly packed array o f circular holes.
Figure 4.22 Antenna Pattern testing setup in the laboratory.
Figure 4.23 A Backward Wave Oscillator (BWO) (M icrowave Generator G4142bM (GPIB)) is used as the LO source.
Figure 4.24 Antenna Pattern Measurement Setup in the laboratory.
Figure 4.25 Antenna Pattern o f the ECEI Array.
Figure 4.26 Antenna Pattern o f the ECEI Array (raw data).
Figure 4.27 Electronics diagram o f the 1-D MIR system.
Figure 4.28 The focal plane beam patterns o f the MIR system.
Figure 5.1 ECE Imaging Observation region in TEXTOR.
Figure 5.2 Original Data from Shot # 94568.
Figure 5.3 The time history o f Mixer 3, IF band 8 . (Channel 3 Frequency 8 )
Figure 5.4 The time history o f Mixer 13, IF band 8 . (Channel 13 Frequency 8 )
Figure 5.5 The Sawteeth Oscillations observed in Shot # 94568.
Figure 5.6 2-D Images show the progression o f images o f a sawtooth crash.
Figure 5.7 2-D The images show the electron temperature profile o f the sawteeth
crash. (S h o t# 94571 q=l layer)
xiv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 5.8 Time histories o f M ixer 13 IF Band 3 (top) and M ixerl4 IF band 4
(bottom). (Shot # 9 6 1 3 8 )
Figure 5.9 Original data o f Mixer 13 IF Band 3 (top) and M ixer 14 IF band 4
(bottom). (Shot # 94566)
Figure 5.10 Time histories o f M ixer 12 IF Band 6 (top) and M ixerl2 IF band 7
(bottom). (Shot # 94567)
Figure 5.11 Time histories o f LO Frequency (a) and Ip (b) and B T (c), Signal o f
Mixer 12 IF band 7 (d). (Shot # 94590)
Figure 5.12 The time histories o f M ixer 4 IF Band 3 (top) and M ixer 9 IF band 3
(bottom). (Shot # 95250)
Figure 5.13 Images o f MHD Oscillation (Part I).
Figure 5.14 Images o f MHD Oscillation (Part II).
Figure 5.15 Images o f MHD Oscillation (Part III).
Figure 5.16 Complex field amplitude from theTEXTOR MIR system
cutoff layer is swept through the focal plane o f the imaging optics. It shows
as the
the cut-off
layer is m oving from the core side to the edge as density is ramped.
Figure 5.17 Quadrature signals from MIR multichannel detector array. (Discharge
# 93064)
Figure 5.18 Poloidal rotation measurement via MIR system.
Figure 5.19 Time history o f Poloidal rotation induced by NB1.
Figure 6.1 Electron cyclotron radiation frequencies o f the two lowest harmonics
in DIII-D.
Figure 6.2 Screen shot o f Lens Data Manager Window.
XV
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 6.3 Side View o f the ECEI Optical System.
Figure 6.4 Top V iew o f the ECEI Optical System.
Figure 6.5 Gaussian Beam calculation o f the central Channel.
Figure 6.6 Color output o f Gaussian Beam Trace o f the Side View .
Figure 6.7 Color output o f Gaussian Beam Trace o f the Top View .
Figure 6.8 3-D view o f the complete system.
Figure. 6.9 Ray Trace o f the top channel.
Figure 6.10 MTF Analysis o f the design.
Figure 6.11 Point Spread Function o f the Center Channel.
Figure 6.12 Electron cyclotron radiation frequencies o f the two low est harmonics
in NSTX with a central magnetic field o f 0.4 T.
Figure 6.13 Left picture (a) shows the relationship between the curvature radius o f
the cutoff surface (at 45 GHz) and the central density o f the plasma. The right picture (b)
shows the relationship between the location o f the cutoff surface (at 45 GHz) and the
central density o f the plasma.
Figure 6.14 1-D Antenna Array for the NSTX MIR system.
Figure 6.15 Screen shot o f Lens Data Manager W indow o f the N ST X 1-D MIR
system.
Figure 6.16 Side V iew o f MIR optical design for NSTX.
Figure 6.17 Gaussian Beam calculation o f the central channel.
Figure 6.18 Color output o f the Gaussian Beam Trace o f Side V iew .
Figure 6.19 3-D view ing o f the complete NSTX 1-D MIR system.
Figure 6.20 shows the Point Spread Function o f the center channel.
xvi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 6.21 2-D Antenna Array for the NSTX MIR System.
Figure 6.22 Screen shot o f Lens Data Manager W indow o f the N ST X 2-D MIR
system.
Figure 6.23 Side V iew o f the N STX MIR Optical Design.
Figure 6.24 Gaussian Beam Trace.
Figure 6.25 Color output o f Gaussian Beam Trace o f the Side View .
Figure 6.26 3-D view ing o f the complete N ST X MIR system.
Figure 6.27 The picture shows the KSTAR Tokamak.
Figure 6.28 Electron cyclotron radiation frequencies o f the three lowest
harmonics in KSTAR with a central magnetic field o f 3.5 T.
Figure 6.29 Conceptual Design o f KSTAR ECEI system.
Figure 6.30 KSTAR ECEI Imaging Optics configuration.
Figure 6.31 Screen shot o f Lens Data Manager W indow for the KSTAR ECEI
system.
Figure 6.32 Side V iew o f the ECEI Optical D esign for KSTAR.
Figure 6.33 Top V iew o f ECEI Optical D esign for KSTAR.
Figure 6.34 Color output o f Gaussian Beam Trace o f the Side View.
Figure 6.35 Screen shot o f Lens Data Manager Window.
Figure 6.36 Side V iew o f the ECEI Optical System.
Figure 6.37 3-D view o f the complete system.
Figure 6.38 Gaussian beam trace o f the center channel.
Figure 6.39 Color output o f Gaussian Beam Trace o f the Side View.
Figure 6.40 Color output o f Gaussian Beam Trace o f the Top View.
xvii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 7.1 N ew W ilkinson Power Divider Design.
Figure 7.2 The Structure o f the Power Divider D esign in the Software Agilent
ADS.
Figure 7.3 AD S layout o f the W ilkinson Divider w hose center frequency is 4.5
GHz.
Figure 7.4 Simulation result o f one Wilkinson Divider.
Figure 7.5 Mixer M odule Four distinct frequencies are used. 16 modules are
needed in the 2-D MIR system.
List of Tables:
Table 1.1 Diagnostics for electrostatic turbulence in tokamaks.
Table 3.1 Compare some results o f two optical design.
Table 4.1 VCO List
Table 4.2 LO Frequency Assignment
Table 4.3 Mixer List
Table 4.4 Dichroic plate diameter versus Cutoff Frequency
Table 6.1 Field points in CODEV which is defined in Lens> System data>
Fields/Vignetting.
Table 6.2 Field points in CODEV which is defined in Lens> System data>
Fields/Vignetting.
X V lll
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
Chapter I
Introduction and Motivation
1.1 Controlled Thermonuclear Fusion
It is well known that if a nucleus o f deuterium fuses with a nucleus o f tritium, an
a-particle and a neutron are produced, w hile sim ultaneously a significant amount o f
energy is released (the m ost familiar exam ple is the hydrogen bom b) [1]. These reactions
require extrem ely high temperature because the particles need sufficiently high kinetic
energy to overcom e the Coulom b barrier to fuse. Som e o f the m ost important fusion
reactions are those involving deuterium and/or tritium [ 1].
D + D —>T + p + 4.0 M eV
D + D - > 3H t + n + 3 3 M e V
D + T - * 4H e + n + 11.6MeV
Because the D + D and D +T reactions represent a virtually inexhaustible supply of
fuel, research in controlled nuclear fusion is aimed at “producing electricity from sea
water”, with the energy released from fusion reactions o f the isotopes of Hydrogen, i.e.
Deuterium and Tritium 1. Due to the extrem ely high temperature required for fusion
reactions, the fuels are in a fully ionized state. They are neutral globally because the
charge o f the positive ions is balanced by the negative charge o f the electrons. These
ionized overall charge neutral gases are called plasmas when their parameters are such
that collective interactions are o f importance. [1, 2] W hen the plasmas are heated to a
1 Here, it should be noted that tritium is not naturally occurring and must therefore be “bred”. [1]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2
sufficiently high temperature (on the order o f 10 8 K), fusion reactions occur with a
relatively high rate due to collisions among particles from the tail o f the M axwellian
distribution. In addition to the required high temperature, the plasmas need to be
sufficiently dense and their energy needs to be confined long enough to produce
sufficient reactions for the process to be self-sustaining. In a m agnetic confinem ent
fusion reactor, the ion temperature, Tj, must be around 10-20 keV , w hile the product of
n;xE must be around 2 -5x10
20
-3
m" s, where n; is the ion density, and xE is the energy
confinem ent time o f the plasma. The required value o f the product niTET |is about 5x10
21
m s keV [1], External heating is required before a fusion reactor reaches the condition of
ignition, i.e., the plasm a is self sustained when the heating pow er o f the fusion products
balances the plasma pow er loss. In the case o f the D +T reaction, the ignition condition is
nxE > 3x10
20
3
m s when Tj is about 10 keV. If Tj is close to 30 keV , nxE has a minimum
requirement for ignition, which is > 1.5x10
20
3
m 's [Fig. (1.1)]. [3]
10
100
10
T (keV)
Fig. 1.1 The required values o f nxE to obtain ignition plotted as a function of
temperature T (After Ref. 1).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.2 Tokamak Confinement and Instabilities
Because the high temperature (on the order o f 10 8K) needed for these fusion
reactions precludes confinem ent by material containers, one must em ploy other w ays to
ensure that the plasma is sufficiently dense and confined long enough to produce
sufficient reactions for the process to be self-sustaining. One o f the approaches under
active investigation for an eventual energy source is to use a m agnetic field to confine the
plasma (magnetic confinem ent), where the m ost successful configuration has been the
tokamak [1], Figure 1.2 is a schematic o f an early em bodim ent o f the tokamak concept.
Here, the toroidal magnetic field (
) is generated by external coils, which are
symm etrically distributed around the torus, surrounding the vacuum vessel. Thus, from
Ampere law, the toroidal magnetic field strength has a l/R dependence within the coils.
The poloidal magnetic field ( B q ) is generated by the toroidally flow ing plasma currents.
The resultant total magnetic field has a helical geometry, with the field lines wrapping
around the torus both toroidally and poloidally, forming nested magnetic surfaces within
the vacuum vessel, as shown in Fig. 1.3. [3]. Each magnetic surface (at a minor radius r)
is characterized by a safety factor, q, which is defined as [ 1]:
A
2m-2Bt
2n
fJ0 l p (r)R
where A<p is the change of toroidal angle along the field line when the poloidal angle has
changed by 2 n , and I p (r) is the total plasma current within the minor radius r. If the
field line closes on itself after m poloidal and n toroidal rotations, q = n/m, and the
magnetic surfaces with rational q values are called rational surfaces. U sually, the lower
order rational surfaces are subject to stronger instabilities [2, 3].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4
Iron Core
Primary
Windings
Toroidal Field
Coils —---- *
Plasma
Fig 1.2 Schem atic o f a tokamak illustrating the principles o f operation. The donut­
shaped electrically conductive plasma has a major radius R, and a minor radius a and
constitutes the secondary winding o f the transformer configuration. The toroidal fields
( B q ) generated by the coils, and the poloidal fields ( B q ) generated by the plasma current
(Ip) com bine to form nested magnetic surfaces. [3]
The plasma particles (electrons and ions) gyrate around the field lines, while their
guiding center follow s the helical field lines o f a m agnetic surface. The cross-field
transport is lim ited due to the small Larmor radius (compared to the size o f the vacuum
vessel) o f the particles in the strong magnetic fields. It is w ell known that diffusion
processes scale as the square o f the step length. Consequently, if that step length were the
Larmor radius, the diffusion coefficient would scale inversely as the magnetic field B
squared which leads to an extrem ely favorable confinem ent scenario. Unfortunately,
other (anomalous) processes affect this. The isolation between the high temperature
plasmas and the wall o f the vacuum vessel (usually at room temperature) is achieved by
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
introducing a material limiter or a magnetic configuration called a divertor, which defines
the outermost magnetic surface [1]. In tokamak equilibrium, the inner magnetic surfaces
are shifted towards the low field side o f the tokamak with respect to the outermost
magnetic surface. This relative displacem ent o f the m agnetic surfaces is called the
Shafranov shift [1].
~ l/R
Rail Limiter
Plasma
Vacuum Vessel
Fig. 1.3 The helical magnetic fields wrap around the torus toroidally and
poloidally, forming the nested magnetic surfaces. The separation o f the plasma from the
vacuum vessel can be achieved by using material limiters, which define the outermost
magnetic surface. In tokamak equilibrium, the innermost magnetic surface is shifted (A)
towards the low field side o f the tokamak with respect to the outermost magnetic surface.
Generally, the plasma pressure, density, temperature, and current density profiles
are centrally peaked with radial gradients therefore present in tokamak plasma
equilibrium. These gradient forces can drive instabilities in the plasma. The strongest
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6
instabilities in tokamaks are those which are described by the magnetohydrodynamic
m odel o f the plasma. They are named M HD instabilities, or m acroinstabilities, as the
wavelengths are comparable to the minor radius o f a tokamak [1]. The instabilities with
wavelengths comparable to the ion Larmor radius (or electron radius in the case of the
electron temperature gradient instability) are termed m icroinstabilities [1, 3]. Som e
fluctuations o f m acroscopic nature are benign, coherent, M H D -like, and appear to coexist
with the equilibrium state. H ow ever, other fluctuations o f m acroscopic nature are
associated with uncontrolled or quasiperiodic behavior such as disruptions, edge
localized m odes (ELM s), sawtooth oscillations, or fishbones w hich can be associated
with global or local rapid redistribution o f energy. [1 ,4 ]
Although research in controlled nuclear fusion began in the 1950s, the major
lim iting factor for the success o f tokamaks is the so-called anom alous transport
phenomenon, i.e., plasmas lose their energy and particles at a rate much faster than that
predicted from classical Coulomb collisions. It has been long proposed that the
underlying reason for anomalous transport is the m icroscopic turbulent fluctuations due
to plasma instabilities. Microturbulence is an irregular fluctuation in the plasma of
electrons and ions. The fluctuations caused by gradients o f density and temperature form
unstable w aves and eddies that transport heat from the super-hot core across nested
magnetic surfaces out to the much cooler plasma surface and, ultim ately, to the tokamak's
walls. This phenomenon is referred to as energy transport. [4-23]
A major purpose o f these turbulence studies is to identify specific theoretical
m echanism s
with
experimentally
measured
fluctuations.
Empirical
relations
are
compared with theoretical turbulence m odels to determine which physical processes are
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
7
important. In order to predict more accurately the confinem ent property o f a tokamak, to
optim ize a tokamak reactor design, or to be able to actively control the fluctuations, it is
desirable to obtain a clear physics understanding and picture of the turbulent transport
process. [3] Here, understanding o f the plasma is expected to proceed as did advances in
understanding o f ordinary fluid turbulence, which were made possible by im aging and
visualization. Figure 1.4 shows two sim ple exam ples o f classical fluid imaging.
Fig. 1.4 Classical fluid imaging. Left picture is the turbulences o f water going over
rocks in a river. Right picture is the V otices Produced by a Water Strider (From
http://tardis.union.edu/~andersoa/M ER033_F04/StudentFluidsPics/fluids_pictures.htm )
To reveal the relation between the fluctuations and transport, it is essential to
measure the characteristics of electron density fluctuations n, electron temperature
fluctuations T , the radial component o f the magnetic flux density fluctuations B r and
the toroidal component o f the electric field fluctuations E g (or q> and the poloidal wave
number k g ) , and the correlation between these fluctuating quantities. The technologies of
microturbulence diagnostics were briefly reviewed in [6 ] and more recently in detail by
N. Bretz [4], In addition, Bihe D eng summarized those technologies into tables in his
dissertation (see Reference 3).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
Shown in Table 1.1, in the plasma edge, the fluctuation quantities ne, Te and ( p ,
and the correlation between these quantities can be measured by Langmuir probes; thus,
it is possible to calculate the turbulent fluxes from the m easurem ents, and compare them
with those calculated from profile measurements. In the plasm a core, however, the only
extensively investigated fluctuation quantity until recently is the density fluctuation.
Am ong the density fluctuation diagnostics listed in Table 1.1, the m icrowave/laser
scattering is the m ost w idely used and w ell-developed m ethod [4, 39]. The heavy ion
beam probe (HIBP) is also important diagnostic technique for measuring plasma density
fluctuations [25, 26]. The discrimination o f the poloidal wavenumbers is extrem ely
important for understanding the anomalous transport in the core o f TEXTOR. Sample
volum es and sensitive wave number ranges o f several typical fluctuation diagnostics are
shown in Figure. 1.5. The FIR scattering measurements have shown that the fluctuations
in TEXT peak at k ~2-3 cm '1. H owever, the spatial resolution o f the scattering diagnostic
at ka~2-3 cm ' 1 is poor. The HIBP, on the other hand, is not sensitive in this range o f
wavenumber. ECE Imaging has the best spatial resolution. [Reference 3]
T ab le 1.1 D iagnostics for electrostatic turbulence in tokamaks (after R efs.3 ,4 and 6 ).
Langmuir Probe [24]
ne, q>, Te
High spatial resolution, 0 < k < 10 cm ' 1
Restricted to edge plasmas (T < 50 eV )
H eavy Ion Beam Probe
(HIBP) [25,26]
Beam Em ission
Spectroscopy (BES) [27,28]
Charge Exchange
ne , Q
Spatial resolution: (r, 6 , </>) 1 x 0.5 x 0.1cm , k < 4 cm ' 1
ne, (from Ha or D a em ission)
Spatial resolution 1-2 cm , k ~ 0.1-2 cm ' 1
Sensitive to M HD activities and edge fluctuations
Ti , nl , v Ui, (em ission from impurities)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9
Recombination Spectroscopy
(CXRS) [29]
Spatial resolution 1-2 cm, k ~ 0.1-2 cm '1
Sensitive to M HD activities and edge fluctuations
Optical [30-32]
f ( n , T, impurity) -> ne
Spatial resolution: chord averaged
C ollective M icrowave or Far
Infrared (FIR) Laser
Scattering [33-39]
Phase Scintillation and Phase
Contrast Imaging [40,41]
Reflectometry and
Reflectometry Imaging
[42-44]
Enhanced Scattering [45,46]
ne
Spatial resolution: diamond-shaped sample volum es
k ~ 2-20 cm '1, w ell developed technique
Spatial resolution: chord averaged
k ~ 1 cm '1
ne , w ave cutoff
Spatial resolution: (r, 0 , ) ~ l c m x 5 cm , for kr < 2ki
Measurements affected by fluctuation level.
ne , w ave resonance
For kr > 2ki, lim ited application
Electron Cyclotron Em ission
(ECE) [47-50]
ECE Imaging (ECEI)
[43,51-54,55]
Te
Spatial resolution: (2-4 cm) x (<1 cm ), no time resolution
Restricted to plasma core (optically thick plasm as), 1-D
Spatial resolution: ~1 cm, k < 3 cm '1, no time resolution
Restricted to plasma core (optically thick plasmas)
2-D measurements
11(d)
»
Fig. 1.5 Sample V olum es and Sensitive W ave number Ranges o f Typical
Fluctuation Diagnostics, (a) FIR Scattering, sensitive to 2 < k < 12 cm"1; (b) H eavy Ion
Beam Probe, &< 1.5 cm '1; (c) ECE Imaging, k < 3 cm '1; (d) Phase Contrast Imaging, line
averaged, 0.4 < k < 12.9 cm '1.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
1.3 Introduction to Electron Cyclotron Emission Imaging (ECEI)
Electron cyclotron em ission (ECE) in m agnetized plasm as arises from the
acceleration associated with the gyro-motion o f electrons and subsequent radiation at
harmonics o f the cyclotron frequency, (Oce . In a tokamak or stellerator, the ECE
frequency depends on the major radius R o f the devices, leading to a mapping between
coce and R. In optically thick plasmas, i.e. plasmas with sufficiently high density and
electron temperature T e, the intensity o f the ECE radiation is proportional to the local T e
value. (Note that because h v «
kTe , the Rayleigh-Jeans Law can be used here to
describe the radiation). Consequently, intensity m easurem ents o f optically thick ECE
harmonics yield information about the plasma electron temperature and its fluctuations
[56]. Conventional ECE radiometry has been a standard diagnostics tool for magnetic
fusion plasmas for over twenty five years [57]. H owever, it is lim ited to one dimensional
horizontal measurement along the major radius with relatively poor poloidal spatial
resolution as is shown schematically in Figure 1.6 (a).
To address the abovem entioned limitations, electron cyclotron em ission imaging
(ECEI) system s have been developed which have demonstrated excellent poloidal spatial
resolution and have produced one dimensional spatially resolved measurements along a
vertical plasma chord. [58, 59] Unlike conventional ECE diagnostics, the sample volumes
o f the ECE im aging diagnostic system s are aligned vertically, and can be shifted across
the plasma cross-section by varying the local oscillator (LO) frequency, making it
suitable for 2-D measurements o f electron temperature profiles and fluctuations [60,61].
The sample volum es are imaged onto the 1-D antenna array by the optical system (see
Fig. 1.6 (b)). Figure 1.6 shows the basic structures o f both a conventional ECE
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11
radiometer and the ECE imaging system for purposes o f comparison. The spatial
resolution o f the ECE radiometer is about 2~4m . Only 1-D measurements can be done by
ECE radiometer. ECE im aging can provide better spatial resolution (~ lc m ) and 2-D
measurements. The poloidal/radial w ave numbers and correlation lengths o f T e
fluctuations in the plasma core can also be obtained by properly positioning the focal
plane of the im aging system [60, 61]. D ue to these unique features, ECEI is an ideal tool
for Te fluctuation measurements.
Antenna
E lectronics
-
o
/ cc5 cc —
Imaging Opti
Cb)
Fig. 1.6 Comparison between Conventional ECE radiometer (a) and ECE Imaging
system (b)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12
1.4 Introduction of Microwave Imaging Reflectometry (MIR)
Electron density measurements play an essential role in the study and operation o f
magnetically confined plasmas. M icrowave reflectom etry [56, 62] is a radar technology
where the plasma density (and fluctuations thereof) is inferred from the group delay o f
electromagnetic w aves that are reflected by a plasma cutoff surface. It has found
extensive use for the detection o f short-scale turbulent fluctuations in tokamaks due to its
relatively sim ple implementation and its high sensitivity to sm all perturbations o f
electron density. A similar application is the discovery o f the ionosphere which was
originally investigated by Sir Edward Appleton. A radio w ave launched up to the
ionosphere is reflected. B y a slight change o f w avelength, it is possible to measure the
time taken by the w aves to travel to and from the layer. Thus, the position o f the
reflecting layer can be identified. [72]
Imaging Reflectom etry is related to Doppler reflectometry. Currently, Doppler
radar has many applications, including im aging radar interferometry to investigate
plasma irregularities in midlatitude sporadic E layers [63]; solar radar for detecting the
arrival times o f Earthward-directed Coronal M ass Ejections, the main cause of
increasingly costly geomagnetic storms.
(http://www.lofar.org/science/urdlOQ/Solar Terrestrial.html);
and Doppler radar im aging used for high resolution observations o f the ionosphere and
clear-air turbulence. [64,65]
Despite the sim ple underlying physical process, it is very difficult to extract
quantitative information from the measured signals o f reflectometry. This is caused by
two phenomena. First, the use o f the reflectometry to detect fluctuations is based upon the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13
principle that by measuring the scattered phase o f incom ing m icrowaves from a
fluctuation and inhom ogeneous plasmas, valuable information including the wavenumber spectrum o f the fluctuations and their locations can be extracted from the
scattered EM w ave fluctuations them selves. W hen the amplitude o f the fluctuations is
sufficiently small, i.e. in the range o f the B om Approxim ation (the B om Approximation
w as introduced by M ax B om which is a useful technique for solving problems
concerning the scattering o f atomic particles.), it is hoped that a localized density
fluctuation w ave packet would yield the same form in the scattered phase signal. A s the
fluctuation amplitude increases, various peaks o f the phase response evolve with
distinct .growth rates. This leads to steepening and distortion o f the scattering phase shift
due to a single wave-num ber fluctuation. The sim ultaneous coexistence o f large
amplitude fluctuations with nearby w ave numbers com plicates the task o f resolving the
response at each w ave number. [66]. This work has resulted in analytic expressions for
the scattering phase shift, identification o f the controlling nondim ensional parameters for
the validity o f the Bragg resonance picture and the B om approximation and indications of
the challenges to interpretation posed by fluctuations that cause scattering beyond the
B o m approximation. [67]
The second reason for the difficulty in obtaining useful information from
reflectometry signals is due to the fact that when the plasma permittivity fluctuates
perpendicularly to the direction o f propagation o f the probing beam, as in the case o f
tokamak plasmas, where turbulent fluctuations vary in both radial and poloidal directions,
the spectral components o f the backward wave propagate in different directions. This
m ay result in a com plicated interference pattern on the detection plane, from which it is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14
very difficult to extract any quantitative information about the fluctuations under
investigation. [68] It is shown in Figure 1.7 that the ideal 1-D reflectometry and the 2-d
reflectometry.
1- d i M M a r a s i i y
(P h a s e F luctuation only)
2- d ( M M a r a s i r y
( P h a s e a n d A m plitude F luctuations)
R eflection
R eflection
Fig. 1.7 Left picture shows that the ideal 1-D reflectometry only considers phase
fluctuation. Right picture shows in the case o f 2-D fluctuations, the reflectometer receives
a com plicated, m ixed signal containing both amplitude and phase fluctuations.
The chaotic behavior o f standard ID reflectometry is due to the interference of
reflected w aves at the point of measurement. This is caused by the scattering o f reflected
w aves over a large angle by the 2D structure o f tokamak fluctuations. Reference 64
show s that a mapping o f fluctuations near the cutoff surface o f the plasma could be
obtained from the phase o f measured signals if the reflected w aves are collected with a
w ide aperture antenna, follow ing which an im age o f the cutoff is made onto an array of
m icrowave detectors. Despite som e com plications, such as the need for a large machine
port
on
the
tokamak
and arrays o f m icrowave
detectors,
M icrowave
Imaging
Reflectom etry has the potential for providing new and important information on the
spatial structure o f turbulent fluctuations in tokamaks and spherical tori. [68-71]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15
1.5 Overview of the thesis
A com bined ECEI/MIR system was developed and installed on the TEXTOR
tokamak in 2003. This is a collaborative project involving the UC D avis Plasma
Diagnostic Group, the FOM Institute for Plasma Physics ‘R ijnhuizen’, the Netherlands,
and Princeton Plasma Physics Laboratory (PPPL) researchers, Drs. E. M azzucato, H.K.
Park and Tobin Munsat. This dissertation is concerned with the developm ent o f the
ECEI/MIR system and is primarily concentrated on the optical design for the TEXTOR
system
as w ell
as system s for several other magnetic
fusion
devices.
Related
experimental results w ill be m entioned.
The theoretical basis o f ECEI, which is the same as that for conventional ECE
diagnostics, including the ECE theory and the principle o f m easurem ents o f temperature
fluctuations, is summarized in Chapter 2. A lso, the theoretical basis o f M IR, which is
similar to that o f conventional Reflectom etry, with the MIR theory and the principle of
electron density fluctuations, are presented in Chapter 2.
In Chapter 3, details are presented o f the com bined M IR/ECEI optical system
design in the TEXTOR tokamak. Chapter 4 is concerned with details o f som e o f the IF
electronics associated with the 2-D ECEI and 1-D MIR system s. In addition, Chapt.4
describes the 2-D ECEI system setup and laboratory characterization tests. Chapter 5
describes representative measurement results from the ECEI/M IR system on the
TEXTOR tokamak. In Chapt.6, the MIR optical design for the N S T X device and the
ECEI/MIR com bined optical system s design for DIII-D tokamak and K STA R and JT-60
are presented. O ngoing and future developm ent activities will be provided in Chapt.7.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References:
[1]. J. W esson, Tokam aks, Oxford, Clarendon Press, (1987).
[2], E. Teller, Fusion, N ew York Academ ic Press, (1981).
[3]. B.H. D eng, Two dim ensional electron cyclotron em ission im aging study o f electron
tem perature p ro files an d fluctuations in Tokamak pla sm a s, Ph.D. dissertation, UC D,
(1999).
[4]. N. Bretz, D iagn ostic Instrumentation f o r M icroturbulence in Tokamaks, Rev. Sci.
Instrum., 68, 2927 (1997).
[5]. P.C. Liewer, M easurem ents o f M icroturbulence in Tokam aks an d C om parisons with
Theories o f Turbulence a n d Anom alous Transport, Nucl. Fusion, 25, 543 (1985).
[6]. A.J. W ootton et al., Fluctuations and A nom alous T ransport in Tokamaks. Phys.
Fluids B2, 2879 (1990).
[7]. F. Wagner and U. Stroth, Transport in Toroidal D e vices-T h e E xperim entalist's View,
Plasma Phys. Control. Fusion, 3 5 ,1 3 2 1 (1993)
[8]. J.W. Connor, Tokamak Turbulence - E lectrostatic o r M agnetic?, Plasma Phys.
Control. Fusion, 35, B 293 (1993).
[9]. W. Horton, D rift Wave Turbulence and A nom alous Transport, in B asic Plasm a
Physics, Vol. 2, edited by A .A . Galeev and R.N. Sudan, E lsevier Science Publishers
B .V ., p.383 (1984).
[10]. W. Horton, D rift W aves an d Transport, to appear in the R eview o f M odem Physics,
(1999).
[11]. A.L. Sanin, K. Tanaka, L.N. V yacheslavov, K. Kawahata, T. Akiyama, T.
Tokuzawa, Y. Ito, S. Tsuji-Iio, S. Okajima, Im aging interferom eter f o r plasm a density
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
17
profile and m icroturbulence study on LHD, 30th European Physical Society Conference
on Controlled Fusion and Plasma Physics (N IFS-780). NIFS. pp.41-4, (2003).
[12]. K. Tanaka, L.N. V yacheslavov, A. Sanin, T. Akiyam a, K. Kawahata, T. Tokuzawa,
Y. Ito, S. Tsuji-Iio, S. Okajima, H. Yamada, S. Morita, M. G oto, J. M iyazaw a, K. Ida, Y.
Takeiri, M. Yokoyam a, S. Murakami, A. W akasa, P article tran sports a n d related
turbulent flu ctuations on LHD,
30th European Physical Society
Conference on
Controlled Fusion and Plasma Physics (N IFS-780). NIFS. pp.65-8, (2003).
[13]. Yang Chen, S.E. Parker, Sim ulation o f turbulence an d tran sport f o r Tokamak
p lasm as in general geom etry,
IEEE Conference Record - Abstracts. 31st IEEE
International Conference On Plasm a Science (IEEE Cat. N o.04C H 37537). IEEE. pp.336,
(2004).
[14]. D .D . Ryutov, D.C . Barnes, B .S. Bauer, J.H. Hammer, C.W . Hartman, R.C.
Kirkpatrick, I.R. Lindemuth, V. Makhin, P.B. Parks, D .B . Reisman, P.T. Sheehey, R.E.
Siem on, P article an d heat tran sport in a dense w all-confined M TF plasm a (theory and
sim ulations), IAEA;IOP. Nuclear Fusion, vol.43, no.9, pp.955-60, (2003).
[15]. S.I. Itoh, K. Itoh, M. Yagi, N ovel turbulence trig g er f o r n eoclassical tearings m ode
in Tokamaks, Physical R eview Letters, vol.91, no.4, pp.045003/1-4, (2003).
[16]. J. Candy, R.E. W altz, Anom alous tran sport scaling in the DIII-D Tokamak m atched
by supercom puter simulation, Physical R eview Letters, vol.91, no.4, pp.045001/1-4,
(2003).
[17]. V .V . Parail, Energy and pa rticle tran sport in plasm as with tran sport barriers, IOP
Publishing. Plasma Physics & Controlled Fusion, vol.44, suppl.5A, pp.A 63-85, (2002).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18
[18]. P.B. Snyder, G.W . Hammett, E lectrom agnetic effects on p la sm a m icroturbulence
and transport, Physics o f Plasmas, v o l.8, no.3, pp.744-9, (2001).
[19]. B. W eyssow , Som e aspects o f anom alous tran sport due to stochastic m agnetic
fields, AN S. Fusion Technology, vol.41, no.2T, pp.285-92, (2002).
[20], B. W eyssow , N eoclassical tran sport p ro p e rties o f tokam ak plasm as, A N S. Fusion
Technology, vol.41, no.2T, pp.216-24, (2002).
[21], N.L. Cardozo, Anom alous tran sport due to m agnetic turbulence, A N S. Fusion
Technology, vol.41, no.2T, pp.276-84, (2002).
[22]. M.Z. Tokar, F.A. K elly, The role o f p lasm a-w all interactions in therm al instabilities
at the tokam ak edge, Physics o f Plasmas, v o l.10, n o .11, pp.4378-86, (2003).
[23]. M.Z. Tokar, Theoretical m odels f o r tran sport barriers, A N S. Fusion Technology,
vol.41, no.2T, pp.268-75, (2002).
[24]. Ch.P. Ritz, R.V. Bravenec, P.M . Schoch, R.D. Bengtson, J.A. Boedo, J.C. Forster,
K.W. Gentle, Y. He, R.L. Hickok, Y.J. Kim, H. Lin, P.E. Phillips, T.L. Rhodes, W.L.
Rowan, P.M. Valanju, and A.J. W ootton, Fluctuation-Induced E nergy Flux in the
Tokam ak Edge, Phys. Rev. Lett. 62,1844 (1989).
[25]. A. Ouroua, R.L. Hickok, T.P. Crowley, K.A. Connor et al., TEXT-upgrade 2 M eV
H eavy Ion Beam P robe, Rev. Sci. Instrum., 61, 2986 (1990).
[26]. A.J. W ootton, P.M Schoch, The H eavy Ion Beam P robe, International School o f
Plasma Physics 'Piero Caldirola' Diagnostics for Contemporary Fusion Experiments,
Proceedings o f the Workshop, Varenna, Italy, 27 A ug.-6 Sept. 1991, Edited by P.E. Stott,
et al., Italy: Editrice Compositori, 1991. p. 521-40.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
19
[27]. S. Zoletnik, S. G. Fiedler, K ocsis, G.K. M cCormick, et al., D eterm ination o f
Electron D ensity Fluctuation C orrelation Functions via B eam Em ission Spectroscopy,
Plasma Phys. Control. Fusion, 40, 1399 (1998).
[28]. W. Mandl, R.C. W olf, M .G. von Hellermann, and H.P. Sum m ers, B eam Em ission
Spectroscopy as a C om prehensive P lasm a D iagn ostic Tool, Plasm a Phys. Control.
Fusion, 35, 1373 (1993).
[29]. R.C. Isler, An O verview o f Charge-exchange S pectroscopy a s a P lasm a D iagnostic,
Plasma Phys. Control. Fusion, 36, 171 (1994).
[30]. S.J. Zweben, J. M cChesney, and R.W. Gould, O ptical Im aging o f E dge Turbulence
in the Caltech Tokamak, Nucl. Fusion, 23, 825 (1983).
[31]. P.D. Hurwitz, B.F. Hall, and W.L. Rowan, D etector A rra y f o r M easurem ent o f
H igh-Frequency Fluctuations in Visible and N ear-U V Em ission fro m Tokamaks, Rev.
Sci. Instrum., 6 3 ,4 6 1 4 (1992).
[32], P.D. Hurwitz and W.L. Rowan, A pplication o f a Three Sam ple Volume S(k,co)
Estim ate to O ptical M easurem ents o f Turbulence on TEXT, Rev. Sci. Instrum., 66, 441
(1995).
[33]. E. M azzucato, Sm all-scale D ensity Fluctuations in the A d ia b a tic Toroidal
C om pressor, Phys. Rev. Lett., 36, 792 (1976).
[34]. C.M. Surko, and R.E. Slusher, Study o f the D ensity F luctuations in the A diabatic
Toroidal C om pressor Scattering Tokamak Using C O 2 Laser, Phys. Rev. Lett., 37, 1747
(1976).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
[35]. H. Park, D.L. Brower, W .A. Peebles, N .C . Luhmann, Jr. e t al., D evelopm ent an d
A pplication o f M ultichannel C ollective Scattering System s, R ev. Sci. Instrum., 56, 1055
(1985).
[36]. D.L. Brower, W .A . Peebles, S.K. Kim , N .C . Luhmann, Jr., A pplication o f FIR
H eterodyne
D etection
to
C ollective
Scattering
M easurem ents
of
Tokamak
M icroturbulence, Rev. Sci. Instrum., 59, 1559 (1988).
[37]. W .A. Peebles, R.L. Savage, Jr., D.L. Brower, S.K. K im et al., P lasm a D iagnostic
A pplication s on the TEXT Tokamak Using a H igh P ow er, Twin Frequency O ptically
Pum ped F ar-infrared Laser, Inter. J. Infrared and M illim eter W aves, 8, 1355 (1987).
[38]. D.L. Brower, N.C. Luhmann, Jr., W .A. Peebles, Ch.P. Ritz e t al., The A pplication o f
H om odyne Spectroscopy to the Study o f Low -frequency M icroturbulence in the TEXT
Tokamak, Inter. J. Infrared and M illim eter W aves, 7, 447 (1986).
[39]. N.C., Luhmann, Jr., W .A. Peebles, L aser D iagn ostics o f M agnetically Confined
Therm onuclear Plasm as, In L aser H andbook, V ol. 5, Edited by: M . Bass, M.L. Stitch,
Amsterdam, Netherlands: North-Holland, 455 (1985).
[40]. R. Nazikian and L.E. Sharp, C O 2 L aser Scintillation Interferom eter f o r the
M easurem ent o f D ensity Fluctuations in P lasm a Confinem ent D evices, Rev. Sci.
Instrum., 58, 2086 (1987).
[41]. R. Chatterjee and G.A. Hallock, F irst R esults fro m the P hase C ontrast Imaging
System on TEXT-U, Rev. Sci. Instrum., 68, 676 (1997).
[42]. E. M azzucato, M icrow ave R eflectom etry f o r M agnetically Confined Plasm as, Rev.
Sci. Instrum., 69, 2201 (1998).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
21
[43]. N.C. Luhmann, Jr. S. Baang, D.L. Brower, S. B u m s, e t al., M illim eter and
Subm illim eter W ave D iagn ostic System s f o r C ontem porary Fusion Experim ents, In
D iagnostics f o r C ontem porary Fusion Experim ents, ISPP-9 'Piero Caldirola', Edited by:
P.E. Stott, e ta l., 135 (1991).
[44]. N.C. Luhmann, Jr., 3-D R eflectom etric Im aging o f Turbulence in NSTX, a proposal
submitted to D oE , (1998).
[45]. I. Fidone, Enhanced Incoherent Scattering o f the U pper-hybrid Resonance,
I, C old
P lasm a Theory, Phys. Fluids, 16, 1680 (1973).
[46]. I. Fidone, G. Granata, Enhanced Incoherent Scattering a t the U pper-hybrid
Resonance, I I , Warm P lasm a Theory, Phys. Fluids, 16, 1685 (1973).
[47]. G. Cima, et al., Core Tem perature Fluctuations and R ela ted H eat Transport in the
Texas Experim ental Tokam ak-U pgrade, Phys. Plasmas, 2 ,7 2 0 (1995).
[48]. G. Cima, C. Watts, and R.F. Gandy, C orrelation R adiom etry o f E lectron Cyclotron
R adiation in TEXT-U, Rev. Sci. Instrum., 66, 798 (1995).
[49]. S. Sattler and H.J. Hartfuss, Intensity Interferom etry f o r M easurem ent o f Electron
Tem perature Fluctuations in Fusion Plasm as, Plasma Phys. Control. Fusion, 35, 1285
(1993).
[50]. C. Watts et al., M easurem ent o f Tem perature Fluctuations fro m E lectron C yclotron
Em ission, Rev. Sci. Instrum. 66, 451 (1995).
[51]. N.C., Luhmann, Jr., C.W. Dom ier, H .-X.L. Liu, X .-H . Qin, et al., A dvanced
M illim eter, Subm illim eter and P icosecon d A rray Technology f o r P lasm a D iagn ostics, In
Conference Proceedings, MM 92. Brighton, UK, 14-15 Oct. 1992. Tunbridge W ells, UK:
M icrowave Exhibitions and Publishers, 348 (1992).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
22
[52]. R.P. Hsia, et al., H ybrid Electron C yclotron Em ission Im aging A rray System f o r
Texas Experim ental Tokam ak U pgrade, Rev. Sci. Instrum. 68, 488 (1997).
[53]. B.H. D eng, e t al., E C E Im aging D iagnostic a t the RTP Tokam ak: Perform ance and
First M easurem ents o f T e - Fluctuations, 1998 ICPP & 25th EPS Conf. on Contr. Fusion
and Plasma Phys., Praha, Czech Republic, Europhysics C onference A bstracts, V ol. 22c,
1454 (1998).
[54], B.H .D eng, et al., M ode Structure o f Turbulent E lectron Tem perature Fluctuations
in the Texas Experim ental Tokamak U pgrade, Phys. Plasmas, 5, 4117 (1998).
[55]. R.F.G. M eulenbroeks et al., Off-axis Saw tooth-like In stabilities N ear q= 3/2, 2, and
3 in RTP, 1998 ICPP & 25th EPS Conf. on Contr. Fusion and Plasm a Phys., Praha,
Czech Republic, E urophysics Conference A bstracts, V ol. 22c, 750 (1998).
[56] I.H. Hutchinson, Principles o f Plasm a D iagn ostics, N ew
York, Cambridge
University Press, 2002.
[57]. A.E. Costley, R.J Hastie, J.W.M. Paul, J. Chamberlain, E lectron Cyclotron
Em ission from a Tokamak Plasm a: Experim ent an d Theory. Phys. Rev. Lett., 33, 758
(1974).
[58]. B.H. D eng, R.P. Hsia, C.W. Domier, S.R. B um s, T.R. H illyer, N.C. Luhmann,Jr.,
Electron C yclotron Em ission Imaging D iagnostic System f o r R T P , Rev. Sci. Instrum., 70,
998 (1999).
[59]. B.H. D eng, C.W . Dom ier, N.C. Luhmann, D.L. Brower, G. Cima, A.J.H. Donne, T.
Oyevaar, M.J. van de Pol, E C E imaging o f electron tem perature and electron
tem perature fluctuations (invited). Review o f Scientific Instruments, vol.72, n o .l, pt.1-2,
pp.301-6, (2001).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
23
[60]. B.H. D eng, et al., E C E Im aging D iagn ostic a t the RTP Tokamak: Perform ance an d
F irst M easurem ents o f T e - Fluctuations, 1998 ICPP & 25th EPS Conf. on Contr. Fusion
and Plasma Phys., Praha, Czech Republic, Europhysics Conference Abstracts, V ol.
22c,
1454 (1998).
[61]. B .H .D eng, et al., M ode Structure o f Turbulent Electron Tem perature Fluctuations
in the Texas E xperim ental Tokamak U pgrade, Phys. Plasmas, 5, 4117 (1998).
[62]. E. M azzucato, M icrow ave reflectom etry f o r m agnetically confined plasm as. R eview
o f Scientific Instruments, vol.69, no.6, pp.2201-17, (1998).
[63] H. Bahcivan, D. L. H ysell, M. F. Larsen, and R. F. Pfaff, The 3 0 M Hz im aging radar
observation s o f auroral irregularities during the JO U LE cam paign, J. G eophys. Res.,
110, (2005).
[64] C.E. Valladares, S. Basu, K. Groves, M .P. Hagan, D. H ysell, A.J. M azzella, R.E.
Sheehan, M easurem ent o f the latitudinal distributions o f to tal electron content during
equatorial sp rea d F events, Journal o f G eophysical Research, vol. 106, no.A 12, 1 D ec.
2001, pp.29133-52,(2001).
[65] D.L. H ysell, J.L. Chau, Interpreting the D o p p le r spectrum o f coherent sc a tte r from
topside equatorial sp rea d F, Journal o f Atmospheric & Solar-Terrestrial Physics, vol.66,
no. 17, N ov. 2004, pp. 1549-57,(2004).
[66] A.E. Chou, B.B . Afeyan, B.I. Cohen, The B ragg resonance pictu re o f one­
dim ensional fluctuation reflectom etry beyond the B o m
approxim ation, R eview o f
Scientific Instruments, vol.66, no.2, p t.l, Feb. 1995, pp. 1216-20. (1995).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
24
[67] E.Z. G usakov, A .V . Surkov, Spatial and w avenum ber resolution o f D oppler
reflectom etry, Plasma Physics & Controlled Fusion, vol.46, no.7, July 2004, pp. 1143-62.
Publisher: IOP Publishing, UK, (2004).
[68]. E. M azzucato, M icrow ave im aging reflectom etry f o r the m easurem ent o f turbulent
fluctuations in tokamaks. Plasma Physics & Controlled Fusion, vol.46, no.8, pp. 1271-82,
(2004).
[69]. E. M azzucato, T. Munsat, H. Park, B.H . D eng, C.W . D om ier, N.C . Luhmann,
A.J.H. Donne, M.J. van de Pol, Fluctuation m easurem ents in tokam aks w ith m icrow ave
im aging reflectom etry. Physics o f Plasmas, vol.9, no.5, p p.1955-61, (2002).
[70]. T. Munsat, E. M azzucato, H. Park, B.H. D eng, C.W. Dom ier, N.C. Luhmann, J.
Wang, Z.G. Xia, A.J.H. Donne, M.J. van de Pol, M icrow ave im aging reflectom eter f o r
TEXTOR (invited). R eview of Scientific Instruments, vol.74, no.3, pp.1426-32, (2003).
[71]. H. Park, C.C. Chang, B.H. D eng, C.W. Dom ier, A.J.H. D onne, K. Kawahata, C.
Liang, X.P. Liang, H.J. Lu, N.C. Luhmann, Jr., A. M ase, H. Matsuura, E. M azzucato, A.
Miura, K. M izuno, T. Munsat, K. and Y. Nagayam a, M.J. van de Pol, J. W ang, and Z.G.
Xia, W-K. Zhang. R ecent Advancem ents in M icrow ave Im aging P lasm a D iagnostics.
Invited R eview Article: R eview o f Scientific Instruments, (2001).
[72], E.V. Appleton, Recent ionospheric researches. [Journal Paper] Bulletin o f the
International Union o f G eodesy and G eophysics, no. 11, pp. 516-521. UK, (1940).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
25
Chapter II
Theoretical Basis of Electron Cyclotron Emission
Imaging (ECEI) and Microwave Imaging Reflectometry
(MIR) Diagnostics
2.1 ECE Imaging
2.1.1 Introduction
Electron cyclotron em ission (ECE) radiometers have becom e routine plasma
diagnostic instruments for electron temperature profile m easurem ents in tokamaks for
thirty years [1,2], and the theory o f ECE is w ell-established [3,4,5]. An ECE imaging
diagnostic system is actually a multi-channel heterodyne ECE radiometer. Consequently,
the theoretical basis o f the ECE Imaging diagnostic is the same as that for conventional
ECE radiometers.
2.1.2 Electron cyclotron emission (ECE)
In m agnetically confined plasmas, the electrons gyrate around the magnetic field
lines. This gyro-m otion gives rise to electromagnetic radiation at the gyration frequency
coce = eBtlm e and its harmonics, na>ce, where n = l, 2 ,... is the harmonic number, e is the
electron charge, Bt is the magnetic field strength, and me is the electron mass at rest.
Relativistic effects are neglected in this simple introductory discussion although they are
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
26
o f importance for fusion relevant plasmas with electron temperatures w ell in excess o f 10
keV or when there is a significant population o f so-called suprathermal electrons. D etails
regarding relativistic effects may be found in Ref. 6-7. This radiation is anisotropically
emitted, with a line spectrum and is polarized. For k //B t, where k is the wavenumber in
the direction o f observation, it is right-hand circularly polarized. For kU B t, it is linearly
polarized, and is referred to as the O-m ode (X -m ode) when the electric field is parallel
(perpendicular) to the magnetic field, respectively (see Fig. 2.1).
Fig. 2.1 (a) show s O-mode. (b) show s X -m ode. (after R eference 9)
In tokamaks, there is a m onotonically varying m agnetic field with radius over the
plasma cross-section given by
(2 . 1. 1)
where R is the major radius and Bo is the m agnetic field value at the plasma center with
radius Ro. This leads to a sim ple relationship between the electron cyclotron (EC)
radiation frequency and the point o f em ission, or the resonant layer position: [8]
( 2 . 1.2 )
ymeR
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
27
where y - (1 - / ? 2)~1/2 represents the relativistic shift due to the m ass increase, j6 = v / c ,
and v is the electron thermal velocity.
For present-day, moderate size tokamaks with typical m agnetic flux densities of
about 2 T, the ECE radiation frequency is in the m illimeter w ave range. Figure (2.2)
displays the ECE radiation frequencies o f the first (fc) and second (2,fc) harmonics in
TEXTOR. It is seen that the variation o f the magnetic field strength results in a spatially
varying resonant electron cyclotron frequency. This relation ensures that the ECE
diagnostic is a “local” diagnostic, in which spatial resolution in one dim ension is
achieved by spectrally resolving the measured radiation frequency, presuming that the
plasma is optically thick. For a fixed frequency, there is a finite, but small width o f the
resonant layer [3,8]. This will affect the spatial resolution o f the diagnostic.
TEXTOR frequencies
300
E C H -------
150
(mj
£O
< /f ////////////////////////////^ ^
1.4
1.0
14
ft (m)
2.0
2.2
Fig. 2.2 Electron cyclotron radiation frequencies o f the tw o low est harmonics in
TEXTOR with a central magnetic field o f 2.25 T. Plotted together are the plasma
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
28
frequency (f0), right hand cutoff frequency (ft) and left hand cutoff frequency (ft) for a
parabolic density profile with the central densities shown in the figure.
Plotted together in Fig. (2.2) are the plasm a frequency (ft), which is the cutoff
frequency for the O -m ode propagation, as w ell as the right hand cutoff frequency (ft) and
left hand cutoff frequency (ft) for the X -m ode propagation. The definition o f these
quantities can be found in [9]. They are calculated by assum ing a parabolic density
profile with the central densities indicated in the figure. For the conditions shown in Fig.
2.2, the fundamental O -m ode from 1.8 m <R < 2.05m cannot propagate out o f the plasma
to the low field side due to the cutoff at the plasm a frequency. The first harmonic Xm ode cannot propagate to the low field side as it is always converted and absorbed at the
left hand cutoff layer (ft). Thus, the fundamental X -m ode has no diagnostic application
for devices without access to the high field (interior) region. Details o f the wave
propagation, cutoff, and resonance can be found in [9].
Considering only the plasma radiation (no incident w aves), the radiation intensity
that reaches the observation point is given by:
I(co) = I B( 1
-0
(2.1.4)
where f t is the B lack B ody radiation intensity at temperature T
(2.1.5)
and r is the optical thickness defined as:
( 2 . 1 .6 )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29
where a{af) is the absorption coefficient. If z «
conversely, if z »
1, the plasma is said to be optically thin;
1, the plasma is optically thick. (Ref. 9)
As the condition for the Rayleigh-Jeans lim it, h o )/k BT « 1 , holds for m illimeter
wave radiation in keV temperature range plasmas, Eq. (2.1.4) can be rewritten as
/(<!))= ^ - ( 1 - 0
%n c
(2.1.7)
where Te is the plasma electron temperature.
2.1.3 Principles of ECE radiometry
Equation (2.1.7) shows that the measured ECE radiation intensity depends on the
optical thickness z [Eq. (2.1.7)] and local temperature Te. The optical thickness z is
actually a local quantity for tokamak plasmas [3]. It depends on the interaction between
the w ave and the plasma at resonance. Equation (2.1.7) can be rewritten as
7 ( f l > ) = ^ ^ ( l - e ~ T{R))
8n bc l
(2.1.8)
In optically thick plasmas ( z> > 1), the observed ECE radiation intensity is
proportional to the plasma temperature:
(2-1.9)
8n c
Thus, the plasma electron temperature profiles can be obtained from frequency resolved
measurements o f ECE radiation.
The critical point is then to measure the plasma radiation which satisfies the
condition z » 1. Detailed discussion o f this subject, including the optical thickness o f the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
fundamental x-m ode, can be found in Ref. 4 and Ref. 8 and the references contained
therein. For typical tokamak plasma parameters, only the first harmonic (fundamental) Om ode and the second harmonic X -m ode tend to be optically thick. Thus, they are the
harmonics o f diagnostic importance. In m ost cases, the second harmonic X -m ode is
em ployed for ECE radiometric measurements. One important reason is that the shorter
wavelength leads to better spatial resolution o f the diagnostic when using diffractionlim ited optics. Another important reason is that the fundamental O -m ode is easily cutoff
at the plasma frequency, w hile the second harmonic X -m ode is cutoff at much higher
densities, as shown in Fig. 2.2.
Based on Eq. (2.1.9), the plasma electron temperature profiles can be obtained
from
frequency
resolved
measurements
of
optically
thick
ECE
radiation. ECE
radiometers have becom e routine diagnostic instruments for tokamaks and stellarators,
for measuring the tim e evolution o f plasma electron temperature profiles. M icrowave
heterodyne receivers are used in ECE radiometers [2, 4, 8]. Heterodyne system s are
w idely used due to their high sensitivity and good frequency resolution (thus spatial
resolution). In these system s, ECE radiation in the m illim eter w ave frequency range is
m ixed with the local oscillator (LO) signal and down converted to a convenient lower
frequency IF. A s shown in Fig. (2.3), for a fixed IF frequency ( / / / r ) and bandwidth
( B i f ), the ECE radiation selected is comprised o f both the upper side band (U SB ) and
the lower side band (LSB). In a double side band (D SB ) radiometer, both the upper and
lower side bands are detected; w hile in a single side band (SSB ) radiometer, only one of
the side bands is detected. [8]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
31
LSB
USB
►
fLO' %
f LO fLO+ f IF
Fig. 2.3 The LO frequency ( f LQ ), IF frequency ( f [ F ), and IF bandwidth ( B [ F )
determine the frequency range o f ECE radiation to be detected, (after Ref. 8)
Figure (2.4) is a schematic o f a conventional, m ultichannel, double-side-band
heterodyne ECE radiometer. The ECE radiation is received by a single receiver along the
major radius. D ue to the radial variation o f the magnetic field, it can receive a continuous
spectrum. The received m icrowave radiation is split into several channels by the pow er
divider. Each channel has a m icrowave mixer, operating at a separate LO frequency.
These frequencies determine the corresponding sample volum e positions o f each channel
[Eq. (2.1.2)]. The IF signal processing circuits are sensitive to both the U SB and LSB.
The IF bandwidth determines the sample volum e thickness. The output voltages o f the
video detection circuits are proportional to the input powers o f the IF signals, which are
in turn proportional to the local electron temperatures Te(R). The tim e evolution o f the
electron temperature profile can then be obtained from the recorded video signals. As
shown in Fig. (2.4), each identical channel is comprised o f an LO source, a mixer, and a
post detection channel. The multi-channel measurement is achieved by sw eeping the LO
frequency during a single plasma discharge; consequently, a broadband m ixer and a
sweeping LO source are required. [8]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32
Band
Video
Pass
Detection Filter
IF
Power
Aplifier Mixer Divider
HgH
L o t :
f o c B oc 1/R
Antenna
«
Plasma
- ®
1
Lot
Fig. 2.4 Schem atic o f a double-side-band heterodyne ECE radiometer for a
tokamak. (after Ref. 8)
Single side-band (SSB) receivers are also w idely utilized for ECE diagnostics [2].
Figure (2.5) is a schematic o f an SSB receiver. The frequency o f the LO source is fixed.
The IF signal from the mixer and pre-amplifier has a broad bandwidth, usually 2-18 GHz.
D ue to the broad IF bandwidth, the U SB and LSB signals correspond to ECE radiation
from different plasm a volum es, and consequently are not distinguishable after the m ixing
process. Thus, a side band filter is required in front o f the in order to suppress one o f the
side bands. The LO frequency is chosen so that the selected side band corresponds to
ECE radiation from the plasma. This broadband IF signal is then split into channels with
different center frequencies, which determine the channel positions. The bandwidth of the
bandpass filters after the power divider determines the sample volum e thickness o f each
channel. Details o f the instrumental arrangements o f the various ECE radiometers are
different, depending on the conditions of the tokamak, and the m icrowave components
utilized, as reviewed in [2], [8]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
Video
Detection
Section
u
<D
Band
Pass
Filter
Power
D ivider
Pre-amplifier M ixer
Sideband
Filter Antenna
N
<
60
t
O
H
LO
Fig. 2.5 Schem atic of a single-side-band heterodyne ECE receiver. (After Ref. 8)
2.1.4 Spatial Resolution of ECE Diagnostics
In plasma physics research, high spatial resolution diagnostic instruments are
extremely desirable. Conventional heterodyne system s have lim ited spatial resolution in
the transverse direction o f the sightlines. Shown in Figure (2.4), the sam ple volum es in
the transverse direction are determined by the Gaussian beam pattern o f the optics, or the
lens-antenna configuration. A s the divergence o f the beam pattern is inversely
proportional to the beam waist diameter, the design should be a trade o ff between the
resolutions o f different channels. Thus, in the 100 GHz range, the spatial resolution in the
transverse direction is typically 2-5 cm in diameter [10]. An im aging approach is required
to improve the resolution in the transverse direction.
In the longitudinal (along the sight line) direction, the spatial resolution is the
thickness of the radiation layer. It is determined by the natural radiation line width and
the bandwidth o f the heterodyne receiver. Details are discussed in Ref. 8. For the second
harmonic X-m ode, the longitudinal spatial resolution is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34
\
AR = R
i_ Z k _ + 2.36 si n(0)(—
+ 4_
) ^2
( 2 . 1 . 10 )
/
where Aco is the total bandwidth o f the EC radiation to be collected, 0 is the angle
between the sight line and the perpendicular direction, w hich is 1.5° for TEXTOR [8].
For Te - 2 keV , B, = 2.25 T, Aco/27t =500 M H z, / =120 G Hz and assuming the antenna
receiving angle is 1.5° with respect to the perpendicular direction, the spatial resolution in
TEXTOR (R =1.80 m) is about 3.3 cm.
2.1.5 Temperature Resolution of the Radiometers
The temperatures measured by radiometers are subject to system noise as w ell as
the intrinsic thermal noise o f the plasma radiation. According to Bekefi [11], these noise
sources set a m inimum detectable change in the temperature given by:
where T is the temperature o f the object to be measured, Tn is the system noise
temperature, Aty is the bandwidth o f the radiation to be collected, and x is the integration
time. For ECE radiometers, the plasma temperature is typically on the order o f 1 keV,
w hile Tn is typically about 1 eV. Thus, the resolution lim it o f an ECE radiometer is
primarily determined by the intrinsic thermal noise level. [8]
2.1.6 The ECE Imaging Diagnostic
The first ECE imaging diagnostic system was developed and installed on TEXTU in 1995 [10]. It was successfully utilized to measure 1-D and 2-D electron temperature
profiles, and to study M HD phenomena. Figure 2.6 is the conceptual picture o f the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
arrangement o f an ECEI system. The im aging optics, the im aging array, the LO source,
and the signal processing electronics are the building blocks o f the system . These
building blocks are mounted on a m echanical framework, w hich usually consists o f a
motorized translation stage.
Compared with Fig. 2.4, it is apparent that an ECEI system differs from
conventional ECE radiometers primarily in that it utilizes an im aging array as the
receiver. The array elem ents are com bined m icrowave antenna/mixers, and are aligned
vertically. The im aging optics, which consists o f the lenses and mirrors, focuses the ECE
radiation from the plasma onto the array. A ll channels measure at the same frequency;
hence, the sample volum es are vertically aligned in the resonant layer, with the horizontal
position determined by Eq. (2.1.9). The antenna pattern o f the array com bines with the
im aging optics to determine the Gaussian beam pattern o f each channel. The cross section
o f each beam pattern in the resonant plane lim its the extent o f the sample volum e in the
direction transverse to the sight line. To m inim ize the sam ple volum e sizes, the focal
plane o f the im aging optics, or the beam waist location, is required to coincident with the
resonant layer location. Thus, the ECEI system achieves the optimal spatial resolution.
[8]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
Imaging
Array
Imaging
Optics
Focal Plane of
ECE Imaging
B ~ 1/R
LO
Source
Fig. 2.6 Conceptual picture o f an ECE imaging diagnostic system. The high
spatial resolution is achieved by positioning the focal plane o f the optics in the same
plane o f the sample volum es, which is determined by the resonance condition.
As each channel measures at the same frequency, the sample volum es are
contained within a single resonance layer. Thus, the measurements at a fixed frequency
are ID in nature. H owever, w e use the im aging array to achieve the advantage o f 2D
measurements. A vertically-aligned m ixer array is built to collect broad bandwidth
radiation. In essence, this attaches broadband m ulti-frequency heterodyne radiometer
electronics to each elem ent of the one dimensional ECEI array. [12]
The other advantage o f the ECEI system is the flexibility in fluctuation
measurements. Conventional ECE diagnostics can only perform radial correlation
measurements. This can also be done by ECEI, when the sample volum es are positioned
across the plasma center. In addition, the ECEI diagnostic can perform poloidal
correlation measurements, when the sample volum es are displaced from the plasma
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
37
center. Important information such as the poloidal wavenumbers and correlation lengths
o f the Te fluctuations are made possible only through the developm ent o f ECEI. [8]
2.2 Microwave Imaging Reflectometry (MIR)
2.2.1 Theoretical basis of Conventional Reflectometry
Reflectom etry is a form o f radar technology which relies on the total reflection o f
an electromagnetic w ave at a cutoff layer where the local refractive index goes to zero.
Shown in Fig. 2.7, when a w ave o f a certain frequency propagates through a plasma with
density increasing in the direction o f propagation, it m ay arrive at a point where the
electron density equals the cutoff density nc. (Here, only the O -m ode cutoff is used to
explain the basic idea o f the reflectometry. The relationship betw een the frequency and
the plasma density w ill be discussed later.) The w ave w ill be evanescent at higher
frequency, i.e., the w ave w ill be reflected from the cutoff point and propagate back down
the density gradient and out o f the plasma the way it cam e in. From the earliest
observations o f reflectometry, it was discovered that the phase and amplitude o f the
reflected w ave fluctuate strongly. It thus turns out that reflectom etry is one of the most
sensitive ways to measure plasma density fluctuations. [3]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
>
>
f
Source
f+(D
Detection
rc
ri
r
►
Fig. 2.7 Schematic representation o f m icrowave reflectometry. rc is the position
o f the cutoff layer; ne is the electron density o f the cutoff layer; <p is the phase shift o f the
reflected wave. (After Ref. 13)
For reflectometry, the cut-off frequency is determined by the local electron
density, which w ill increase towards the center o f the plasm a when the electron density
increases. A typical plasma electron density profile is shown in Fig.2.7. U sually, the Om ode (E//Bt) cutoff at f0 or the X -m ode (E 1 B t) cutoff at fR are em ployed for
reflectometry diagnostics. In the MIR system for TEXTOR, the X -m ode cutoff is used
for better spatial resolution (due to the higher frequency and higher spatial resolution).
(Ordinary mode)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( 2 . 2 . 1)
39
(y « = ^ [ ® c + K 2 + 4 <
) 1' 2 ]
(R and L extraordinary m ode)
(2.2.2)
a 't = | [ - ' y c + ( ® 2 + 4 < ) ' / 2 ]
where,
eB
(2.2.3)
m e
The phase difference between the launched and reflected w aves (traveling in the
r direction and measured at the plasma edge) is given by </> - 2I cq
\ £ d r (apart from
an additive constant) where k0 is the free-space wave number o f the probing wave,
is the plasma permittivity, and rc is the position o f the w ave cutoff.
Measurement o f Q thus determines the location o f rc . B y sw eeping the frequency o f the
probing wave and recording the phase history from the beginning o f the plasma
discharge, the electron density profile can be determined (or the B -field for the case o f Xm ode if the density is known).
Since its first use for the investigation o f low frequency microturbulence in
tokamak plasmas [14,15], m icrowave reflectometry has becom e w idely used for density
profile and fluctuation measurements as well as magnetic field investigations [16-24], In
the presence o f density fluctuations, the reflected electrom agnetic w ave spectrum is
broadened with a strong weighting by those fluctuations in the vicinity o f the cutoff layer.
In the simplest case o f small amplitude fluctuations and a 1-D plane stratified plasma
permittivity, £ = £Q(r) + £ { r ) , with £ ( r ) « 1 , the fluctuating com ponent o f the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
measured phase is given by the 1-dim ensional geom etric optics approximation [25].
2 -1
*
Pc
£ (r )
J
{22A)
4 7^ 7
The power spectrum o f the reflected phase fluctuations is related to that o f the density
fluctuations by Ref. 3
r,(k ,.)= ? rM k 20 Lnr n(kr)/\kr\
In
the
M s (ndE/dn)
above,
(225)
L n = n l ( d n / d r ) r=^
c , and it was assumed that
is
the
density
scale
length,
k < ji /(k0Le )] n ,
Le = (ds^ l dr)~l
r
u v u e J where
c.
It is important to point out that the fluctuating phase o f the reflected w ave is
dominated by the change in permittivity close to the cu toff layer, due to the factor
l / V ^ o O ) in the integral, which becom es very large near the cutoff (as the group
velocity approaches zero). The measurement o f fluctuating phase therefore represents a
localized measurement of fluctuations near the cutoff layer, rather than a combined
measurement o f modulations along the entire ray trajectory. Indeed, this is one o f the
m ost valuable features of reflectometry as a fluctuation diagnostic.
In
standard
electron
density
fluctuation
measurements
with
m icrowave
reflectometry, the probing wave is launched and received on the equatorial plane using a
pair o f small antennas. Assum ing the plasma cutoff layer behaves as a 1-D random phase
screen due to microturbulence, the electric field o f the reflected m icrowave [18, 20, 26,
27] is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and h is the fluctuation o f electron density.
2.2.2 Microwave Imaging Reflectometry
The density fluctuation h can be derived from the phase fluctuation o f the
reflected wave. Actually, the turbulent fluctuations are m ultidim ensional (see Fig. 2.8).
There are large radial and poloidal variations, and the assumption o f ID is not valid. For
m ultidimensional turbulent fluctuations, the electric field o f the reflected m icrowave
signal is
( 2 . 2 . 8)
Fig. 2.8 Computer simulation o f the cutoff surface o f plasma. It shows that the
turbulent fluctuations are multidimensional.
The signal w e measure w ill include the effect o f scattering and reflecting from the
corrugated cutoff layer and the phase change. Thus, it is extrem ely difficult to infer the
spectrum o f h from the measured (j (see Fig.2.9). This is a long outstanding issue for
plasma reflectometry.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
Incidence W avefront
Reflection W avefront
Radial
Radial
URL
I
m
Poloidal
(a)
Poloidal
Fig.2.9. Comparison o f 1-D (a) and 2-D (b) reflectometry. For 1-D fluctuations,
(a) the reflection layer w ill m ove back and forth in the radial direction, resulting in the
phase changes in the reflected wave; w hile for 2-D fluctuations, (b) the backward field
propagating along different directions results in a com plicated interference pattern at the
detector plane, so that both the amplitude and phase o f the reflected w ave w ill be
disturbed by the fluctuations perpendicular to the probing beam , leading to a breakdown
o f the simple relationship between phase fluctuations and density fluctuations.
The numerical simulation studies by Dr. E. M azzucato show a virtual cutoff
surface, located behind the actual cutoff surface, from which the return w aves appear to
be reflected to an observer at the plasma edge (Fig. 2.10) [26]. Because the refractive
index o f the plasma in a tokamak is less than unity, the reflected w aves are distorted and
reflected at a real surface which is closer than the virtual cutoff surface. Figure 2.11
shows the amplitude modulation o f the reflected waves from the sim ulation. At the
virtual cutoff surface, where r = r^n, the modulation o f the reflected w ave amplitude is
minimum (Fig.2.11). It is also shown in [18] that density fluctuations can be recovered
from the phase changes of the reflected w ave at the virtual cu toff (r = rmin), which is
beyond the actual cutoff layer (r = rc). Therefore, it is o f crucial importance to use
imaging optics to map the virtual cutoff layer onto the detector plane. (Fig.2.12) [26, 27]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
\
cutoff (n=0)
virtual
cutoff
n<1
n=1
Fig. 2.10. Schem atic representation o f beam trajectories in the vicinity o f the
cutoff layer. Return rays appear to an observer at the plasma boundary to have undergone
specular reflection at the virtual cutoff location.
30 0
25 0
rmin
200
0.5
-5 0
-3 0
10
10
30
50
X [cm]
Fig. 2.11. Isometric surface plot o f the normalized field amplitude o f the reflected
w ave, from the numerical simulations in Ref. 26. The plasma boundary is labeled rb, rc is
the cutoff location, and rmm is the location o f the virtual cutoff, w hich exhibits a minimum
distortion of the field amplitude, [from Ref. 26 © 2001 IAEA]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
44
imaging can restore phase front
o p tic s
Fig. 2.12 Imaging optics is used to map the virtual cu toff layer onto the detector
plane. The amplitude modulation is sm allest at the virtual cutoff layer. Then phase
modulation information is achieved at the detector plane.
1-D r e c e i v e r h orn
S olid a n g l e
c o l l e c t e d with
MIR mirrors
W indow
0 .0
0 ,2
0 .4
0 .6
0 .8
x[m]
Fig. 2.13
Comparison o f Conventional
1-D m icrow ave reflectometry and
M icrowave Imaging Reflectometry. (courtesy o f Dr. Tobin Munsat)
As shown in Fig. 2.13, to obtain com plete fluctuation information, w e should
collect reflection signal within a receiving angle as large as possible. Although w e only
want pure phase fluctuations (i.e., no amplitude fluctuations), the reflected signal are
com pletely m ixed by phase and amplitude fluctuations. Unfortunately, receiving devices
can not normally be positioned very close to the cutoff layer; for exam ple, all diagnostic
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
components should be put outside o f the window on TEXTOR. H ow ever, with large
optical com ponents, a larger solid angle can be collected by Im aging Reflectom etry. The
receiving system o f an MIR system is shown schem atically in Fig, 2.14. Here, all
imaging optics com ponents are drawn as lenses. H owever, in the initial MIR tests,
problems were encountered with the use o f refractive optics. Specifically, there were
standing waves formed between lens elem ents. Consequently, there was interference
between source and detection stages, i.e. the m icrowave signal transmitted by the source
was reflected by lenses before it reached the plasma. Consequently, the detection array
received the spurious reflections. T o remove the spurious reflections, w e decided to use
primarily reflective optics in the MIR system. Tilting the lenses slightly to remove the
spurious reflection is also possible.
Imaging
Imaging
Focal Plane of
MIR Imaging
Fig. 2.14 Conceptual picture o f R eceiving System o f MIR (Lenses Based)
In later chapters, the combination o f the Electron Cyclotron Em ission Imaging
(ECEI) diagnostic technique and M icrowave Imaging Reflectom etry is discussed. Thus,
w e are able to measure both ne and f e simultaneously at essentially the same spatial
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
location, which is important to understand the relation betw een fluctuations and
anomalous transport. [6]
References:
[1]. A.E. Costley, R J . Hastie, J.W.M. Paul and J. Chamberlain, E lectron Cyclotron
Em ission fro m a Tokamak Plasm a: Experim ent an d Theory, Phys. Rev. Lett. 33, 758
(1974).
[2], H J . Hartfuss, T. Geist and M. Hirsch, H eterodyne M ethods in M illim etre Wave
P lasm a D iagnostics with A pplications to ECE, Interferom etry an d R eflectom etry, Plasma
Phys. Control. Fusion, 39, 1693 (1997).
[3]. I.H. Hutchinson, Principles o f P lasm a D iagn ostics,
N ew
York, Cambridge
University Press, 1987.
[4]. M. Bom atici, R. Cano, O. de Barbieri, F. Engelmann, E lectron C yclotron Em ission
an d A bsorption in Fusion Plasm as, Nucl. Fusion 23, 1153 (1983).
[5]. M. Bom atici and F. Engelmann, E lectron-cyclotron A bsorption an d Em ission:
“Vexatae q u a estio n es”, Phys. Plasmas 1, 189 (1994).
[6]. B. Buti, R elativistic effects on plasm a oscillation s an d tw o-stream instability. II.
[Journal Paper] The Physics o f Fluids, vol. 6, no. 1, Jan., pp. 100-107., (1963).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
[7]. P.D. Neordlinger, R elativistic effects on plasm a stability. [Journal Paper] The Physics
o f Fluids, vol. 9, no. 1, Jan., pp. 140-142., (1966).
[8]. B.H. D eng, Two dim ensional electron cyclotron em ission im aging study o f electron
tem perature pro files a n d flu ctuations in Tokam ak plasm as, Ph.D. dissertation, U C D ,
(1999).
[9]. F.F. Chen, Introduction to P lasm a Physics, N ew York, Plenum Press (1974).
[10], R.P. Hsia, e t a l , H ybrid E lectron C yclotron Em ission Im aging A rray System f o r
Texas Experim ental Tokamak U pgrade, Rev. Sci. Instrum. 68, 488 (1997).
[11]. B.H. D eng, et al., Electron C yclotron Em ission Im aging D iagn ostic System f o r RTP,
Rev. Sci. Instrum., 70, 998 (1999).
[12] J. Wang et al., "Two-dimensional Electron Cyclotron Em ission Imaging Diagnostic
for TEXTOR," Rev. Sci. Instrum. 75, 3875 (2004).
[13] C. Laviron, A.J.H. Donne, M.E. M anso, J. Sanchez, “Reflectom etry techniques for
density profile measurements on fusion plasmas,” Plasma Physics & Controlled Fusion,
vol.38, no.7, July 1996, pp.905-36. (1996)
[14]. E. M azzucato, D ensity Fluctuations in the A diabatic T oroidal C om pressor, Bulletin
o f The American Physical Society 20, p. 1241 (1975).
[15]. E. M azzucato, D ensity Fluctuations in the A d ia b a tic Toroidal C om pressor,
Princeton University Plasma Physics Laboratory Report M A T T -1151 (1975).
[16]. E. M azzucato, M icrow ave Reflectom etry f o r M agnetically Confined Plasm as, Rev.
Sci. Instrum. 69, pp. 2201-2217 (1998).
[17], J.L Doane, E. M azzucato and G.L. Schmidt, Plasm a D ensity M easurem ents Using
F M -C W M illim eter Wave R adar Techniques, Rev. Sci. Instrum. 52, pp. 12-15 (1981).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
[18]. E. M azzucato and R. Nazikian, M icrow ave R eflectom etry f o r the Study o f D ensity
Fluctuations in Tokamak P lasm as, Plasm a Phys. Control. Fusion 33, pp. 261-274 (1991).
[19]. A. Costley, M icrow ave R efelectom etry, D iagnostics for Contemporary Fusion
Experiments, ISPP-9 Piero Caldirola, pp. 113-134 (1991).
[20]. E. M azzucato et al., Turbulent F luctuations in TFTR Configurations w ith R eversed
M agnetic Shear, Phys. Rev. Lett. 77, pp. 3145-3148 (1996).
[21]. E. M azzucato and R. Nazikian, R adial Scale Length o f Turbulent Fluctuations in
the M ain Core o f TFTR P lasm as, Phys. Rev. Lett. 7 1 ,1 8 4 0 (1993).
[22]. B.I. Cohen, B.B . Afeyan, A.E. Chou, and N.C . Luhmann, Jr., Com putational Study
o f U ltra-Short Pulse Reflectom etry, Plasma Phys. Control. Fusion 37, pp. 329-344
(1995).
[23]. C.W. Dom ier, N.C. Luhmann, Jr., A.E. Chou, W -M . Zhang, and A.J. Rom anowsky,
U ltrashort-Pulse Reflectom etry (Invited), Rev. Sci. Instrum. 66, pp. 399-401 (1995).
[24], R. Nazikian, G.J. Kramer,and E. V aleo, A Tutorial on the B asic P rinciples o f
M icrow ave R eflectom etry A p p lied to Fluctuation M easurem ents in Fusion Plasm as,
Phys. o f Plasmas 8, p.1840-1855 (2001).
[25]. N. Bretz, D iagnostic Instrum entation f o r M icroturbulence in Tokamaks, Rev. Sci.
Instrum. 68, 2927-2964, (1997).
[26]. E. M azzucato, M icrow ave Im aging R eflectom etry f o r
the
Visualization
of
Turbulence in Tokamaks, Nuclear Fusion, 41, pg.203-213 (2001).
[27]. E. M azzucato, N um erical Study o f M icrow ave R eflectom etry in P lasm as with TwoD im ensional Turbulent Fluctuations, Rev. Sci. Instrum. 69, pp. 1691-1698 (1998).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
Chapter III
Optical Design
3.1 General Optical System Design Considerations
In this chapter, the general aspects o f the optical design for the Electron Cyclotron
Em ission Imaging (ECEI) diagnostic and the M icrowave Im aging Reflectom etry (MIR)
diagnostic, together with the com bined ECEI/MIR system, w ill be discussed. The specific
optical design o f the com bined ECEI/MIR system installed on the TEXTOR Tokamak in
Germany will be discussed in detail later.
3.1.1 Imaging Array
M illim eter w ave im aging arrays integrated with dual dipole antennas and GaAs
beam lead Schottky barrier diode mixers were developed by another U C D avis Ph.D
student, Zhengang X ia [1]. Dual dipole antennas were chosen as the array elem ents for a
number o f reasons: they can be placed close together to achieve high spatial resolution
with compact optical systems; their shape is sim ple and the fabrication is easy; and the
cross talk between channels is relatively small [1]. The structure o f a dual dipole antenna
is shown in Fig. 3.1. The dual-dipole metal patches are form ed on the substrate by
standard photolithography techniques, or by normal printed circuit board fabrication
methods. The diode detectors are mounted at the middle point o f the antenna by using
silver epoxy (EPO XY TECHNOLOGY, INC.).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
Beam Lead Schottky
Mixer IJiode
Fig. 3.1 Structure of a planar dual dipole antenna.
Shown in Fig. 3.2 is a layout o f a 16-channel, dual dipole Schottky Barrier D iode
im aging array [1]. The elements are aligned in the E-plane, which is suitable for MIR
imaging. The IF leads are tapered to 50 Q lines to match the output connector. The
staggered two-line structure improves the spatial resolution for a given elem ent size.
Fig. 3.2 16-channel Imaging array for MIR is fabricated on printed circuit board.
In addition to the bandwidth and sensitivity considerations, the antenna patterns
are extrem ely important parameters in arranging for the system integration. For antennas
mounted on dielectric media, such as the slot bow tie or dual dipole, the w aves tend to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
radiate into the substrate [2], Thus, m ost applications focus the radiation from the
substrate side o f the array. H owever, internal reflections at the substrate-air interface may
excite substrate m odes, which w ill result in power loss and inter channel cross talk [2].
To solve this problem, a substrate lens with an identical dielectric constant is attached to
the substrate side o f the array, as shown in Fig. 3.3. It is seen that the radiation is nearly
normal to the surface, and the internal reflection is elim inated [2]. The radiation pattern
o f the antennas is thus focused along the symmetry axis o f the substrate lens. [3]
Antenna Pattern
Substrate Lens
Transm itting
Antennas
Fig. 3.3 Side view o f an imaging array, show ing the attached hyperhemispheric
lens and the antenna pattern. (After Reference 3)
Fig. 3.4 Left photograph is the back view of the 16-channel MIR Imaging Array.
Right photograph is the assem bly o f the array box.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
52
The substrate lens is closely attached to the im aging array, and is mounted in a
copper-shielding box. Apertures are cut in the cover plates to let through the radiation
and LO power. The sizes o f the apertures are determined by the optical design, which
w ill be discussed in the next section.
3.1.2 ECEI Design Considerations
The goal o f the optical design is to determine the optimum experimental
arrangement to achieve the highest possible resolution of the ECE imaging diagnostic
system . A s discussed in Chapt. 2, spatial resolution is critical for the fluctuation
measurements. The required resolution (~ lc m ) is also a constraint for the design.
R ealistic considerations set a criterion o f the sample volum e size to be about 1 cm, and
the channel spacing should be about the same value.
Sim ilar to other tokamak diagnostics, the ECE imaging diagnostic is lim ited by
the port accessibility. From Fig. 3.5, it is seen that ECEI needs a horizontal tokamak port
extended in the vertical direction. The tokamak surroundings are always crowded with
diagnostics. Therefore, since ECEI is a new diagnostic, the optical design should fit the
system in the space available among the existing diagnostics. Consequently, the optical
path length may have to be increased, and extra lenses/mirrors may have to be utilized.
Other factors that must be considered are: (1) the size o f the lenses/mirrors, which
is directly related to the fabrication cost, (2) the sim plicity o f the optical system, which
should be easy alignment, (3) the stability o f the system performance, and (4) the
efficien cy o f the system , which is related to the signal to noise ratio. The system design is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
a tradeoff among the spatial resolution and the lim iting factors. The main tradeoffs are
summarized in the follow ing.
First, high spatial resolution requires the beam to be focu sed to form a sm all beam
waist in the plasma, as shown in Fig. 3.5. H owever, smaller beam w aist results in more
rapid beam divergence. Because the minimum distance from the plasm a sample volum e
to the first lens is usually fixed by the port accessibility, the faster divergence o f the beam
leads to larger lens size and fabrication cost. It is also lim ited by the size o f the available
port.
Second, high spatial resolution requires also requires sm all channel spacing.
Hence, the antenna elem ents o f the im aging array should be placed close to each other.
This small spacing lim its the perm issible bow-arm length o f the antenna, thereby
affecting the frequency response and sensitivity o f the array.
Third, few er lenses w ill make it easier to adjust the system , which also helps to
ensure more stable system performance. More optical com ponents w ill make it easier to
tune the beam to fit the system requirements.
Finally, to m inim ize the inter-channel cross talk, the side lobes o f the beam
pattern should be m inim ized. Side lobes may occur from the edge diffraction o f the
optical com ponents, or from the side lobes o f the antenna patterns. To reduce the side
lobes originating from the edge diffraction, the sizes o f the optical com ponents should be
constrained to be more than tw ice the Gaussian beam diameter. [4] This will also reduce
the power loss in the optics. To reduce side lobes due to the antenna, the chosen antenna
type should have patterns with small side lobe levels and a w ell-defined main lobe. The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
beam width of the antenna pattern w ill determine the width o f the Gaussian beam waist.
Thus, its choice should m eet the spatial resolution requirements discussed above.
Imaging
Imaging
Focal Plane o f
Array
Optics
ECE Imaging
Fig. 3.5 Conceptual picture o f ECE im aging diagnostic system (based on lenses).
[2] The high spatial resolution is achieved by positioning the focal plane o f the optics in
the same plane o f the sample volum es, which is determined by the resonance condition.
Finally, the ECE Imaging system design considerations are summarized as
follow s.
•
The size o f all the optical com ponents should be reasonable and all system
components should be capable o f installation without conflicts.
•
The tokamak window size is a very important limitation for optical design.
Normally, the window is assigned by som e administrator o f the tokamak facility.
Thus, the size o f window is fixed. The beams should pass through the window
with negligible power loss.
•
To m axim ize the spatial resolution o f the imaging system, the Gaussian beam
radius
we
at the 1/e electric field strength of the detection system in the E-plane
should be reasonable. It is related to the frequency and the optical system . For
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
example, w E is about 1cm for TEXTOR. The Gaussian beam radius
wh
electric field strength o f the detection system in the H -plane should be
at the 1/e
w h
<
5w
e .
Since the m agnetic field is m ostly in the H-plane, in w hich the fluctuations have
long correlation lengths, the spatial resolution in this direction is less critical. (Fig.
3.6)
•
U se as few a number o f optical elem ents as possible. Sim ple and good
performance is the design target.
^
E
Fig. 3.6 The conceptual picture o f the beam spot o f the system (one dimension).
The ellipses represent the beam spots. Here, w E is the Gaussian beam radius at the 1/e
electric field strength o f the system in the E-plane,
wh
is the Gaussian beam radius at the
1/e electric field strength o f the system in the H-plane, and d is the spacing between
contiguous channels.
•
For the im aging system, the spacing between channels “d” in the E-plane at the
measurement point should be d~1.2w E (Fig. 3.6). Small d will result in data oversampling. A large value for d will decrease the channel number.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
•
If the special resolution obtained is not satisfactory, changes may have to be made
to the array parameters, i.e., the array elem ent spacing and the antenna pattern. A s
the system is usually antenna lim ited instead o f diffraction limited, the antenna
pattern usually determines the sample volum e sizes, and the array elem ent spacing
determines the plasma sample volum e spacing. Thus, a preliminary design should
be performed according to the tokamak conditions, so that the array parameters
can be chosen from several designs. After the array is fabricated, a final design
based on the actual array parameters can be performed.
•
Arrange for as many channels as possible. With the limitation o f the w indow , we
need to perform a tradeoff between channel number and spatial resolution.
•
The sight lines o f the im aging system should be horizontal or diffuse a little at the
resonance layer because w e want the system to be able to detect a larger region of
the plasma.
•
A s shown in Fig. 3.5, the LO power is coupled to the array from the backside. As
the array is extended in the E-plane, the LO beam should be transformed to an
elliptical beam, extended in the E-plane, and focused onto the array. The beam
width should be sufficiently wide to cover the entire array. It is chosen as a
com prom ise between the uniform illum ination o f the channels, and the power
lo ss.[3]
3.1.2 MIR Design Considerations
A typical MIR system based on lenses is shown in Fig. 3.7. It consists o f two sub­
system s, a) a transmitting system to send out m icrowaves to illuminate the plasma, b) a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
receiving imaging system to detect the reflected w aves with the im aging array. A beam
splitter is used to com bine them.
Imaging Lenses
Beam Splitter
Imaging Array;
Cutoff Surface
Window
LO Source
Illumination Source
Plasma
Fig. 3.7 Conceptual picture o f MIR System (based on lenses)
The system design considerations are as follow s.
•
Similar to ECEI, the size o f all the optical components should be reasonable and
all system s should be capable o f installation without conflicts.
•
There is interference between source and detection stages, i.e. the m icrowave
signal transmitted by the source suffers reflection by the lenses before it reaches
the plasma. Thus, the detection array receives these spurious reflections in
addition to the actual signal. To remove the spurious reflection, reflective optics
are em ployed in the MIR system. Tilting the lenses slightly to rem ove the
spurious reflection is also possible.
•
The tokamak window size is also a very important lim itation for the optical
design o f MIR. The beams should pass through the w indow with negligible power
loss.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
58
•
For the receiving system, to m axim ize the spatial resolution o f the imaging
system, the Gaussian beam radius
we
at the 1/e electric field strength o f the
detection system in the E-plane should be w E~ lc m , and the Gaussian beam radius
w H at the 1/e electric field strength o f the detection system in the H-plane should
be w H<
5w
e .
Since the magnetic field is primarily in the H-plane, in which the
fluctuations have long correlation lengths, the spatial resolution in this direction is
less critical. (Fig. 3.8 and Fig. 3.9) These requirements are sim ilar to those for
ECEI.
Imaging
Arrav
Imaging
Focal Plane of
MIR Imaging
Fig. 3.8 Large diameter imaging optics im age the plasma cutoff layer onto the
m ixer array; hence, the sample volum es coincide with the focal plane o f the imaging
optics.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
W&
Fig. 3.9 Conceptual picture o f the beam spot o f the transmitting system and
receiving system (one dimension). The large ellip se represents the transmitting beam spot.
Small ellipses represent the receiving beam spots. Here, w E is the Gaussian beam radius at
the 1/e electric field strength o f the detection system in the E-plane,
wh
is the Gaussian
beam radius at the 1/e electric field strength o f the detection system in the H-plane, and d
is the spacing between contiguous channels.
•
For the receiving system, the spacing between channels “d” in the E-plane at the
measurement point should be d~1.2w E(Fig. 3.9).
•
Similar to the case o f ECEI, w e wish to arrange for as many channels as possible.
With the limitation o f the window, we need to perform a tradeoff between channel
number and spatial resolution.
•
The size o f the beam spot o f the transmitting system at the cutoff layer should be
greater than that covered by the receiving system, but not too much greater in
order to m inim ize the power loss (Fig. 3.9).
•
For the transmitting system, w e want all the power to illuminate the plasma. The
required size o f optical components should be greater than three times the
transmitting Gaussian beam radius.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
•
For the receiving system , w e want the detection region to be as large as possible.
•
The sight lines o f the receiving system should be perpendicular to the plasma
cutoff layer with a cutoff frequency. This is essential to m axim ize the reflected
power in the receivers. (See Fig. 3.10)
Mirror or Lens
Window
Incident Beam
Edge
Plasma
Cutoff Layer
Gaussian
Beam Waist
Fig. 3.10 Conceptual picture o f the sight lines o f receiving system.
•
The radius of curvature o f the wave front o f the transmitting system at the
measurement point should be close to the curvature radius o f the plasm a cutoff
layer, so that the incident beam will be received with less power loss.
3.1.3 Combined ECEI/MIR System
Shown in Fig. 2.2 o f Chapter Tw o, the ECEI and MIR system s on the TEXTOR
tokamak operate with comparable, but disparate frequencies. Specifically, for TEXTOR,
the ECE Imaging system uses 110-135 GHz, and the MIR system uses 84-90 GHz. Thus,
it is possible to configure a com bined ECEI/MIR system which m akes it possible to
measure electron temperature Te and electron density ne fluctuations sim ultaneously
using a single port. The local correlations between Te and ne fluctuations can thus also be
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
studied. A conceptual picture o f a com bined ECEI/MIR system is shown in Fig. 3.11. A
dichroic plate is used to separate the ECEI and MIR system s. The dichroic plate works
like a high pass filter, which reflects a low frequency wave com pletely and lets the high
frequency wave pass
W in d ow
Notch Filter
Electronics
Mirror E
Mirror H
Sputter
MIR
Illumination
Source
Electronics
Fig. 3.11 Conceptual picture o f Combined ECEI/MIR system s. A Notch filter is
used to protect ECEI array because the ECRH heating system o f TEXTOR tokamak uses
140 GHz frequency, which is near the ECEI band.
In previous ECEI system s, w e em ployed a dichroic plate as a high-pass filter to
reject the stray ECRH power at lower frequency than the filter cutoff frequency.
H owever, in som e system s, the ECRH frequency is in the m iddle o f the signal frequency
region. Consequently, there is a need for a band-stop filter (Notch Filter) which only
rejects the signal at the ECRH frequency and allows all other frequency signal to pass.
Currently, a 140 GHz notch filter is under development in our group.
The com bined system design considerations are sim ilar to those for ECEI and
MIR. Som e different considerations are listed as follow s.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
62
•
A mirror based optical system is needed. Because the MIR optical system
requirements are more strict than those for ECEI, the MIR optical system was
designed first. ECEI then uses the same mirrors as for MIR.
•
The mirrors o f the ECEI optical system are fixed by the requirements o f MIR.
Thus, the optical situation is more com plicated for ECEI. M ore optical
components are needed for the ECEI optical system. Spatial resolution and
plasma coverage can not be optimum as w ould be possible for a separate ECEI
system.
•
A Dichroic plate is needed to separate the signals for the ECEI and MIR systems.
The optical system should include it in simulation.
•
Tilting mirrors are used. The question is how tilting the mirrors w ill affect the
aberrations o f the beam trace. W e have two choices: tilting the mirrors
horizontally or vertically.
•
Tilting the mirrors vertically (see Fig. 3.11) increases the geometrical aberrations
o f the optical system.
Shown in Fig. 3.5, the spherical aberration w ill result in
different beam waist positions for each channel, i.e. the beam waist o f the center
channel is further than those o f edge channels.
Tilting the mirrors vertically
makes the beam waist closer on one end o f the array and further on the other end.
Finally, the maximum difference am ong all the beam waist positions is larger.
The electric field orientation o f our detecting array is vertical in order to receive
the polarized X-m ode m icrowave (see Fig. 2.1). Tilting the mirrors horizontally
makes less effect on the beam waist positions. For a one dim ensional antenna
array, the spacing between the staggered channels is usually small. The aberration
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
because o f tilting mirrors horizontally is negligible. For the com bined TEXTOR
ECEI/MIR system , the space near the port is lim ited so that it is im possible to tilt
the mirrors horizontally; thus, tilting the mirrors vertically is the only choice.
Details o f the optical design and considerations will be discussed in Sec. 3.2,
based on the optical design for TEXTOR.
3.2 Optical System Design of the TEXTOR ECEI system
3.2.1 Introduction o f CODEV
Our group required professional software to com plete the optical system design.
Consequently, w e chose CO DEV which calculates on the principles o f Geometrical
optics in some functions like V iew Lens and Real Ray Trace, 3D V iew ing, etc. In these
functions, a wave travels along the line which starts from som e point on the object
surface and ends som ewhere on the image surface. When the w aves encounter optical
surfaces, these rays obey S n ell’s Law and the Law o f R eflection. In other functions like
Gaussian Beam Trace, the w ave behavior obeys a physical optics calculation which is
called wave-based or diffraction-based calculations in CODEV. [5]
Figure 3.12 show s a screen shot from the program. A navigation w indow provides
a way to keep track o f all the w indow s you are working with. The lens data manager
window is the main numerical view o f the primary lens data. The comm and window is
used to input som e commands directly. Graphics are generated in the plot window.
CODEV provides many ways to analyze your design, like Radial Energy Analysis,
Geometrical Analysis, Point spread Function, W avefront A nalysis, etc.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
Lens Data Manager
Navagation W indow
5 L O O tV
E*e E*
Analyse W indow
/
ja llS G J e n
Display fie tfe w
ftu ly s ts
Q p tM u U o n
Is d s
IM ndm i
□ Gii ma ?■ft e iij i i.a11e Iiiy hi w w a 5 or
3 Z I j|H.
’ 1 - E c tl_ M lrra r_ W a n g
9
Sa
^
<s
is
a y no
0
*? i
S li
zixi
L en s D ^ a M an a g er
S y ste m D a ta
S u rfa c e Pro perties
C om m and W r d o w
R e v ie w S p re a d sh e e ts
Listings
■j A nalysis W in do w s
SH*;’’ -inixSurface
Type
Y Radius
XRadius | Thickness
Infinity
Infinity
•60.OKU
Infinity
Infinity
•165.0000
mn nnm
View Len*
G a u ss ia n B eam T rac e
O p tinizalion
P W W in d o w s
E n a Log
j 0 0000
/ 00 0000
! 105.0000
30.0000
100 oooc
120.0000
i?n nnm
Refract |
Y & m * P- | gfsTv !-V uv \ b v H
Mode ISemi-Ape , * ^
__ !__
Refracl
PROPAGATION
B E A K \R A D I U S O R I I K ­
523000.600 Refracl
ON S u \ f ACE
(D E C
DISTA NC E TO
Refract
L|3UR N EXT SURFACE
Refract
0 .0 0 0 0
1 .S 1 0 0
1 .8 1 0 0
523000.600 Refract
9 7 .5 7 3 7
1 .8 1 0 0
1 .8 1 0 0
Refract
1 0 8 .6 6 0 1
2 9 .8 8 0 2
3 1 .1 3 9 4
ATmm Km Pefrarl
Glass
mM23
«*1h x m
«
® |
C le a r te x t
- R A T D I F ; FAN 111 0 3
RAT D IF ;F A N H I 0 2
- R A T D E F;F A N H I 0
SCSI M irr o r uasifl
CODE V>
J
Tent A 1/
±1
| d OH: M C m e te rs
{ A p e rtu re s U sed : U ser-D efin e d Only
Command window
U s e ZX P la n e : N o
IP o ta rb atio n R a y T r a c r g A c tiv e : N o
Plot W indow
Fig. 3.12 Screen Shot of CO DEV. [5]
3.2.1.1
System Data W indow
When a new system design is begun, it is first necessary to find the System Data
at Lens o f the menu bar to define som e basic parameters o f the new system like pupil,
and wavelengths fields/vignetting, System settings, (see Fig. 3.13 and Fig. 3.14)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
Pupil
-Spectrum-------------------
-W avelen gth sFields/Vignettrig
r S elec t Spectrum for U se
W avelength
System Solves
2 6 0 8 6 9 5 .0 0 0 0
System Settings
A dvanced
Afocal
Through F ocus
Chief R ay Aiming
Polarization
- Store Currert Spectrum-
P upl Apodization
Astigmatic Object
Fiber Location
C r s a te N e w S p e c tra - Profile
Coating Waveiengthfran):
R eference W avelength:
W 1 -260 8 6 9 5
-Fictitious G lass M o d d -
G lasses to define th e Dispersion Model
(Up to 2 0 g lasses may b e specified)
Defming W avelengths (3 requrecj)-
|S56.2725
zl
1587.5618
zl
1486.1327
zl
R eset to
Defaults
LtT1
Pupil
W avelengths
FieldIype:
y|
| Object Height
r
w i d e A n g le M o d e
Fields/Vignetting
System S olves
System S ettings
Vignetting
Field
A dvanced
X Height
Afocal
1
Through F ocus
2
Chief R ay Aiming
3
Polarization
*
O .5080
Y H eig tt
- 1 6 .8 9 0 0
I
W eight
1.0000
0.0000
0.0000
1.0000
- 0 .5 0 8 0
1 6 .8 9 0 0
1.0000
j
Color
■Nam
■■■■■
♦Y
“
♦X
-X
-
-V
0 .6 7 9 9
0 .7 8 4 0
0 .7 9 4 2
0 .1 3 6 4
0 .1 3 6 4
0 .1 9 4 4
0 .1 9 4 4
0 .6 7 9 9
0 .7 3 1 2
0 . 7942
0 .7 8 4 0
0 .7 3 1 2
'
Pupil Apodization
Astigmatic Object
Fiber Location
HI
1
S et Vignetting...
F ig.3.13
System
if1
Copxert Fields...
data window. Set wavelength w hose
units are nm and
fields/vignetting. X /Y heights of field are the position o f the object. Y-height o f the two
edge channels o f the 20-channel antenna array o f ECEI is 16.89m m . Because there are
only two channels on the H-plane, the X-height o f these two channels is 0.508m m .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
Pupil
Tilje: j E CE l_M irroi_Wang
W av elen g th s
Fields/v/ignelting
Designer initials: jJW
System U nits: Milimeleis
Xeraporature (D egrees C): (20.0000
Pressure (mmHgJ
3
System Solves
R
A d vanced
Afocal
A pejtures U sed: (U ser-D efined Only
T hrough Focus
Chief R ay Aiming
Polarization
3
-R efe r e n c e S phere Location---------------------C Rgal Exit Pipil
P u p l Apodization
&iBfrtHy
Astigmatic Object
r
U jet D efined
r-
(760.0000
U se ^ -Z Plane for 1st order
calculations & S olves
r R adus/'C ievatureM ode:----------
! <? Rod«s
C
|lOOOOOUOOCOOC
C uvature
Fiber Location
- Global Coordinate*----------------------------------
V
U se global Coordinates for Output
XQflset: p flG G G
X Offset:
R eference Surface: [Object"""
0 0000
3
20if«ot jOCBjao
Tolerances:
f ~ Independent Compensators
Fringe ^ a v e ie n g lh (am]: j 5 4 6 1 0 00
3
Fig. 3.14 System data window. Set system settings. System units is the units used
all along the program which is millimeter.
3.2.1.2 Lens data Manager W indow
In the lens data manager w indow , an optical system is defined here. According to
the definition given by CODEV, Optical system is a collection o f optical surfaces along
with som e properties (system data) that define the rays o f light that w ill interact with the
surfaces. A n optical system in CODEV is a model o f a real optical system that could be
built. It can contain refracting surfaces, reflecting surfaces, or both. In the optical system,
the object and image surfaces should be determined first. The object surface is where the
light is assum ed to start, and the image surface is where the light is usually collected and
analyzed (som etim es an image is formed there, som etim es not). Then, in the lens data
manager w indow , every surface between the object and the im age should be defined and
the distance among any contiguous surfaces should be given. W e can define the surface
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
67
refract or reflect in the refract m ode column. The m edium index is defined in the glass
medium. Surface type and surface name, size, etc. (see Fig. 3.15).
Surface
Surface
#
N am e
Object
I
I
Surface
Type
|
V Radius
X Radius
Thickness
Glass
I Refract
| Mode
X
Y
Semi-Aperture Semi-Aperture
Q
O
S p h e re
Infinity
Infinity
0 .0 0 0 0
iSphere
Infinity
Infinity
100.0000
R efract
6 0 .0 0 0 0 0
60 0 0 0 0 °
2
S p h e re
-60.0000
-60.0000
105.0000
R efract
6 0 .0 0 0 0 0
6 0 .0 0 0 0 °-
Stop
S p h ere
Infinity
Infinity
3 0 .0 0 0 0
R efract
4 8 .0 0 0 0 0
S p h e re
Infinity
Infinity
100.0000
R efract
1 5 0 .0 0 0 0 °
1 5 0 .0 0 0 0 °
S p h ere
■ -165.0000
-165.0000
120.0000
IRefract
150.0000 °
150 0 0 0 0 °
Infinity
3 0 0 .0 0 0 0
120.0000
R efrac t
2 0 0 .0 0 0 0 0
1 20 .0 0 0 0 0 i
-300.0000
Infinity
760 .0 0 0 0
R efract
2 0 0 .0 0 0 0 0
12O.OOOO0 '
C ylinder
Infinity
3 3 0 ,0 0 0 0
120.0000
R efract
2 5 0 .0 0 0 0 0
120 0 0 0 0 0
Cylinder
-360.0000
Infinity
300 .0 0 0 0
R efract
2 5 0 .0 0 0 0 0
1 2 0 .0 0 0 0 0 i
876 .0 0 0 0
R efract
3 2 5 .0 0 0 0 ^
150 .0 0 0 0
-832.5000 v
R eflect
3 3 5 .0 0 0 0 0
150 0 0 0 0 0 I
150 0 0 0 3 0 I
1
4
ES
EF1
5
S
EF2
7
8
C ylinder
C ylinder
EF3
9
:
10
B ea m splitte
S p h ere
Infinity
Infinity
11
H -plane mirr
C ylinder
Infinity
-210 0 .0 0 0 0
12
E -plane mirr
C ylinder
2700.0000
Infnity
1270.0000
13
W indow
S p h ere
Infinity
Infinity
3 0 .0 0 0 0
14
S p h e re
Infinity
Infinity
Im age
S p h ere
Infinity
Infinity
IRefract
5 2 3 0 0 0 .6 0 0
5 2 3 0 0 0 .6 0 0
5 2 3 0 0 0 .6 0 0
5 2 3 0 0 0 .6 0 0
3 6 .0 0 0 0 0 I
R eflect
5 0 0 .0 0 0 0 0
R efrac t
2 1 0 .0 0 0 0 0
7 5 .0 0 0 0 B |
875 .0 0 0 0
R efract
2 1 0 .0 0 0 0 0
7 5 ,0 0 0 0 B I
0.0 0 0 0
R efrac t
9 6 0 0 0 0 .6 0 0
1 1 6 .0 0 0 5 °
1 1 6 .0 0 0 5 °
End Of Data
Fig. 3.15 Screen shot o f Lens Data Manager W indow. It is the final design o f
ECEI.
3.2.1.3 V iew Lens W indow
W hen the system is built, use D isplay>V iew Lens to see the system picture. The
V iew Lens window w ill pop out automatically (Fig. 3.16). In V iew Controls, choose
different cross-sectional view s to see two cross-sections, YZ and XZ. The Z direction is
the light traveling direction. In Ray Definition, change fan o f rays to change the number
o f rays starting from one point at the object surface (Fig.3.17). In lens Drawing, choose
the surfaces color, whether to show dummy surfaces (dummy surface can be defined),
whether to label surfaces or elem ents, whether to show coordinate axes. After all settings,
the com plete optical system will be drawn in the view lens window . Figure 3.18 show s an
example.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
68
R ay Proportion
Plot P a ra m e te r
I
*
Ray Definition
* View Controls
I
|
Im age Orientation
L ens Drawing
j
Title/Offsets
'(• Cross-section view
3
E e fe te n c e surface |i? I 5 3 T
Local cross-sections frZPrZ) p Z
jrJ
C Perspective view
R eference surface
J1
■r
j
Froin j 1
Azimuth angle 137 ;'
Elevation angle |26.60QQ
Element modeling [Fuii
r S u rface R a n g e -
1 °
[im a g e
"3
Angle to rotate cu t
r
10.0000
H i d d e n lin e r e m o v a l
C" Sliced view
R eference surface |
Azimuth angle
1
~7~j
0.0000
Elevation angle 10.0000
NOTE: Projection is w .r.t global coordinates of referen ce surface
O ption S e t..
OK
C ancel
Help
Fig. 3.16 V iew Lens W indow. D ecide which cross-section will be shown in the
plot window.
Farr of R ay s
Field
1
i l l
F ie l
W avelength
¥ 1 - 2 6
2
i l l
F ie l
3
i l l
F ie l
Pupil Angle
No. R ays
Color
Line Style
S tart S u rfa c e End S u rface “7
0 .0 0 0 0
31
D e fa u lt
ID e f a u l t
O b ject
Im age
¥ 1 - 2 6
0 .0 0 0 0
21
D e fa u lt
ID e f a u l t
Obj e c t
Im age
¥ 1 - 2 6
0 .0 0 0 0
31
D e fa u lt
D e fa u lt
0bj e c t
Im age
*
I
l
L ............................. ......................................................I
J
1
Fig. 3.17 Fan of Rays. It means the number o f the traces from one field point on
the object surface.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
■ IH
m \*
^
m
H
—
iSl ft
@
1 iil'liiiin'
/ k m
5 6 8 .1 8
ECEI_Mirroc Wang
Scale:
0.04
HM
JW
jU
± r
M H l H N f v Taxi A 1 A
Fig. 3.18 Picture o f a com plete optical system. The exam ple is the ECEI optical
system.
3.2.1.4 Analysis
At this stage in the design process, w e use Analysis o f the menu bar to analyze the
system, for example, real ray trace, Gaussian Beam Trace, MTF, Point Spread Function,
etc. when choose Analysis>D iagnostics>R eal Ray Trace, Real Ray Trace w indow will
pop out (Fig. 3.19).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
JJiS)
Settings
Oulptf Formal |
Global Coordinates |
Available Items
LOptical Direction Cosine of RayAfter Surface |L)
MOptical Direction Cosine of Ray After Surface (M)
N Optical Direction Cosine of Ray After Surface (N]
Ant^e ef Incidence (ADI)
Angle ef Refraction (AOR)
LDirection Cosine of Surface Normal (SRLJ
MDirection Cosine of Surface Normal (SRMJ
N Direction Cosine of Surface Normal (SRN|
Intensity through Lin Polarizer w/TransmissionAws IIX(FXI)
Intensily through Lin Polarizer w/TransmissionAws IIY(FYI)
Fraction of Light Polarized (PFR)
Intensity Ration: MinorAxis to Major Aids (FTP)
Orientation of Major Ants (FOR)
Right. Left or Linear (PRO)
Real Component of Jones Matrix (JR1)
Real Component of Jones Matrix (JR2)
Real Component of Jones Matrix (JR3)
Real Componer* of Jones Matrix(JR4)
Imaginary Component ofJones Matrix (JIT)
Imaginary Corrponent ofJones Matrix(JI2)
ImaninArii FrininnnptV
^elected Items
X Coordinates cf Ray on Surface |X)
Y Coordinates of Ray on Surface fr)
Z Coordinates of Ray on Su face (Z)
X Direction Tangent (TNX)
Y Direction Tangent (TNY)
Ray Length fromPrior Surface (LEN]
*1
jd
♦]
Mahiv (.11Yl
^ Numeric output format— --------------------Eorawltypec [Fixed
P 123456.12345
Fieldyndth. [T1
Qigis after decimal: |5
Hefc
Fig. 3.19 Real Ray Trace window . Choose output form and give appropriate
settings.
When choosing Analysis>D iagnostics>G aussian Beam Trace, Gaussian Beam
Trace window w ill pop out (Fig. 3.20). The beam half-width at the object surface first
should be input.
Input B eam |
Output Controls |
Color Display I
N ote: L e m must h a v e finite object d istance. Default initial beam
w aist is located at object surface.
At the 'object1surface: [valu es in len s units)--------------------------------B earn half-width
X-direction
jh-81 00
-W a v efro n t radius of curvature—
1
Y-direction
1.81 00
B eam rotation (d egrees)
Option S et...
j
jo. 0000
Y-direction
10.0000
OK
C ancel
X-direction
—
[0 .0 0 0 0
J
Halp
|
Fig. 3.20 Gaussian Beam Trace window. Beam half width is com puted from the
receiving angle o f half bandwidth o f 1/e electric field 15.5 degrees.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
MTF, Point Spread Function, other analyses have the sim ilar operation process.
3.2.2 Optical design parameters
Optical sim ulations for 20 channels have been conducted based on the dual dipole
array pattern at 115 G Hz (wavelength 2608696nm ).
Dual dipole array: E-plane 70 m il spacing, H -plane 40 m il spacing, receiving
angle of half bandwidth o f 1/e electric field: 15.5 degrees outside o f the substrate lens, 24
degrees inside o f the substrate lens. [1]
Mirror E
Substrate Lens
Image Plane
Window
Dichroic Plate
Mirror H
Lenses
5 6 8 . IB
MM
Fig. 3.21 Side view o f ECEI optical System. Only T w o edge channels and the
Center channel are shown here. The beam waist o f the top channel (blue) is further than
those o f the center channel (green) and the bottom channel (red).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
72
Image Plane
Fig. 3.22 Detailed beam structure at the im age plane, 20-channel beam is shown.
It is seen that the positions o f beam waists o f all channels are different. The greatest
difference is about 15 cm.
Substrate Lens
Mirror H
Dichroic Plate
Mirror E
Window
Image Plane
Lenses
5 68.18
MM
Fig. 3.23 Top view of ECEI optical system. Only two channels are displayed in
this H-plane.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
3.2.3 Gaussian Beam Trace
G A U S S I A N
B E A M
P R O P A G A T I O N
EC E I_M irror_W ang
DIMENSIONS = MILLIMETERS
BEAM
WAVEFRONT RADIUS
PHASE
ORIENTATION
OF CURVATURE
ORIENTATION
(DEGREES)
BEFORE REFRACTION
(DEGREES)
X
Y
BEAM RADIUS
ON SURFACE
X
Y
0 .0
0.0
0 .0
0 .0
0 .0
INF
INF
-1 0 0 .3 5 0 6
-2 5 5 .2 1 6 4
- 2 8 5 .0 5 0 9
- 5 2 7 .4 2 4 0
5236.6034
7836.5334
-23B .3596
-4 7 3 .4 5 4 5
-8 4 6 .2 2 4 5
-1 7 0 7 .9 5 1
2536.0575
907.0605
1711.4511
4230.2888
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o o
o o
0.0
o
o
0.0
0 .0
0.0
0.0
0.0
0 .0
INF
INF
-1 0 0 .3 5 0 6
-2 5 5 .2 1 6 4
-2 8 5 .0 5 0 9
-5 2 7 .4 2 4 0
5236.6034
687.8627
-3 1 4 .5 6 6 1
-1 0 1 3 .8 8 1
-9 6 1 .3 1 9 0
-1 8 2 2 .8 2 3
-2 8 2 4 .9 8 7
1695.1979
3230.1046
1319.6654
o o
o o
o o
o o
1.8100
1.8 1 0 0
1.8100
1.8 1 0 0
30 .6205
30.6205
51.9 4 5 8
51.9458
58.0 5 3 9
58.0539
7 1 .6298
71.6298
70.0113
70.0 1 1 3
59.6043
68.9 4 8 9
4 0 .6389
30.0039
4 6 .0656
4 0 .1293
66.7425
87.4 768
1 2 8 . 0 2 62 1 4 5 . 9 9 5 0
9 8 .7375 21 7 .2 4 8 6
55.3 8 8 7
78.1870
54 .8785
76.8399
2 9.4 8 4 8
9.5642
o o
o o
OBJ
0 .0000
1
100.0000
2
105.0000
3
30 .0000
4
100.0000
5
120.0000
6
120.0000
7
76 0.0000
8
120.0000
9
300.0000
10
876.0000
11 - 8 3 2 . 5 0 0 0
12 1 2 7 0 . 0 0 0 0
13
3 0 .0000
14
8 7 5.0000
IMG
* NM
o
o
PROPAGATION
DISTANCE TO
SUR NEXT SURFACE
PO SI T IO N
=****
O
o
WAVELENGTH
1
FIE LD PO S IT IO N -
( 0 .0 0 ,
WAIST RADIUS
BEFORE
REFRACTION
X
Y
DISTANCE FROM
WAIST TO SURFACE
X
Y
1.8100
1.8100
1.8100
4.0672
4.0672
4.0 6 7 2
46.4615
6.3486
6.3486
11.7 7 2 7
11.7727
11.772 7
23 . 0 9 8 6
23.0986
23.0986
2 3 .0986
1.8100
1.8100
1.8100
4.0672
4.0672
4.0672
46.4 615
46.4615
6.4428
6.4428
11.1732
11.1 7 3 2
11.1732
9 .56 10
9.5610
9 .56 10
0.0000
0.0000
100.0000
2 5 3.6518
2 8 3.6518
525.7236
-2 9 3 0 .3 9 3
-6 8 0 .0 5 9 0
306.8892
9 4 7.6614
931.4093
1807.4093
2 6 70.3819
-1 4 0 0 .3 8 2
-2 6 5 7 .8 5 6
-5 0 9 .7 5 1 8
0 .0 0)
0.0000
0.0000
100.0000
25 3 .6 5 1 8
28 3 .6 5 1 0
52 5 .7 2 3 6
-2 9 3 0 .3 9 3
-4 2 7 8 .1 3
22 7 .3 6 8 8
461.2503
818.6133
1694.6133
-2 5 2 7 .1 1 3
-8 9 3 .4 9 6 9
-1 6 8 4 .9 5 4
-2 .8 6 6 8
Fig. 3.24 Gaussian Beam calculation of the central Channel. Beam waist o f Eplane is 9.56m m . Beam waist of H-plane is 23.1m m . The distance from the beam waist o f
the E-plane to the im aging surface is -2.86m m . (Negative number m eans it is on the right
side)
G A U S S I A N
B E A M
P R O P A G A T I O N
E C EI_M ircor_W ang
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0 .0
0.0
0.0
o o
o o
0.0
0.0
INF
INF
-9 7 .9 3 3 0
-2 6 4 .4 9 4 1
-2 9 4 .5 8 7 3
-5 4 7 .1 1 7 5
3339.1466
4984.9141
-2 7 5 .7 7 6 9
- 5 2 2 . 6823
-9 1 3 .8 1 2 2
-1 8 3 0 .2 0 9
2 628.5499
9 1 2 . 6 359
1723.1112
-1 9 7 2 4 .0 3
o o
o o
0.0
INF
INF
-9 7 .9 3 3 0
- 2 6 2 . 8 8 64
-2 9 3 .0 3 7 1
-5 3 9 .2 5 1 2
3891.9661
659.4987
-3 3 6 .0 9 5 2
-1 1 3 3 .4 5 2
-9 8 9 .4 1 9 7
-1 9 1 2 .1 8
-2 2 6 2 .3 5 1
1120.9254
2130.5468
-83 65.276
o
o
o o
o o
0.0
0.0
o o
o o
1.8 1 0 0
1.8100
31.1394
48.3453
5 3.8944
65.6 0 2 7
6 3.6383
62.0 6 3 8
33.3900
43.1285
85.5346
129.6908
188.6899
68.8081
67.6303
10.8 8 0 8
o
o
1.8100
1.8100
29.8802
50.8424
56.7132
69.6030
67.4837
57.2196
43.5684
48.3 2 1 9
64.2945
126.0601
92.8112
41.3274
40.7523
19.8077
BEAM
WAVEFRONT RADIUS
PHASE
ORIENTATION
OF CURVATURE
ORIENTATION
(DEGREES)
BEFORE REFRACTION
(DEGREES)
X
Y
o o
o o
OBJ
0.0000
1
97.5 7 3 7
2
108.6601
3
30.3 4 4 5
4
99.9 0 6 9
5
121.3014
6
118.1903
7 7 53.0051
8
111.9421
9
247.4283
10
941.4568
11 - 8 0 5 . 4 4 5 1
12 1 2 9 5 . 3 8 5 3
13
30.0 0 2 0
14
875.2190
IMG
BEAM RADIUS
ON SURFACE
X
Y
DIMENSIONS = MILLIMETERS
o o
o o
PROPAGATION
DISTANCE TO
SUR NEXT SURFACE
= * * * * * * * * NM
o
o
WAVELENGTH
PO SIT IO N
0.0
0.0
1
FIELD P O S IT IO N =
( 0 .0 0 ,-1 .0 0 )
WAIST RADIUS
BEFORE
REFRACTION
X
Y
DISTANCE FROM
WAIST TO SURFACE
X
Y
1.8100
1.8100
1.8100
4.2 7 8 3
4.2 7 8 3
4.2 7 8 3
39 .0550
6.3 3 7 5
6.3 3 7 5
12.5334
12 . 5 3 3 4
12.5334
19.7762
19.7762
19.7762
19.7762
1.8100
1.8100
1.8100
4.5 740
4.5740
4.6 0 3 3
36.0264
3 6. 1439
6.7252
6.7296
13 . 0 1 7 4
13.0 1 7 4
13 . 0 1 7 4
10.8 7 7 8
10.8 7 9 0
10.8 7 7 8
0 .0000
0 .0000
9 7 .5737
261.0249
291.3695
537.2137
-2 5 8 8 .4 2 4
-6 5 1 .4 0 8 4
3 2 8.9837
1057.2003
951.8215
1893.2783
2 159.6333
-8 6 4 .2 4 8 0
-1 6 2 0 .0 1 3
26.6029
0.0000
0.0000
97.5 7 3 7
262.0719
292.4164
544.4230
-2 2 5 6 .4 3 5
-3 2 9 0 .5 4 4
264.5630
509.5323
865.7084
1807.1652
-2 6 1 2 .6 1
-8 8 9 .8 1 5 7
-1 6 7 8 .5 1 1
1.0295
Fig. 3.25 Gaussian Beam calculation of the bottom Channel. Beam waist o f the Eplane is 10.88 mm. Beam waist o f H-plane is 19.78 mm. The distance from the beam
waist o f the E-plane to the imaging surface is 1.03 mm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
G A U S S I A N
B E A H
P R O P A G A T I O N
EC EI_M irror_W ang
0 .0
o
o
0.0
0.0
0.0
0 .0
0 .0
0.0
o o
o o
o
o
0.0
0 .0
o o
o o
o
o
0 .0
0 .0
0 .0
INF
INF
-9 8 .2 7 8 2
-2 6 4 .6 2 7 6
-2 9 4 .7 6 0 1
-5 4 7 .7 6 7 0
3313.8502
4944.2732
-2 7 7 .1 8 8 8
-5 2 5 .1 9 8 4
-1 0 2 8 .4 7 1
-1 8 3 5 .2 8 4
2692.5933
753.2063
1416.6619
-232 .9025
o
O
0.0
0.0
0 .0
INF
INF
-9 8 .2 7 8 1
-2 6 3 .1 4 0 3
-2 9 3 .3 2 5 9
-5 3 9 .4 9 0 3
3879.8002
659.5159
-3 3 6 .1 S 7 4
-1 1 3 4 .0 4 4
-1 0 9 8 .7 2 4
-1 9 0 9 .9 5 3
-2 8 8 5 .2 6
1795.9458
3423.8195
1407.0513
o
o
0.0
o
o
1.8 1 0 3
1.8 1 0 3
31.1697
48.6657
54.2550
6 5.9556
6 3.9696
62 . 4 0 9 7
33.8583
43.707 9
85.8976
140.0303
20 3 .0 8 5 0
6 4 .6656
63 . 3 2 4 3
16.4 4 2 2
o
o
1.8100
1.8100
29.9859
50.9162
56 .7965
69.6671
67.5 3 5 4
57.2866
43 . 6 2 7 5
4 8 .4011
71.7432
126.0313
96.8030
56.2627
5 5 .7735
31.2567
MILLIMETERS
BEAM
WAVEFRONT RADIUS
PHASE
ORIENTATION
OF CURVATURE
ORIENTATION
(DEGREES)
BEFORE REFRACTION
(DEGREES)
X
Y
o
o
OBJ
0.0000
1
9 7.9200
2
108.4399
3
3 0.3789
4
9 9 .7101
5
121.5374
6
117.8794
7
763.1370
8
112.2881
9
3 60.2324
10
8 2 5 . 8 4 60
11 - 8 6 4 . 6 5 3 5
12 1 2 3 8 . 4 9 0 6
13
3 0 .0011
14
875.1217
IMG
BEAM RADIUS
ON SURFACE
X
Y
DIMENSIONS -
o
o
PROPAGATION
DISTANCE TO
SUR NEXT SURFACE
- * * * * * * * * NM
o
o
WAVELENGTH
PO SI T IO N
0.0
0 .0
1
FIELD PO SI T IO N -
( 0.0 0 ,
WAIST RADIUS
BEFORE
REFRACTION
Y
X
DISTANCE FROM
WAIST TO SURFACE
Y
X
1.8100
1.8100
1.8 1 0 0
4.2763
4.2763
4.2763
38.9637
6.3305
6.3305
12 . 5 2 1 7
12 . 5 2 1 7
1 2.5 2 1 7
23 . 9 7 8 4
23 . 9 7 8 4
23 . 9 7 8 4
23 .9 7 8 4
1.8 1 0 0
1.8 1 0 0
1.8102
4.5518
4.5518
4.5838
3 5 .7727
3 5 .8877
6.6 7 0 8
6.6743
12.9839
12.9 8 3 9
12.9 8 3 9
9.5668
9.5678
9.5668
0.0000
0.0000
9 7 .9200
261.2842
2 91.6631
5 37.4576
-2 5 8 8 .3 8 2
-6 5 1 .4 6 2 3
32 9 .0 7 9 7
1058.1431
1065.2537
1 891.0996
2 708.2300
-1 4 6 9 .7 3 9
-2 7 9 0 .9 7 7
-5 7 8 .9 8 6 9
1.00)
0 .0000
0.0000
97.9200
2 6 2.2538
2 9 2.6327
545.1212
-2 2 6 5 .5 4 5
-3 3 0 4 .2 8 9
2 6 6.4088
5 1 2.5504
986.6983
1 812.5442
-2 6 7 7 .1 9 8
-7 3 6 .7 1 6 2
-1 3 8 4 .3 1 9
154.0330
Fig. 3.26 Gaussian Beam calculation o f the top Channel. Beam waist o f the Eplane is 9.57 mm. Beam waist o f the H-plane is 23.98 mm. The distance from the beam
waist o f the E-plane to the imaging surface is 154 mm.
Fig. 3.27 Color output o f Gaussian Beam Trace: Side V iew .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
5 2 0 .6 3
ECEI_M irror_W ang
S c a le :
o . 05
HU
XZ
JW
Fig. 3.28 Color output o f Gaussian Beam Trace: Top V iew . The radii o f the
Gaussian beam on H-plane at the im aging plane are 29.5 mm, 19.8 mm, 31.3 mm
respectively.
Fig. 3.29 3-D view o f the com plete system. Only the center channel and two edge
channels are shown.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
3.2.4 Real Ray Trace
ECEI_Hirror_W ang
P osition
1 , W a v e l e n g t h = * * * * * * * * NM
X
Y
Z
OBJ
0.50800
-16.89000
0.00000
1
0.50800
-16.89000
0.00000
2
0.49760
-16.54421
-2.32816
STO
0.00000
0.00000
0.00000
4
-0.13909
4 . 62438
0.00000
5
-0.44394
14.76005
-0.66210
6
- 0 . 8 3 648
27.81135
0.00117
7
-0 .98067
36.27317
-2 .20098
8
-2 .37884
72.03230
0.00857
9
-2 .24590
75.53047
-8.01257
10
-1.80416
85.46979
0.00000
11
-0.12999
3 .72975
0.00000
12
1.39304
-53.14594
0.52310
13
3.84552
-74.18730
0.00000
14
3.87509
-74.52369
0.00000
IMG
5.53074
-93.35877
0.00000
OPD =
0 . 0 0 0 Wa v e s
TANX
-0.00016
-0.00011
-0.00464
-0.00464
-0.00307
-0.00325
-0.00122
-0.00183
0.00119
0.00178
0.00269
-0.00211
0.00216
0.00099
0.00189
0.00189
Fig. 3.30 Real Ray Trace o f the bottom channel.
TANY
0.00531
0.00354
0.15415
0 . 15415
0.10203
0.10816
0.07183
0.04692
0.03124
-0.06097
-1.12985
-0.49882
0.54900
-0.01121
-0.02153
-0.02153
LENGTH
0.00000
97.67246
108.59692
30.35464
99.85410
121.36769
118.10147
763.04919
112.03356
2 4 8 . 0 3 640
940.04489
805.10272
1296.42252
30.00190
875.20426
Slope o f the sightline o f t
bottom channel is -0 .0 2 1 5 3 .
E CEI H i r r o r Wang
P osition
1 , W a v e l e n g t h = * * * * * * * * NH
X
Y
Z
OBJ
-0.50800
16.89000
0.00000
1
-0.50800
16.89000
0.00000
2
-0.49760
16.54421
-2.32816
STO
0.00000
0.00000
0.00000
4
0.13909
-4.62438
0.00000
5
0.44394
-0.66210
-14.76005
6
0 . 8 3 648
-27.81135
0.00117
7
0.98067
-2 .20098
-36.27317
8
2.37884
0.00857
-72 .03230
9
2.24590
-75.53047
-8.01257
10
1.60089
-75.64686
0.00000
11
0 . 1 3 689
-4.00192
0.00000
12
-1.49536
56.35499
0.58819
13
-3.84147
72.27878
0.00000
14
-3.87100
72.57801
0.00000
IHG
-5.52478
89.33206
0.00000
OPD =
0 . 0 0 0 Wa v e s
TANX
0.00016
0.00011
0.00464
0.00464
0.00307
0.00325
0.00122
0.00183
-0.00119
-0.00178
-0.00238
0.00227
-0.00221
-0.00098
-0.00189
-0.00189
Fig. 3.31 Real Ray Trace o f the bottom channel.
TANY
-0.00531
-0.00354
- 0 . 15415
-0.15415
-0.10203
-0.10816
-0.07183
-0.04692
-0.03124
0.06097
-0.88507
-0.66161
0 . 6 0 3 17
0.00997
0.01915
0.01915
LENGTH
0.00000
97.67246
108.59692
30.35464
99.85410
121.36769
118.10147
763.04919
112.03356
362.17480
822 . 0 3 3 4 7
863.77150
1241.54286
30.00151
875.16195
Slope o f the sightline o f t
bottom channel is 0.01915.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
3.2.5 Modulation transfer function (MTF)
The modulation transfer function describes how much a piece o f optical
equipment, say a collection o f lenses and/or mirrors, blurs the im age o f an object. The
lenses and mirrors may not be perfect, and even if they are, diffraction lim its the ability to
see finely spaced features. The standard test is to see how w ell alternating white and
black stripes show up (that is, their contrast, the difference betw een the whitest white and
the blackest black) in the image, depending on how finely spaced they are. W idely spaced
features, such as broad stripes, don't lose much contrast, since a little blurring only affects
their edges. Stripes that are sufficiently fine will appear to be a uniform gray after being
blurred by the optical apparatus being tested. The m odulation transfer function appears to
be a measure o f how much bright-to-dark contrast is lost, as a function o f the width o f the
stripes, as the light goes through the optics. Thus, it might be 1.0 for broad stripes, which
are not significantly blurred, and 0.1 for ones almost too narrow to be view ed with the
optics.
The M TF analysis (Fig. 3.32) show s that the system is sensitive to k<4.2cm '',
which is sufficient for m ost plasma electrostatic fluctuations [3].
k = — = 2 ^ x 1 0 x 0 .0 6 6 = 4.14cm -1
/I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78
ECEI_Mirror_Wang
WAVELENGTH HEIGHT
2 6 0 8 6 9 5 . 0 NM******
D I F F R A C T I O N MTF
JU
(0 .4 4 8 , 0.00)
DBG
DEFOCUS I N C 0 . 0 0 0 0 0
0.2
0 .006
0 . 054
S P A T I A L FREQUENCY
(CYCLES/MM)
Fig. 3.32 MTF Analysis o f the design. M TF o f different channels are very near to
the diffraction limit. They are a little worse perhaps due to the diffraction at the edge o f
optical components. R is Radial (or X) M TF which is horizontal M TF (vertical bars) in
local im age surface coordinates; T is tangential (or Y) M TF which is vertical M TF
(horizontal bars) in local im age surface coordinates.
3.2.6 Point Spread Function
Consider a very small point o f light. If the optical system had perfect optics, the
im age of this point on the image side w ould be identical to the original point o f light.
Consequently, if the relative intensity o f this point o f light were plotted as a function o f
distance, on the image, such a plot would look like a pulse. H owever, the optical system
is not perfect so the relative intensity o f the point o f light is distributed across the im age
as a Gaussian curve. This curve is called the "point spread function" (PSF).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
Figure 3.33 show s the center field Point Spread Function. The spot diameter o f
the beam at the resonance surface is 2-3 cm at the E-plane and 5 cm at the H-plane.
P O IN T
SPREAD
F U N C T IO N
ECEI Mirror Wang
Per Cent
r 100- oc
b 50.000
'v
1
(PF '
114.59 mm
0 . 0000
Field = ( 0.000, 0.000) Degrees
Defocusing = 0.000000 mm
Fig. 3.33 Point Spread Function o f the Center Channel.
3.3 Optical System Design of the TEXTOR MIR system
In the com bined ECEI/MIR system, I also worked on the optical system design of
the MIR subsystem although it was not used in the actual system . Here, I will discuss my
optical design and compare it with the final MIR system which was designed by Prof.
Tobin Munsat at the end o f this chapter.
3.3.1 Original Optical design
Optical sim ulations for 5 channels have been conducted based on the dual dipole
array pattern at 88 GHz (wavelength 3410000nm ).
For the dual dipole array (E-plane 90 mil spacing, H-plane 30 m il spacing), the
receiving angle o f the half bandwidth o f the 1/e electric field is 15.5 degrees outside of
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
the substrate lens; consequently, the receiving angle o f the half bandwidth o f the 1/e
electric field is 24 degrees inside the substrate lens. [1]
Field
1
Vignetting
X Height
Y Height
Weight
0 . 0000
0 .0 0 0 0
1 .0 0 0 0
2
0.3810
4 .6 7 2 0
1 .0 0 0 0
3
-0 .3 8 1 0
-4 .5 7 2 0
1 .0 0 0 0
Color
H B B H I
-Y
+X
-X
+Y
-7 4 .4 3 1 9
-7 4 .4 3 1 9
-6 2 .1 7 0 1
-8 4 .2 6 3 8
-7 1 .0 1 7 7
- 6 3 . 0S13
-62. 3
-6 6 .4 6 0 4
-8 4 .2 6 3 8
-6 2 .3 9 0 6
-63. 0
-6 2 .1
A
M
- J
±F
Fig. 3.34 fields/vignetting W indow. XJY heights o f field are the position o f the
object. Y-height o f the two edge channels o f the 5-channel MIR antenna array is
4.572m m . Because there are only two channels in the H-plane, the X -height o f these two
channels is 0.381m m .
S u rfa c e #
S urface
N am e
O bject
S urface
Type
Y R ad iu s
S p h ere
Infinity
S u b s tra te lens
S p h e re
Infinity
S p h ere
L en s MF
C ylinder
S top
5
1
2
3
X R ad iu s
T h ic k n e s s
G la s s
5 8 ,0 0 0 0
-35.0000
Infinity
3 5 0 ,0 0 0 0
S p h e re
Infinity
S p h ere
-140.0000
X
Y
S em i-A p ertu re S em i-A p ertu re
O
R efract
0 .0 0 0 0
Infinity
Infinity
-35:0000
R efract
M ode
'HD'
Refract
Refract
3 5 .0 0 0 0 0
35 0 0 0 0 °
3 5 .0 0 0 0 °
10.0000
'HD'
Refract
6 0 .0 0 0 0 0
6 0 .0 0 0 0 0
Infinity
3 5 .0 0 0 0
'HD'
Refract
4 5 .0 0 0 0 0
4 0 .0 0 0 0 0
-140.0000
Infinity
1 59.0000
Refract
6 0 .0 0 0 0 0
6 0 .0 0 0 0 0
-3 5 0 .0 0 0 0
R eflect
1 8 0 .0 0 0 0 63
9 0 .0 0 0 0 0
8 7 6 .0 0 0 0
^Reflect
2 9 5 .0 0 0 0 0
1 5 0 .0 0 0 0 0
R eflect
3 3 5 .0 0 0 0 0
1 5 0 .0 0 0 0 0
■Reflect
5 0 0 .0 0 0 0 0
1 5 0 .0 0 0 0 0
Refract
2 1 0 .0 0 0 0 0
7 5 .0 0 0 0 0
Refract
2 1 0 .0 0 0 0 0
7 5 .0 0 0 0 0
Refract
1 5 0 .0 0 0 0 0
7 5 .0 0 0 0 0
6
B ea m S plitter
S p h ere
Infinity
7
D ichroic P la te
S p h ere
Infinity
Infinity
8
Mirror H
C ylinder
Infinity
-2 1 0 0 .0 0 0 0
5 5 .0 0 0 0
-8 3 2 .5 0 0 0 v
9
Mirror E
Cylinder
27 0 0 .0 0 0 0
Infinity
1 3 7 3 .0 0 0 0
10
W indow
S p h e re
Infinity
Infinity
3 0 .0 0 0 0
11
S p h ere
Infinity
Infinity
7 0 0 .0 0 0 0
Im age
Y Toroid
3 7 5.0000
2 1 2 5 .0 0 0 0
0 .0 0 0 0
9 6 0 0 0 0 .6
v
3 5 ,0 0 0 0 0
E n d O f D ata
Fig. 3.35 Screen shot o f Lens Data Manager W indow o f my optical design. The
positions o f Mirrors E and H in my design are to the same as in Dr. Tobin M unsat’s
design. W e choose different Lenses and Substrate Lens.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3 7 S .7 9
MH
Fig. 3.36 Side V iew o f MIR Optical System. Substrate lens and tw o focus lenses
are shown in the Lens data manager. Sight lines o f the center channel and two edge
channels are shown to focus on the center o f the cutoff surface.
Mx r r o r
Beam S p lit t e r
M irror
H
W in dow
C utoff la y er
373.13
Fig. 3.37 Top V iew o f MIR Optical System.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
MM
82
3.3.2 Gaussian Beam Trace
G A U S S I A N
B E A M
P R O P A G A T I O N
HIR_MI RR ORS
PROPAGATIONI
DISTANCE TC'
SUR NEXT SURFACE
BEAM
WAVEFRONT RADIUS
PHASE
OR IE NTA TI ON
OF CURVATURE
OR IE NT A TI ON
(DEGREES)
BEFORE RE FRACTION
(DEGREES)
X
Y
BEAM RADIUS
ON SURFACE
X
Y
0 .0
0.0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
IN F
IN F
-5 9 .1 9 8 4
-1 4 3 .5 8 2 3
-2 8 6 .7 7 2 7
-3 1 9 .8 2 2 4
-9 9 9 .0 6 3 3
121 8 .5 5 4 2
-1 9 8 3 .3 7
-2 4 8 7 .3 0 1
2 9 9 8 .4620
5892 .2 3 3 1
-5 0 7 5 .9 8 6
IN F
IN F
-5 9 .1 9 8 4
-1 4 3 .5 8 2 3
-2 2 7 .8 4 4 2
-2 6 1 .6 8 8 9
-6 1 1 .7 5 5 2
9 3 8 .0 4 3 6
-1 7 9 5 .6 4 8
2 6 2 2 .1 1 3 0
7 4 9 .5 1 3 4
1409.4086
988.0 2 3 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
o o
o o
2 .4 4 0 0
2 .4 4 0 0
17.1491
27.5743
2 8 .8 3 9 0
33.2803
63.1640
1 00.0275
158.7033
232 .4 0 5 6
70.6822
69 .2 0 8 6
11.4447
o
o
2 .4 4 0 0
2 .4 4 0 0
17. 1491
2 7.5743
2 8 .5 6 9 5
32.0682
37.7482
51 .9 5 6 5
9 1 .1 6 3 1
67.5633
3 7 .4 5 2 7
3 7 . 2 6 03
3 5 .2 5 9 0
FIELD PO SIT IO N -
DIMENSIONS = MILLIMETERS
o
o
OBJ
0 .0 0 0 0
1
5 8 .0 0 0 0
2
ss.o o o o
3
10.0000
4
3 5 .0 0 0 0
5
15 9.00 00
6 -3 5 0 .0 0 0 0
7
8 7 6.0000
8 -8 3 2 .5 0 0 0
9 1 3 7 3.0000
10
30.0 0 0 0
11
7 0 0 .0000
IMG
= * * * * * * * * NM
o
o
WAVELENGTH
PO SIT IO N
0 .0
0 .0
0 .0
0 .0
( O.OO ,
1
0.00)
WAIST RADIUS
DISTANCE FROM
WAIST TO SURFACE
X
Y
BEFORE
REFRACTION
X
Y
2 .4 4 0 0
2 .4 4 0 0
2 .4 4 0 0
5 . 5 3 69
6.9 5 2 5
6.9 5 2 5
2 2 .8 6 0 5
2 2 .8 6 0 5
2 2 .8 6 0 5
3 4 .3 9 4 4
3 4 .3 9 4 4
3 4 .3 9 4 4
3 4 .3 9 4 4
0 .0 0 0 0
0 .0 0 0 0
5 8 .0 0 0 0
137.7931
219.4 4 5 6
254.4 4 5 6
5 5 0 .7 3 3 0
-9 0 0 .7 3 3 0
1 7 7 6.73 30
-2 6 0 9 .2 3 3
-7 3 0 .1 5 1 8
-1 3 7 1 .4 3 4
-1 4 .5 2 1 7
2 .4 4 0 0
0.0 0 0 0
0.0 0 0 0
2 .44 0 0
2 .44 0 0
58.0 0 0 0
5 .5 3 6 9
137.7931
5 .5 3 6 9
2 6 9 .7 8 9 6
5 . 5 3 69
3 0 4 .7 8 9 6
632.6497
14.1062
1 4.1062 -9 8 2 .6 4 9 7
14 .1 0 6 2 1 8 5 8 .649 7
14.1062 1842.7145
1 1.3 6 0 3 - 4 6 9 .7 1 4 5
11.3 6 0 3 -8 7 1 .5 5 7 3
1 1.3 6 0 3
2 4 5 .9 1 5 6
Fig. 3.38 Gaussian Beam calculation o f the Center Channel. Beam waist o f the Eplane is 11.4 mm. Beam waist of the H-plane is 34.4 mm. The distance from the beam
waist of the E-plane to the imaging surface is -14.5 mm. (N egative number means it is on
the right side) The distance from the beam waist o f the H-plane to the im aging surface is
245.9 mm. This system is astigmatic.
G A U S S I A N
B E A M
P R O P A G A T I O N
PROPAGATIONr
DISTANCE TC)
SUR NEXT SURFACE
OBJ
0 .0 0 0 0
1
57 . 7 2 3 7
2
55.4158
3
10 .0 1 0 9
4
3 5 .0 2 8 5
5
172.1525
6 -3 7 5 .0 7 8 8
7
7 8 9 .6 5 4 6
8 -7 9 8 .5 2 8 7
9 1453.2616
10
30.0133
11
7 0 1 .7 3 6 1
IMG
= * * * * * * * * NM
BEAM RADIUS
ON SURFACE
X
Y
2 .4 4 0 0
2 .4 4 0 0
17.0690
27.4612
28 .4 4 5 1
3 1 .9 0 4 0
37.8602
52 .7 8 1 1
87.3 8 8 1
64.4944
3 4 .7 7 6 0
34.6603
36.8843
2 .4 4 0 0
2 .4 4 0 0
17 .211 8
2 7.2201
2 8.4590
3 2.7944
67.6934
108 .8 1 2 7
14 5 .2 4 7 2
2 1 8 .6028
63.5095
62 . 1 6 9 4
12 . 4 1 9 7
DIMENSIONS = MILLIMETERS
BEAM
WAVEFRONT RADIUS
PHASE
OR IE NTATION
OF CURVATURE
OR IENT AT ION
(DEGREES)
BEFORE REFRACTION
(DEGREES)
X
Y
0 .0
0.0
0.0
0 .0
0 .0
0.0
0 .0
0 .0
0 .0
0.0
0.0
0 .0
0 .0
INF
IN F
-5 8 .9 2 7 8
-1 4 4 .4 7 3 3
-2 8 9 .0 7 9 1
-3 2 2 .0 8 8 2
-1 0 2 7 .9 9 1
1259.7575
-1 9 4 2 .4 0 5
-2 3 5 6 .5 7 2
4 5 6 4 .516 9
9267.3987
-2 8 6 0 .7 6 1
IN F
INF
-5 8 .9 2 7 8
-1 4 4 .4 2 8 4
-2 2 9 .7 3 7 7
-2 6 3 .5 2 0 5
-6 3 0 .9 9 1 5
9 7 9 .5 1 2 5
-1 7 5 0 .9 1 6
2 5 4 2 .5 8 4 4
738.9 8 7 8
1392.9776
-3 0 3 5 .1 1 7
0 .0
0 .0
0 .0
0.0
0 .0
0 .0
0 .0
0 .0
0 .0
0.0
0.0
0 .0
0 .0
FIELD PO SITIO N
WAIST RADIUS
BEFORE
REFRACTION
X
Y
2 .4 4 0 0
2 .4 4 0 0
2 .4 4 0 0
5 .5 9 0 9
7 .0 3 2 0
7 .0 3 2 0
2 3.2563
2 3.2563
2 3.2563
33.7 8 4 1
33.7 8 4 1
33.7 8 4 1
33.7 8 4 1
2.4 4 0 0
2 .4 4 0 0
2.4 4 0 0
5.6 4 7 5
5 .6 5 5 6
5.6 5 5 6
14.5030
1 4.5030
14.5030
14.5030
12.4061
12 . 4 2 0 8
1 2.4061
o
o
o
WAVELENGTH
PO SIT IO N
II
MIR MIRRORS
,
1
1.00)
DISTANCE FROM
WAIST TO SURFACE
X
Y
0.0 0 0 0
0 .0 0 0 0
0 .0 0 0 0
0 .0 0 0 0
57 .7 2 3 7
1 3 8.18 00
2 2 0 .6451
2 5 5 .6737
5 6 4.4 662
-9 3 9 .5 4 5 0
172 9.19 96
-2 5 2 7 .7 2 9
-7 1 0 .6 9 7 0
-1 3 3 7 .3 2 6
6 . 6391
57 .7 2 3 7
138 .4849
2 7 1.4125
3 0 6 .4 4 1 0
6 4 0.1 037
-1 0 1 5 .1 8 3
1 8 0 4.8371
170 9.9 348
-2 5 6 .6 7 3 2
-4 6 2 .6 3 8 3
4 6 0.6999
Fig. 3.39 Gaussian Beam calculation o f the top Channel. Beam waist o f the Eplane is 12.4 mm. Beam waist of the H-plane is 33.78 mm. The distance from the beam
waist o f the E-plane to the imaging surface is 6.64 mm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
83
G A U S S I A N
B E A M
P R O P A G A T I O N
M IR J1IR R0RS
PROPAGATION
DISTANCE TC»
SUR NEXT SURFACE
* NM
BEAM RADIUS
ON SURFACE
X
Y
0 .0
0 .0
0 .0
0.0
0 .0
0 .0
0 .0
0 .0
IN F
INF
-5 8 .9 2 7 8
-1 4 4 .4 2 8 4
-2 2 9 .7 3 7 7
-2 6 3 .5 2 0 5
-6 0 9 .8 9 7 1
9 1 2 .9452
-1 8 5 5 .7 0 9
2709.3912
778.5 3 9 6
1469.1355
323 .3 8 4 8
0 .0
0 .0
0.0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
o
o
0 .0
0 .0
IN F
INF
-5 8 .9 2 7 8
-1 4 4 .4 7 3 3
-2 8 9 .0 7 9 1
-3 2 2 .0 8 8 2
-1 0 1 9 .0 8 2
1208.0342
-2 0 4 0 .8 1 9
-2 6 7 0 .3 8 5
27 9 0 .5003
5 4 2 4 .9 0 9 7
-2 5 2 2 7 .6 4
o
o
2 .4400
2 .4400
17.2118
27 .2 2 0 1
2 8 .4 5 9 0
32 .7 9 4 4
57 .1 8 1 5
88 .7 5 4 4
166 .0413
233 .7 37 6
7 6 .1 2 8 1
7 4 .6 0 3 5
11.8535
MILLIMETERS
BEAM
DJAVEFRONT RADIUS
PHASE
OR IE NT A TI ON
OF CURVATURE
ORIENTATION
(DEGREES)
BEFORE REFRACTION
(DEGREES)
X
Y
o
o
2 .4 4 0 0
2 .4400
17.0690
27.4612
28 .4 4 5 1
31 .9 0 4 0
36 .9 8 0 7
4 9.8784
92 . 1 6 8 6
68.9558
4 1.0924
40.8642
3 5.9316
DIM ENSIO NS -
o
o
OBJ
0 .0 0 0 0
1
5 7.7237
2
55 . 4 1 5 8
3
10.0109
4
35.0285
5
148 .0968
6 -3 2 9 .3 6 0 9
7
96 5 .4766
8 -8 6 0 .2 1 2 0
9 128 5 .2 7 5 3
10
3 0.0156
11
7 0 1.95 72
IMG
=***
o
o
UAVELENGTH
PO SIT IO N
0.0
0.0
1
FIELD PO SIT IO N -
( 0 .0 0 ,-1 .0 0 )
U A IS T RADIUS
BEFORE
REFRACTION
X
Y
DISTANCE FROM
U A I S T TO SURFACE
X
Y
2 .4 4 0 0
2 .4 4 0 0
2.4 4 0 0
5 .5 9 0 9
7 .0 3 2 0
7 .0 3 2 0
23 .2 5 6 3
23 . 2 5 6 3
23 .2 5 6 3
3 5 .8 9 1 7
3 5 .8 9 1 7
3 5 .8 9 1 7
35.8 9 1 7
2 .4400
2.4400
2 .4400
5 .6 4 7 5
5 .6 5 5 6
5 .6 5 5 6
1 4 .5 0 3 0
1 4 .5 0 3 0
1 4 .5 0 3 0
1 4.5030
1 1.0045
1 1 .0 1 9 9
1 1 .0 0 4 5
0 .0 0 0 0
0 .0 0 0 0
57.7 2 3 7
1 3 8 .4 8 4 9
2 7 1 .4 1 2 5
3 0 6 .4 4 1 0
6 1 6 .0 4 8 0
-9 4 5 .4 0 8 9
1 9 1 0 .8855
1 9 4 6 .9 1 3 6
-6 6 1 .6 3 8 2
-1 2 3 9 .9 1 5
5 5.9572
0 .0 0 0 0
0 .0 0 0 0
57.7 2 3 7
1 3 8 .1800
2 2 0 .6 4 5 1
2 5 5 .6 7 3 7
540.4 1 0 6
-8 6 9 .7 7 1 4
1835.2480
-2 6 9 5 .4 6
-7 6 2 .2 0 9 1
-1 4 3 7 .0 4 7
-4 4 .6 5 7 4
Fig. 3.40 Gaussian Beam calculation o f the bottom Channel. B eam waist o f the Eplane is 11.0 mm. Beam w aist o f the H-plane is 35.9 mm. The distance from the beam
waist o f the E-plane to the im aging surface is -44.7 mm. (N egative number means it is on
the right side)
342.47
M I R MI RRORS
S cale:
MM
0.07
Fig. 3.41 Color output o f Gaussian Beam Trace: Side View .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
937.94
M I R M I RR O R S
Scale:
0.07
MM
18-Feb-05
Fig. 3.42 Color output o f Gaussian Beam Trace: Top V iew .
Fig. 3.43 3-D view ing of the complete system. Only the center channel and two
edge channels are shown. The positions o f the channels are different. The maximum is 50
mm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
85
3.3.3 Real Ray Trace
The Y radius o f the cutoff layer is 375 mm. The X radius o f the cutoff layer is
2175 mm. (Figure 3.35) A ll sightlines are required to be perpendicular to the cutoff
surface. Thus, the required slope should be the coordinates o f the ray on the surface X /Y
divided by the X /Y radius o f the cutoff layer.
Ithe coordinates o f ray on surface X|
Slope x = -------------------------------------------------- X radius o f the cutoff layer
Slope =
|the coordinates o f ray on surface Y|
Y radius o f the cutoff layer
OBJ
1
2
3
STO
5
s
7
8
9
10
11
IMG
H IR MIRRORS
P osition
1 , W a v e l e n g t h = * * * * * * * * pin
X
Y
Z
0.38100
4.57200
0.00000
0.38100
4.57200
0.00000
0.36623
4.39208
-0.27860
0.03924
0.00000
0.46653
0.00000
0.00000
0.00000
-0.13732
-1.63239
-0.00958
-1.07526
-18.07667
0.00000
-3.11879
-52.43158
0.00000
-7.42094
-101.87134
-0.01311
-6.71145
-164.49839
5.01572
-5.42017
-62.02022
0.00000
-5.40628
-61.12771
0.00000
-4.78276
0.59806
-2 1.07493
OPD =
0 . 0 0 0 Waves
TANX
-0.00039
-0.0002 6
-0.00592
-0.00392
-0.00392
-0.0054 6
0.0082 6
-0.0082 6
-0.00099
0.00106
0.0004 6
0.00089
0.00089
TANY
-0.00474
-0.00312
-0.07101
-0.04665
-0.04665
-0.06490
1.13881
-1.13881
-0.49393
0.65618
0.02975
0.05717
0.05717
LENGTH
0.00000
57.72168
55.41878
10.01095
35.02874
172.15572
375.08565
789.64785
798.50857
1453.27512
30.01328
701.74230
Fig. 3.44 Real Ray Tracing o f the top channel. Slopey=0.0562. T A N Y =0.05717.
They are very close. Slopex=0.0022. T A N X =0.00089.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
OBJ
1
2
3
STO
5
6
7
8
9
10
11
IMG
HIR_MIRRORS
P o sition
1,
X
-0.38100
-0.3 8 1 00
-0.36623
-0.03924
0.00000
0.13732
0.94419
2.73863
7.99873
7.23442
6.09240
6.07851
5.45479
W a v e l e n g t h = * * * * * * * * uh
Y
Z
-4.57200
0.00000
-4.57200
0.00000
-4.39208
-0.27860
-0.46653
0.00000
0.00000
0.00000
1.63239
-0.00958
15.87323
0.00000
46.04048
0.00000
109.78598
-0.01523
170.96936
5.41850
65.81197
0.00000
64.84417
0.00000
0.61821
21.40170
OPD =
0 . 0 0 0 Waves
TANX
0.00039
0.00026
0.00592
0.00392
0.00392
0.00546
-0.00725
0.00725
0.00107
-0.00099
-0.00046
-0.00089
-0.00089
TANY
0.00474
0.00312
0.07101
0.04665
0.04665
0.06490
0.87811
-0.87811
-0.66724
0.49753
-0.03226
-0.06201
-0.0 6 20 1
LENGTH
0.00000
57.72168
55.41878
10.01095
35.02874
148.09865
329.36493
965.47669
860.19176
1285.28696
30.01561
701.96404
Fig. 3.45 Real Ray Tracing of the bottom channel. Slopey= 0.0571. T A N Y =0.062.
They are very close. Slopex=0.0025. T A N X =0.00089.
The position error generated by the slope o f beam trace w ill be less than 4m m
along a 4 meter distance in H-plane. The diameter o f the beam at the measurement
position is 72 mm. The position error o f the H-plane is negligible.
3.3.4 M odulation transfer function (MTF)
The MTF analysis (Fig. 3.46) show s that the system is sensitive to k<4 cm '1,
which is sufficient for m ost plasma electrostatic fluctuations [3],
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
MI R M I R R O R S
DIFFRACTION MTF
1 8 -F eb -O S
DEFOCUSING
0 .0 0 0 0 0
'X,
SPATIAL FREQUENCY (CYCLES/HH)
Fig.3.46 M TF Analysis o f the design. MTF o f different channels are very near to
the diffraction limit. They are a little worse perhaps due to the diffraction at the edge o f
optical components.
3.3.5 Point Spread Function
POINT SPREAD FUNCTION
M I R M IR R O R S
T H U » I - .MD.--4.17H
3 h (« ro F iri9 - )
nt>
Figure 3.47 Point Spread Function o f the center point. The spot diameter of the
beam at the resonance surface is 2 cm at the E-plane and 6 cm at the H-plane.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
3.3.6 Tobin Munsat’s Optical Design
R eference 6 provides som e detail about M icrow ave Imaging Reflectometry. I
used C O D E V to analyze his design and compare it with my optical design.
S urface #
S urface
N am e
I
Surface
I
Y Radius
X R adius
T h ic k n e ss
O bject
I
Type
S p h ere
Infinity
Infinity
0.0 0 0 0
1
Sphere
Infinity
Infinity
9 9 .5 0 0 0
Sphere
-60.0000
-60.0000
45.0 0 0 0
S phere
600.0000
680 .0 0 0 0
5 0 .0 0 0 0
Infinity
-750.0000
40.0 0 0 0
2
S u b s tra te Lens
3
4
I G la s s I
R efract
'HD'
'HD'
1
Y
1
X
1
| S em i-A perture| Sem i-A perture|
0
O
R efract
60.0000 0
6 0 .0 0 0 0 °
R efract
60.0000 0
6 0 .0 0 0 0 °
m
Refract
125.0000 0
125.0000
Refract
125 .0000 B
125.0000 °
Refract
40.0000 0
4 0 .0 0 0 0 °
R eflect
180.0000 B
L ens MF
Cylinder
S phere
Infinity
Infinity
154.0000
6
BM Splitter
S phere
Infinity
Infinity
-374.0000
7
D ichroic
Sphere
Infinity
Infinity
876.0000
R eflect
295.0000
8
Mirror H
Cylinder
Infinity
-2100.0000
-832.4000 v I
R eflect
335.0000 B
150.0000 B l
9
Mirror E
Cylinder
2700.0000
Infinity
1481.0000
R eflect
500.0000
150.0000 ° 1
Infinity
Infinity
B80.0000
R efract
m
210.0000 m
375.0000
2125.0000
0 .0 0 0 0
R efract
375.0000 ®
Stop
10
S phere
Im age
Y Toroid
[
v
m
90.0000 B l
150.0000 B J
75.0000 B
2 1 2 5 .0 0 0 0 ®
End O f D ata
Fig. 3.48 Screen shot o f Lens Data Manager W indow o f Dr. M unsat’s optical
design. A larger Substrate Lens is used.
396.83
M IR _ M IR R O R S
Scale:
0.06
MM
25-May-05
Fig. 3.49 Side V iew o f Dr. Munsat’s MIR Optical System .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
89
Fig. 3.50 3-D view ing o f the com plete system. Only the center channel and two
edge channels are shown.
G A U S S I A N
B E A M
P R O P A G A T I O N
MIR MIRRORS
PO SIT IO N
o
o
o o
o o
o
o
0 .0
o o
o o
o
o
0.0
0.0
o
o
o
o
IN F
IN F
-1 0 0 .1 9 8 6
-1 9 7 .4 5 1 7
-4 1 0 .6 5 7 6
-3 0 9 .2 9 9 3
-4 6 1 .3 6 9 6
8 3 3 .6 5 8 9
-1 7 0 8 .5 8 5
2 5 4 0 .6 5 1 1
685.6679
-7 4 .3 1 2 4
o
o
0 .0
0 .0
INF
INF
-1 0 0 .1 9 8 6
-1 9 7 .4 5 1 7
-4 1 0 .6 5 7 6
-3 7 1 .0 9 2 6
-5 2 1 .8 5 8 2
892.6722
-1 7 6 6 .4 9 7
-3 0 3 9 .5 3 3
1586.9746
9 3 5 .7 7 7 4
o o
o o
0 .0
0 .0
0 .0
o
o
2 .44 0 0
2 .44 0 0
29.2222
37.8109
43.0425
49 .425 5
104.8096
189.929 4
318.1348
473.1410
129.6115
6.4579
o o
o o
2 .4 4 0 0
2 .4 4 0 0
29.22 22
3 7.8109
43.0425
48.2320
68.3358
1 1 7.4603
232.8675
182.763 8
9 4.1247
53 .2 2 2 9
BEAM
WAVEFRONT RADIUS
PHASE
OR IE NTA TI ON
OF CURVATURE
ORIENTATION
(DEGREES)
BEFORE REFRACTION
(DEGREES)
X
Y
o
o
OBJ
0.0000
1
9 9.5000
2
4 5.0000
3
5 0.0000
4
4 0.0000
S
154 .0000
6 -3 7 4 .0 0 0 0
7
87 6 .0000
8 -8 3 2 .4 0 0 0
9 1481.0000
10
700.0000
IMG
BEAM RADIUS
ON SURFACE
X
Y
DIMENSIONS = MILLIMETERS
FIELD PO SITIO N
U A I S T RADIUS
BEFORE
REFRACTION
X
Y
2 .4 4 0 0
2 .4 4 0 0
2 .4 4 0 0
5 .6 0 5 6
6.7293
8 .2 2 8 8
8 .2 2 8 8
8 .2 2 8 8
8 .2 2 8 8
17.9644
17.9644
17.9644
o
o
o
PROPAGATION
DISTANCE TO
SUR NEXT SURFACE
jjM
ii
WAVELENGTH
,
1
0.00)
DISTANCE FROM
U A I S T TO SURFACE
Y
X
0.0 0 0 0
2 .4 4 0 0
2 .4 4 0 0
0 .0 0 0 0
2 .4 4 0 0
9 9 .5 0 0 0
1 9 3.1119
5 .6 0 5 6
4 0 0 .6 2 0 1
6.7293
6 . 7 2 93
360.2 9 1 1
6 . 7 2 93
514.2 9 1 1
6.7293 -8 8 8 .2 9 1 1
6.7293 17 6 4 .2 9 1 1
6.7293 3 0 1 0 .1 6 6 5
5 . 7 3 65 - 1 5 2 9 . 1 6 7
5 . 7 3 65 - 8 2 9 . 1 6 6 5
0 .0 0 0 0
0 .0 0 0 0
99 .5 0 0 0
1 9 3.1 119
4 0 0.6201
3 0 3.5659
4 5 7.5659
-8 3 1 .5 6 5 9
1707.5 659
-2 5 3 9 .9 6 6
-6 8 4 .3 2 4 8
1 5 .6752
Fig. 3.51 Gaussian Beam calculation o f the center Channel. Beam waist o f the Eplane is 5.7 mm. Beam waist o f the H-plane is 18.0 mm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Comparisons between my optical design and that o f Tobin M unsat are listed in
Table 3.1
Table 3.1 Compare som e results o f tw o optical design
Radius o f Beam W aist at
Radius of Beam W aist at H-
Average Spacing of
E-plane (mm)
plane (mm)
Channels (mm)
M y design
11
34
10
T ob in’s D esign
5.7
18
5
From the data shown in Table 3.1, Dr. M unsat’s design achieves a smaller beam
w aist and channel spacing at the cutoff layer. Smaller beam waist m eans better spatial
resolution and smaller detection region covered, but it also m eans a larger beam radius at
the w indow and mirrors, and thus more power loss. M y design has bigger beam waist
w hich means less power loss at the window and mirrors. Consequently, in my design
with 5 channels can achieve greater sensitivity than T obin’s design. W ith a bigger spot
size and channel spacing m y design can cover a larger plasma region than T obin’s
design. The spatial resolution in my design (the radius o f the spot is about 1cm) is
appropriate for our MIR system. Our PPPL colleagues were not concerned about power
loss, and thus Tobin traded it off for better special resolution. Som e measurement results
o f ECEI and MIR w ill be discussed in the next chapter.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
References:
[1] Zhengang Xia, The investigation o f dual dipole antenna im aging array an d
developm ent ofS ch ottky diode fabrication , Master Dissertation, U C D , 2002.
[2]. D .B. Rutledge, D .P Neikirk, and D.P. Kasilingam , In tegrated C ircu it Antennas, in
Infrared and M illim eter W aves, 10, Ed. by K.J. Button, N ew York: Academ ic Press,
1983.
[3]. B.H. Deng, Two dim ensional electron cyclotron em ission im aging stu dy o f electron
tem perature profiles an d fluctuations in Tokamak plasm as, Ph.D. dissertation, UC D ,
1999.
[4], D. Veron, Subm illim eter Interferom etry o f H igh-D ensity Plasm as, in Infrared an d
M illim eter W aves, 2, Ed. by K.J. Button, N ew York: Academ ic Press, p. 67, (1979).
[5]. Optical Research A ssociates manual.
[6]. T. Munsat, E. M azzucato, H. Park, B.H . D eng, C.W. Dom ier, N .C . Luhmann, J.
W ang, Z.G. Xia, A J.H . D onne, M.J. van de Pol, M icrow ave im aging reflectom eter f o r
TEXTOR (invited). R eview o f Scientific Instruments, vol.74, no.3, pp. 1426-32, (2003).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92
Chapter IV
ECEI and MIR Electronics Systems
4.1 TEXTOR ECEI Electronics
In the com bined ECEI/MIR system , new ECEI electronics were developed by the
UC D avis Plasma D iagnostics Group to operate as a wideband IF system with single
sideband (SSB ) operation as illustrated in Fig. 4.1. Here, the previously em ployed
wideband scanning BW O w as replaced by an extrem ely stable, high pow er (50-100 mW )
fixed frequency solid-state oscillator, resulting in a highly reproducible system that
should require only a single set o f calibration measurements. Placed at the input o f the
im aging array, facing the plasma, is a dichroic plate w hose cutoff frequency is just
slightly greater than that o f the LO source, and which thereby functions as a high pass
filter to ensure SSB operation. Because o f the 1/R dependence o f the toroidal magnetic
field, different vertical chords therefore correspond to different IF frequencies.
A
nominal 3-7 GHz IF bandwidth was em ployed and thus a corresponding 4 GHz RF
bandwidth portion o f the second harmonic cyclotron em ission layer w as observed. On the
TEXTOR device, for exam ple, this w ould translate to a radial plasma coverage o f 5-6
cm. [1] M y work is concentrated on the LO m odule and M ixer M odule design which is
discussed in Section 4.1. I also participated in ECEI Antenna Array Testing which is
discussed in Section 4.3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
93
2-D array of sampling volum es
t focal plane (resolution ~ 1 cm)
o*u
local
oscillator
detector
array
► R (~1/f)
Fig. 4.1 Schem atic diagram illustrating how 2-D electron temperature
images are obtained via ECEI. (courtesy of Dr. Hyeon Park)
LOS
Video
Am ps
BP Filters
IF Amp
Power
Divider
IF Am ps
Mixers
Detectors
Figure 4.2 Schematic diagram illustrating the arrangement o f the wideband IF
electronics for the 2-D ECEI system.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94
The basic layout o f the ECEI IF electronics is show n in Fig. 4.2. First, the
downconverted 3 - 7 GHz radiation is am plified by 35 dB using low n oise preamplifiers
placed within the array enclosure box. Low loss m icrowave cables (17 m in length, 1
dB/G Hz loss) transmit these m icrowave signals out o f the TEXTOR bunker where the
signals are am plified by an additional 20 dB. These input signals are introduced into a
multi-channel wideband IF electronics board which was designed and fabricated in the
course o f this dissertation work. In the exam ple provided in Fig. 4.2, an 8 channel system
is shown although w e actually developed a 16 channel system to provide high resolution
im ages for physics studies. Here, each input signal is divided into a number o f separate
signals through a 16-way power divider. Each o f these outputs is m ixed with an LO
signal with a distinct frequency. The output o f each o f these second downconversions
(the first was made on the antenna array by m ixing the plasm a RF signals with the array
LO) is then bandpass filtered (nominal passband o f 5-150 M H z), IF am plified, rectified
and then video am plified for subsequent data acquisition.
The key to making 2-D ECEI a cost-effective diagnostic is in driving down the
price o f these wideband IF multichannel electronics m odules. W ith the exception o f a low
noise preamplifier for each antenna array elem ent (which is housed in the enclosure box
holding the antenna array), w e em ployed low cost printed circuit board technology on
high
performance
m icrowave
laminates
coupled
with
low
cost
surface
mount
com ponents. For exam ple, the 16-way pow er divider is im plem ented as a microstrip
printed circuit w hile the mixers, amplifiers, filters and detectors are low cost surface
mount com m ercially available components.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
95
The source o f the multi-channel LO signals (L O l through L 0 8 in Fig. 4.2) are a
series of low pow er VCO oscillators (below ~7 GHz). Each LO source is am plified to
+19 dBm and then pass through a 16 channel power divider (one LO channel output per
array channel) to provide 16 output signals o f level +5 dBm as required by the m ixers o f
the wideband IF ECEI boards.
W e fabricated 8 -channel LO sources (frequencies from 3 .3 -6 .8 GHz with a
frequency spacing o f 500 M H z between sources) and one 16 channel wideband ECEI
module. These frequencies are chosen to avoid harmonics o f the low er frequency LO
signals from entering the higher frequency passbands. The m ultichannel source and test
ECEI module were made available for both laboratory testing in our m illim eter-wave
facilities, and for field testing on the TEXTOR tokamak.
W e fabricated a full set o f 16 ECEI m odules and a set o f 8 16-way power
dividers, which permit 16x8 pixel electron temperature im ages to be acquired.
4.1.1 Power D ivider D esign
The W ilkinson power divider is a solution to the problems associated with the
lossless T-junction which possesses nonmatched and non-isolated output ports. The
resistive T-junction divider can be a solution for the matching problem; however, the
isolation issue cannot be solved. In addition, this solution leads to pow er loss because o f
the resistive structure o f the resistive T-junction divider. The W ilkinson pow er divider is
a lossy three port network and it has the property o f being lossless when the output ports
are matched. In addition, isolation between output ports can be achieved in the W ilkinson
power divider. The dissipated power in the W ilkinson power divider arises from the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
reflected power. There are tw o general types o f W ilkinson pow er dividers; the first one is
the equal power divider and the second one is the unequal pow er divider.
-A
Port 1
Fig. 4.3 Conceptual Picture o f an Equal Power Divider.
The equal power division concept concerns dividing the input pow er into tw o or
more equal pow er outputs. The most com m only em ployed configuration is the three port
network equal two way divider. It is also called a 3-dB pow er divider. In this type o f
divider, there are four different sections: 1) Input port, 2) Quarter-wave transformers, 3)
Isolation resistors, and 4) Output ports. The input and output ports are identical and the
value o f the impedances o f them is Z0.
The reflected power for the input pow er at port-1 is zero (Sn = 0 ). All the power
is transferred at that frequency. The quarter-wave transformer portion leads to the
matched ports. The function o f the isolation resistor is to isolate the output ports. If there
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
is a coupling effect between output ports or in other words, if the pow er com ing from one
output port has an effect on the other output port, perfect division o f the pow er cannot be
possible. This isolation resistor avoids the coupling effects o f the output ports. The output
ports are the ports out of which the divided pow er em erges. These ports have the same
impedance value as that o f the input ports.
2
Term
Terml
Num-1
Z = 50O hm
DA_W DCc u p le r1 _ p o w e r_ 4 5 _ te s t
DA WDCc nplerB
Subst="M! ub1"
F=4.5 GH:
Zo=50 Ohi 1
Delta=0 m
Term
Term 2
Num=2
Z=50 Ohm
T e rm
Term 3
Num=3
Z=50O hm
M Sub
MSUB
M Subl
H=20 mil.
Er=3.05
Mur=1
Cond=1 .OE+50
Hu=3:9e+034 mil
T=1.34 mH
TanD=0
Rough=0 mil
S -P A R A M E T E R S
S_Param
SP1
Start*2 GHz
Fig. 4.4 W ilkinson D ivider M odule in A D S design. Center Frequency 4.5G H z
A W ilkinson power divider splits the pow er at the input (port 1) between the two
outputs (ports 2 and 3). The signals at the outputs are in phase. A ll three ports will be
matched, and ports 2 and 3 will in general be w ell isolated from each other. (Shown in
Figure 4.4) In A gilent-A D S, the substrate o f the PCB board should be defined firstly. For
W ilkinson power divider components, Subst is the microstrip substrate name; F is the
designed center frequency o f this power divider (in hertz); Zo is the characteristic
impedance o f beams (in ohms); K is the ratio o f power out port 2 to pow er out port 3
(K = l for the equal power divider); Wgap is the width o f gap for the isolation resistor
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
(W gap=30m ils to m eet the resistor size w e used); D elta is the length added to quarterw ave branches for tuning performance (D elta=0 is the default number).
W e chose GM L 1000 High Frequency Laminate for our PCB circuit fabrication.
Information about GML 1000 is needed for A gilent-A D S to define the substrate o f the
Microstrip lines. Based on the datasheet o f the com pany, GM L 1000 is double sided
copper clad high frequency laminate, with a low loss (Tan delta), tight thickness control
and stable dielectric constant (Er), GML 1000 is a thermoset polym er alloy (TPA) system
so the substrate is rigid and w ill not creep. Suggested applications include filters,
couplers, antennas, power supplies, low noise block down converters, repeater radios and
other wireless devices. Substrate thickness 20 m ils. Dielectric Constant 3.05 +/- 0.05
from
2-10
GHz.
Dissipation
Factor
0.0030-.0060
from
2-10
GHz.
(http://www.gilam .com /m ain_gilp.htm l). After the substrate and all parameters for the
pow er divider are set up in A D S, choose D esign Guide> Passive Circuit > Microstrip
Control W indow > D esign Assistant to design the W ilkinson D ivider automatically.
Figure 4.5 shows a W ilkinson Divider designed by A ginlent-A D S (The center frequency
F=4.5G H z; Zo=50ohm s; K = l; W gap=30 mils; D elta=0). Figure 4 .6 show s the Sparameter simulation result o f this 2- way Pow er Divider. Inside the required band 3-7
GHz, the ripple is less than 0.3dB which is an acceptable result. For an 8 -w ay power
divider, three stages o f the 2-way W ilkinson power divider are needed, in which the
ripple is about 1 dB.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
-O
o
(a)
(b)
Fig. 4.5 D esign Assistant (a) and layout (b) of the W ilkinson D ivider whose
center frequency is 4.5 GHz.
ml,-
Fig. 4.6 Simulation Result o f one W ilkinson Divider. S 21 and S 31 are shown.
4.1.2 Testing the Pow er Divider
To ensure that A D S design yielded believable results, I designed an 8 -way power
divider compared with the real circuit which was fabricated by AP Circuits
(http://www.apcircuits.com /) . The design band is 3-7 GHz. Variation o f Insertion Loss in
the band is less than ldB .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
Fig. 4.7 W ilkinson ( 8 -Way) power divider D esign in A D S. G M L -1000 (20m ils)
High Frequency Laminate is used.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
101
Fig. 4.8 W ilkinson (8-w ay) Pow er Divider. 50 ohm loads are connected to the
ports when S-parameter measurements are performed.
............. ~
my \ _
freq= 3790G H z
d6(S(2A ))=-9.50a
‘
\
\ m1 /
f \
\
/
\
/
m2
freq=6.650GBz
4B(S(2.1))=-9'i975
'/
\
I
\
;
'
i
!
\
\
/
\
/
\
/
\
|
;
}
i
\
/
\
!
\
/
\
/
\
/
V
fr«q, GHz
Fig. 4.9 S-parameter result o f A D S Simulation. From 3-7 GHz, the insertion loss
varies from 9.0 dB to 9.975 dB.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
102
•9
■1 0
11
12
S21
S31
13
-S51
- S61
■1 4
15
16
2
3
4
5
6
7
8
9
10
F r e q u e n c y (OH?)
Fig. 4.10 Test result o f the 8-way power divider. Compared with Fig. 4.9, testing
result is 1-2 dB worse than the A D S simulation. H owever, it is still acceptable for
application in the ECEI system . The shapes o f testing and sim ulation are very similar.
A D S design is used in the later electronics box.
4.1.3 Printed Circuit Local Oscillator (LO) M odules
The VCO circuit diagram is shown in Fig. 4.11. A total o f 8 local oscillator (LO)
signals are required to downconvert the 2-D ECEI signals, with 16 LO outputs per
frequency. Each LO signal is generated from a low cost VCO, which is power divided
and amplified using low cost, low noise gain blocks (N B B -310). At the last stage, 16
channels o f LO output are provided.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
103
F AMP
Pow er D ivider
IF A M P
Pow er D ivider
IF AM P
CH 10
CH I
IF A M P
CH 12
Pow er Divider
CH 13
CH 14
CH I 5
IF AM P
Power Divider
CH 16
Pow er D ivider
Fig. 4.11 Diagram o f LO Module.
The features o f the amplifier N B B -310 follow:
(httD://w w w .rfm d.com /D ataBooks/db97/N BB-310.D df)
□
Frequency: D C -12 GHz
□
Gain: 11.5 dB (4.0-8.0 GHz)
□
N oise Figure: 4.9 dB at 3 GHz
□
M axim um Output Power: 15 dBm
□
50 ohm I/O Matched for High Frequency use
□
Single Power Supply Operation 5.0V
□
Cost: $5.98 (quantity o f 100)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
104
Figure 4.12 shows the S-parameter testing result o f the amplifier N B B -3 1 0 which
is tested on an HP 8 5 10C Vector Network Analyzer.
12
8
6
A
2
5
2
8
ID
Fig. 4.12 S-parameter M easurement o f the N B B -310. S 21 is shown. |S 2i|> 7 dB (37 GHz).
In Fig. 4.11, the 16 way power divider generates 12-14 dB insertion loss and the
2-stage N B B -310 amplifier provides amplification in excess o f 14 dB. The output signal
should exceed +5 dBm to m eet the requirement o f the subsequent m ixer circuits. The
VCO components should provide at least +5 dBm. Four kinds o f VCO are used in the LO
m odules and are listed in Table 4.1.
Table 4.1 VCO
VCO
Frequency
Pow er Output
Tune Voltage
Supply V oltage
Range (GHz)
M inim um (dBm)
V T (V)
Vcc (V)
H M C 358M S8G
5.8-6.8
8
0-10
+3
M V 129SM
4.0-4.8
8
0.5-12
15
M V 152SM
3.12-3.87
5
1-10
11
M V 156SM
4.6-5.3
6
1-10
11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105
Table 4.2 LO Frequency Assignm ent
Frequency
V C O M odel
Tune Voltage V t (V )
(GHz)
Supply Voltage V cc
(V)
3.20*
M V 152SM
2.137
11.00
3.80
M V 152SM
7.91
10.99
4.30
M V 129SM
4.24
15.09
4.80
M V 156SM
3.974
11.02
5.30
M V 156SM
9.28
11.03
5.80
H M C 358M S8G
1.289
3.01
6.30
H M C 358M S8G
3.095
3.00
6.80
H M C 358M S8G
7.72
3.00
* M V 152SM is unstable near 3.3 GHz, the frequency jum ped between 3.24 GHz
and 3.33 GHz. Finally, its, frequency was set to 3.20 GHz.
Fig. 4.13 Show n above is an LO m odule with an output frequency o f 4.3 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
106
4.1.4 Printed Circuit Power D ivider and M ixer M odules
The circuit diagram is shown in Fig. 4.14. The input signal (3 - 7 G Hz) is
amplified by gain block N B B -310. The signal then passes through the 8-w ay W ilkinson
Power divider and is m ixed with 8 LO frequencies. The m ixers are M B A -591, M B A -671.
The IF signal is passed through white SM A cables which are the backside o f the board to
the follow ing module.
"CfP
cm;
cm—
■’HI
LO) ■
L 02-
*
L 03-
Input
L 04-
Signal
L05 -
IP AMP
LOfi1.07 -
LOSM lx« i s
Powat Divider
Fig. 4.14 Diagram o f M ixer M odule.
Table 4.3
M ixer
LO Power
LO/RF Frequency
IF Frequency
M axim um
Level (dBm)
Range (GHz)
Range (M Hz)
Conversion
Loss (dB)
M BA -591
7
2.80-5.90
D C -1000
9.0
M BA -671
7
2.40-6.70
D C -1000
9.2
http://www.minicircuits.com/
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 4.15 Printed Circuit IF Am p/Detector/V ideo Amp M odules
The IF Am p/Detector/V ideo Amp M odules were designed by Dr. Calvin Dom ier,
one o f the ECEI design team members. The mixer output signals are am plified by 20 dB,
then ac coupled and bandpass filtered to 5-150 M Hz (MCL SA L F -146). Each filtered
signal is then rectified/detected (Agilent H SM S-2825). Since this last m ixing process is
double sideband, collecting power on both sides o f the LO signal, this translates to an
effective RF bandwidth o f 300 M Hz. The post-detector signals are video am plified by
4 5 -5 5 dB to extend the linear output range o f the detectors to match the input range o f
the 12-bit digitizers. A variable lowpass filter is em ployed, capable o f setting the output
bandwidth from as low as 70 Hz (for laboratory testing) to as high as 240 kHz (for
plasma turbulence measurements). The final output signal for each channel is buffered to
drive 50 ohm loads.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 4.16 One M ixer M odule and one IF A m p/D etector/V ideo Am p M odule are
installed inside a metal box. They are connected by 8 white SM A cables. Left is the
M ixer M odule which show s its backside.
a am*
- t* c
Fig. 4.17 Printed Circuit IF Am p/Detector/V ideo Amp M odule. (D esigned by Dr.
Calvin Dom ier)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 4.18 Com plete ECEI Electronics Box.
4.2 Antenna Array Box
Previous ECEI system s [2-5] em ployed slot bow tie antenna elem ents to collect
the m illim eter-wave radiation. In this ECEI system , a dual dipole antenna has replaced
the bowtie antenna. The dual dipole antenna offers numerous advantages over the slot
bowtie antenna, including superior H-plane antenna patterns and a w ider intermediate
frequency (IF) bandwidth. Perhaps its clearest advantage in plasma im aging is its
compact layout that is ideally suited to packing into a tightly staggered array format, as
can be seen in the array shown in Fig. 4.19. Small beam lead Schottky m ixer diodes are
placed at the center o f each antenna. W ideband baluns convert the m icrowave signals
from balanced (at the antenna) to unbalanced (at the output connector) transmission line
format. This new array and the associated baluns are designed by Zhengang Xia, one o f
my colleagues, and are part o f his PH.D dissertation research.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 4.19 Left Picture show s the dual dipole array placed on the substrate lens.
Right picture show s one dual dipole antenna.
Fig. 4.20 These two pictures show the 20 channel dual dipole printed circuit
antenna/mixer imaging array (two view s), incorporating wideband baluns and low noise
m icrowave preamplifiers.
A quasi-optical dichroic plate consists o f a metal plate with a tightly packed array
o f circular holes and acts as a highpass filter. It is mentioned in Section 4.1 that a high
pass filter is used to ensure the wideband IF system operated with single sideband (SSB).
(Shown in Fig. 4.21)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I ll
Table 4.4 D ichroic plate diameter versus Cutoff Frequency
Diameter (inch)
0.0680
0.0655
0.0630
0.0 6 0 6
0.0580
Cutoff Frequency (GHz)
102.7
106.6
110.8
115.1
120.2
Fig. 4.21 M etal plate with a tightly packed array o f circular holes.
A similar plate (0.0680” dia., 102.7 GHz cutoff frequency) is utilized on the LO
port for EM noise suppression. It is useable for LO frequencies from 104-120 GHz.
Tuning the BW O frequency (set at or below cutoff) with the appropriate dichroic plate
selection allow s for wideband frequency coverage. In the actual system , 105 - 127 GHz
tunable coverage is achieved.
4.3 TEXTOR ECEI Antenna Array Testing
Prior to installation on TEXTOR, the channel positions and focal plane beam
patterns o f the ECEI system were characterized in the laboratory. W e duplicated the same
ECEI optical system as the actual TEXTOR system. The system setup is shown in Fig.
4.22. The RF source sends out the microwave signal which is reflected by a movable
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
metal rod to simulate the plasma radiation. A s the rod m oves, the signal received by
different channels o f the antenna array permit the determination o f the array pattern, i.e.
the spatial resolution and channel spacing. The tw o photographs contained in Fig. 4.23
and Fig. 4.24 show the setup in the laboratory.
RF Source
Focusing
Lenses
Focusing Lenses
R e fle c tiv e M irrors
O
I
"1
O
C om puter
Fig. 4.22 Antenna Pattern testing setup in the laboratory. The RF signal is m ixed
with the LO and amplified by the initial EF amplifier which is installed in the array box.
Then the m ixed IF signal (3-7G H z) is transmitted to the Electronics B ox, and
downconverted to an IF signal (5-150M H z) which is inputted to the computer by a D A Q
card.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
Fig. 4.23 A Backward W ave Oscillator (BW O ) (M icrow ave Generator G 4-142bM
(GPIB)) is used as the LO source. The mirrors are identical to those used in TEXTOR
except for the smaller size.
Fig. 4.24 Antenna Pattern Measurement Setup in the laboratory.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
0.8
C 0.4
0.2
-100
-80
-60
-40
-20
0
D ista n c e (m m )
80
Fig. 4.25 Antenna Pattern o f the ECEI Array (normalized).
Figure 4.25 shows the norm alized E-plane (vertical direction) focal plane patterns
measured at 115 GHz, with the corresponding raw signals provided in Fig. 4.26. The
plots are generated by translating a metal rod across the focal plane region. The rod in
this way acts as a line source scattering radiation from a source positioned below the
scattering rod. The norm alized signals demonstrate relatively clean patterns with an inter­
channel spacing is a uniform 11 mm on all channels, with a 3 dB beam spot size that
varies from 12 to 13 mm and with relatively low side lobe levels. Standing waves arising
from reflections between (a) the scattering rod and the scattering source horn, and (b) the
scattering source rod and the ceiling (from which a finite reflection is observed), account
for the small (few %) perturbations in the observed patterns. The H-Plane (toroidal
direction) spot size is approximately 9 mm, with an inter-channel (staggered) spacing of
only 8 m m as compared to 32 mm in the previous TEXTOR ECEI system that em ployed
slot bowtie antenna elements. [1]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
115
The raw signals reveal signal amplitudes that change markedly betw een channels.
This arises from a number o f factors. First is a difference in detector sensitivity due
primarily to LO drive levels which vary significantly from channel to channel but also
due to variations in diode performance. With sufficient LO drive, this produces less than
a factor o f 2 variation in signal sensitivity. Typically, how ever, this effect might give up
to a factor o f 3 variations. Second is that the lower channel numbers have a focal region
considerably closer to the scattering source, and thus have a signal level that varies as one
over the distance (to the horn) squared. This accounts for som e o f the sawtooth behavior
observed in Fig. 4.26 (compare, for exam ple, the relative sensitivities o f channels 2-5).
Third is that the focal plane distance, m eaning here the distance from the scattering rod to
the array which corresponds to the sm allest spot sizes, itself varies from channel to
channel due to spherical aberration effects. This focal plane distance decreases as one
m oves away from the center of the array. In the plots shown here, the array was
positioned such that channels halfway to the edge were roughly at their optimum location.
Lastly, the staggered nature o f the interleaved antenna array results in focused beams
whose centers are offset toroidally (H-plane). This makes the signal levels o f the odd vs.
even channels quite sensitive to hom placement and scattering rod orientation (i.e. large
variations in the odd-even signal levels are seen by relatively small changes in the
toroidal orientation o f the scattering rod). One factor to note, how ever, is that in operation
on the TEXTOR device the black body nature o f the plasma em issions has the effect o f
elim inating signal variations from all but the first o f these factors, nam ely variations in
diode performance and LO drive.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
1 1 -2 1 -1 1
2003
3.5
3
2.5
>
2
£L
<
E
1.5
0.5
0
-100
0
-50
50
Distance (mm)
Fig. 4.26 Antenna Pattern o f the ECEI Array (raw data).
4.4 TEXTOR MIR Electronics
Follow ing the UC D avis laboratory tests, the MIR detection system was shipped
to PPPL. The final system test was performed at PPPL before shipping to TEXTOR.
Figure 4.27 shows a schematic o f the electronics portion o f the 1-D system.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
140 MHz
LO
V id eo
Am ps
o #
Input
Signal
IF Amp
l> #
P o w er
D ivider
IF
Am ps
Mixers
B P Fllters
l-Q M ixers
Fig. 4.27 Electronics diagram o f the 1-D MIR system.
The top figure o f Fig. 4.28 shows the channel positions and focal plane beam
patterns o f the MIR system . The detection system can provide 10 cm poloidal coverage
(vertical direction). The bottom figure o f Fig. 4.28 displays the m easured channel width
for each o f the fifteen channels. 1.1 cm poloidal resolution is achieved.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
S c o tte r in g - r o d respon se o f MIR syste m (n o rm a liz e d )
1-------1-------.-------1-------.-------,-------.-------.-------1-------1-------.-------.-------.-------1-------1------
'
I-------1-------
intensity
[a r b ]
i
y [cm ]
ch a n n el width
[cm]
C hannel w idth vs. p o sitio n
0.5
0.0
-6
-4
-2
0
2
4
y [cm ]
Fig. 4.28 The focal plane beam patterns of the MIR system.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6
119
References:
[1] J. W ang et a l , "Two-dimensional Electron Cyclotron E m ission Im aging D iagnostic
for TEXTOR," Rev. Sci. Instrum. 75, 3875 (2004).
[2] B. H. D eng, R. P. Hsia, C. W. Dom ier, S. R. Bum s, T. R. H illyer, N. C. Luhmann, Jr.,
T. Oyevaar, and A. J. H. Donne, E lectron C yclotron Em ission Im aging D iagnostic
System f o r RTP, Rev. Sci. Instrum. 70, 998 (1999).
[3] G. Cima, K. W. Gentle, A. W ootton, D. L. Brower, L. Zeng, B. H. D eng, C. W.
Domier, and N. C. Luhmann, Jr., E lectron heat dijfusivity in the saw tooth ing tokam ak
core. Plasma Phys. Controlled Fusion 40, 1149 (1998).
[4] B. H. D eng, D. L. Brower, G. Cima, C. W. Dom ier, N. C. Luhmann, Jr.,and C. Watts,
M ode
Structure
o f Turbulent Electron
Tem perature
Fluctuations
in
the
Texas
Experim ental Tokamak U pgrade, Phys. Plasmas 5, 4117 (1998).
[5] B. H. Deng, C. W. Dom ier, R. P. Hsia, N. C. Luhmann, Jr., D. L. Brower,G. Cima, A.
J. H. Donne, T. Oyevaar, and M. J. van de Pol, E C E im aging o f electron tem perature and
electron tem perature fluctuations (invited). Rev. Sci.Instrum. 72, 301 (2001).
[6]. B.H. D eng, Two dim ensional electron cyclotron em ission im aging study o f electron
tem perature profiles and fluctuations in Tokamak plasm as, Ph.D. dissertation, UC D ,
1999.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
120
Chapter V
TEXTOR
ECEI/MIR Data Analysis
5.1 ECEI system
A s discussed in Section 1.2, M H D instabilities and Sawtooth O scillations are
associated with global or local rapid redistribution o f energy.[1-8] Dr. Tobin Munsat
provided considerable advice about ECEI data analysis which was utilized in this
dissertation research. W e used software IDL which is a product o f Research System s, Inc.
to download and analyze data. A ll the related programs o f IDL can be found in Appendix
I. The emphasis o f this chapter is the illustration that the TEXTOR ECEI/M IR com bined
system was successfully com m issioned and that it provides high quality good data. It
provides an understanding o f the capability o f the instrument.
5.1.1 Sawteeth O scillations
The sawteeth instability was first observed in 1974 [9]. One year later, it was
explained by the resistive magnetic reconnection m odel o f B .B . K adom tsev [10].
H owever, new experimental results with refined diagnostics after the m id 1980s have
revealed discrepancies in various aspects o f this M HD m odel [1, 11].
One o f the first types o f plasmas to be studied with the 2-D ECEI diagnostic were
neutral beam heated plasmas which exhibited sawteeth. (TEXTOR discharge #94568:
Ip=400 kA, 5 X=2.3 T, ne( 0 )= 4 x l0 19 m'3, T e(0)~ 1 keV, Pnbi=3 M W ). Figure 5.1 show s the
detection region o f our ECEI system in discharge #94568. The blue circles are the
surfaces o f q = l, 2, 3. Figure 5.2 shows the real data o f our ECEI system . Figure 5.3 and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
121
5.4 shows som e sawteeth in discharge #94568. Figure 5.5 show s a sawteeth picture which
is filtered by a low pass filter.
Fig. 5.1 ECE Imaging Observation region in TEXTOR. The parameters o f this
shot are as follow s: Bo=2.3 [T]; Ip=400 [kA]; Shafranov shift= 3 [cm], ECEI LO
Frequency = 1 1 0 GHz. The red cross points show the position o f all channels.
Fig. 5.2 Original Data from Shot # 94568. The time length o f the sampling is 7
seconds. The length of all data is 1404000 points, (http://ipptwu.ipp.kfa-iuelich.de/ which
is the data links homepage o f the TEXTOR Tokamak)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122
Fig. 5.3 The time history o f M ixer 3, IF band 8. (Channel 3 Frequency 8)
3:5
Fig. 5.4 The time history o f M ixer 13, IF band 8. (Channel 13 Frequency 8)
Shot
9 4 5 6 8 , Channel 9, F r eq u en cy 5
1.05
3
A/VIa'1)
A,
1. 00
i
■s
0.95
' AJ
!\J
l\r,
I [i 1 A
KrJ V
3.00
«4
AI
W/AV
3.02
ryv
I^,A
!/ ■ v
3.04
r'A/
1
1 A /A /
„ A'-',
fT
I
,v A-' /
3.06
t (s)
Fig. 5.5 The Sawteeth O scillations observed in Shot # 94568. The period o f the
sawteeth is about 35 ms.
The test Te fluctuation measurement for the new ECEI system is m = l oscillations
(sawteeth). The fundamental physical process o f magnetic reconnection is still an
outstanding issue and requires 2-D measurement o f Te and plasma current to understand
the entire reconnection process. The test plasma conditions for the ECEI experim ent were
as follow s; Ip = 400 kA, B t = 2.3-2.4 T, ne(0)= 2- 4 1013cm'3, and Te(0) ~1 keV. In order
to reduce the noise level further, - 1 0 identical “sawteeth” oscillations are averaged. The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
123
sequence o f “sawteeth” crash is clearly illustrated in Figure 5.6-5.7. N ote that the
inversion radius drawn here may not be an accurate quantity due to lack o f a current
profile measurement (q ~ l). Here, the hot island approaches the inversion radius and
reconnects to the m agnetic surface o f the inversion radius at the low field side without
high poloidal number ballooning mode. After the reconnection process is com pleted, heat
spreads in the m ixing zone along the inversion radius w hile the cold island sets in inside
o f the inversion radius. Here, the crash time is - 1 5 0 /tsec and one period o f m = l m ode is
- 1 7 0 msec. The preliminary analysis demonstrates that the temperature in the vicinity o f
the inversion radius is not perturbed through the crash whereas the hot spot is clearly
present before and after the crash. This observation indicates that the ballooning
characteristic is absent in these images. (Reference 13)
The new 2-D ECEI system can achieve excellent spatial resolution (-1 cm). This
high spatial resolution range could cover about a 20 cm region o f plasm a perpendicularly.
The system can achieve 200k points/s data rate. These allow ed a com prehensive study o f
Te fluctuations in TEXTOR, which included the 2-D m easurem ents o f the spatial
distribution o f Te fluctuations.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
1
2
3
4: Pre-crash
5: Mid-crash
6: Post-crash
Fig. 5.6 2-D Images show the progression o f im ages o f a sawtooth crash. The
inversion layer is estimated as the double white curve. The “hot spot” (yellow in the
false-color scale) breaks through the inversion layer at the lower right com er o f the field
o f view . (Shot # 9 4 5 7 1 q = l layer) (Ref. 12, 13)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
q=1 s u r f a c e
Fig. 5.7 2-D The im ages show the electron temperature profile o f the sawteeth
crash. (Shot # 94571 q = l layer) (Ref. 12, 13)
id
y
Fig. 5.8 Tim e histories o f M ixer 13 IF Band 3 (top) and M ix e r l4 IF band 4
(bottom). (Shot # 9 6 1 3 8 )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
126
Fig. 5.9 Original data o f M ixer 13 IF Band 3 (top) and M ix erl4 IF band 4
(bottom). (Shot # 94566)
V
\
\ \
v
Y
V
j
- '' v
1
,v V :
V
Fig. 5.10 Tim e histories of M ixer 12 IF Band 6 (top) and M ix erl2 IF band 7
(bottom). (Shot # 94567)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
127
1.4
1.0
QA
' Q.a
(a)
' C4
CJ
C.O L_
1.0
[see]
* 354
Iu a c )
2.205
1.D
.i
: [fiflc]
Fig. 5.11 Tim e histories o f LO Frequency (a) and Ip (b) and B T (c), Signal of
M ixer 12 IF band 7 (d). (Shot # 94590)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
128
5.1.2 MHD Oscillations
Because o f finite resistivity near rational q surfaces in tokamaks [1], the normally
conserved magnetic flux surfaces are able to tear and reconnect and form so-called
magnetic islands or tearing m odes. The growth and stability o f these m odes is determined
by the local resistivity and current density gradient. Plasma rotation is thought to play an
important role in the stabilization o f a tearing mode. Tearing m odes in ohm ically heated
plasmas usually rotate in a toroidal direction counter to the plasma current. The rotation
frequency is often associated with the sum o f toroidal plasma rotation and the electron
diamagnetic drift at the m odes’ rational q surface. (Reference 6) Figure 5.13-5.15 show
that the plasma rotation mode. Our colleagues in PPPL and FOM are working on a more
detailed analysis o f the data together with the physics o f the reconnection process.
S h o t9 5 2 5 0 _ C h a n n e l_ 4 _ F re q u e n c y _ 3 ;
MHD m ode
.36
1.3 0
1.800
<S>
1 .SOS
S h o t 9 5 2 5 0 _ C h a n nel—
9—
F requency
3;
MHD m o d e
1 .9 5
1.90
1.85
1.7 5
1 .7 0
1 .8 0 8
1.804
(b )
Fig. 5.12 The time histories o f M ixer 4 IF Band 3 (top) and M ixer 9 IF band 3
(bottom). (Shot # 95250)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
129
Fig. 5.13 Images o f M HD Oscillation (Part I). Plasm a rotates clockw ise. Cold part
(blue) goes down and hot part (red) occupies the im aging region.
Fig. 5.14 Images o f M HD Oscillation (Part II). Cold part (blue) intrudes from the
top and hot part (red) is expelled from this region and reenters after 0.5 ps. The period of
the M HD O scillation is about 1 ps.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
130
Fig. 5.15 Images o f M HD O scillation (Part HI). The cycle continues. Cold part
(blue) and hot part (red) go through this region by turns.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
131
5.2 MIR system
One o f our colleagues, Dr. Tobin Munsat, is the person w ho has worked on the
MIR data analysis. Here, I include som e o f his results for the sake o f com pleteness, (see
References 14-15)
In the experiment, both the probing frequency (84G H z, X -m ode) and the focal
plane o f the optics were held fixed. In addition, the electron density w as ramped during
the shot to m ove the cutoff surface through and beyond the focal plane o f the im aging
optics. Figure 5.16 (a)-(d) are the quadrature signals plots (norm alized to unit average
power) over a 3 m sec tim e window as the cutoff m oves through the optical focal plane
because o f a density rise. Cutoff positions are 1.93 m (a), 1.99 m ( b ,c ) , and 2.06 m (d). In
this experiment, both the probing frequency and the focal plane o f the optics were held
fixed, and the electron density was ramped over the course o f the shot to bring the cutoff
surface through and beyond the focal plane o f the optics. W hen in focus, the data shape is
essentially a circular annulus, which means that the amplitude m odulations are reduced
and the phase modulation is the main part. When out o f focus, the amplitude modulation
increases dramatically. The plots o f Figure 5.16 (e) and (f) are the pow er spectrum o f the
signal phase for out-of-focus(e) and in-focus (f) cutoff positions. (R efem ce 14) Figure
5.17 show s the quadrature signal plots of the 16-channel array when the new TEXTOR
MIR optics is in focus.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
132
T £ \ T O R Quadrature s i a n a k
into focus
b a ck out o f fo cu s
0
■, -:<A"Sryt. ;i. <>•; •
-2
0
(b)
-2
-2
-1
0
(c)
unfocused spectrum
focused spectrum
v /
100
10
IkHz]
100
(f)
Fig. 5.16 Com plex field amplitude from the TEXTOR M IR system as the cutoff
layer is swept through the focal plane o f the im aging optics. It show s the cut-off layer is
m oving from the core side to the edge as density is ramped.
D is c h a rg e 9 3 0 6 4
Channel 2
Chamei 3
Channel t
4
0
-20
-4 0
•4
C hannel 5
-4 0
0
4
Channel 6
40
20
0
0
-4 0
-20
-4 0
-2 0 0 2 0 4 0
C hannel 9
40
-20
•4 0
0
40
Channel 13
-4 0
0
40
Channel 14
-10
0
10
Channel 15
-2 0
0 20 40
Channel 16
40
0
-4 0
-4 0
0
40
Fig. 5.17 Quadrature signals from MIR multichannel detector array. (Discharge #
93064)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
133
The poloidal velocity o f the turbulent structures over a w ide spectral range is
presented in Figs. 5.18(c) and 5.18(d), for two tim e slices taken during neutral-beam
injection heating and just after the turnoff o f the neutral beam, respectively. The
corresponding com plex spectra for a central channel are shown in Figs. 5.18(a) and
5.18(b). Figure 5.19 show s the time history o f Poloidal rotation induced by N B I from 4.4
sec to 4.76 sec. The velocity slow s and reverses after the N B I turn-off. (Reference 13)
10"
10"
5
10
10
10 "
10,-6
"
10'
10
108
10s
-5
•7
•7
109t—
-1000
-500
0
500
1000
10-1000
'9L—
-500
f [kHz]
-200
-100
0
f [kHz]
0
500
1000
f [kHz]
100
200
-200
-100
0
100
200
f [kHz]
Fig. 5.18 Poloidal rotation measurement via M IR system, (a) Broad frequency
spectra and estimated initial velocity is +31.5 km /sec during N B I (co-beam ), (b) Narrow
frequency spectra and after NBI off. Rotation reverses and settles at -17.5 km/sec.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
134
1
1
HIHi
1 1
Fig. 5.19 Time history o f Poloidal rotation induced by NBI. (4.4 sec - 4.7 6 sec)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
135
References:
[1]. J. W esson, Tokamaks, Oxford, Clarendon Press, (1987).
[2]. E. Teller, Fusion, N ew York Academ ic Press, (1981).
[3]. F. Porcelli, A. Airoldi, C. Angioni, A. Bruschi, P. Buratti, F. Califano, S. Cirant, I.
Fum o, D. Grasso, E. Lazzaro, A .A . Martynov, M. Ottaviani, F. Pegoraro, G. Ramponi, E.
R ossi, O. Sauter, C. Tebaldi, O. Tudisco, M odelling o f m acroscopic m agnetic islands in
tokamaks. Nuclear Fusion, vol.41, no.9, Sept. 2001, p p .1207-18, (2001).
[4]. V.S. Udintsev, B.P. van M illigen, F.C. Schuller, A. Kramer-Flecken, B.H. D eng,
C.W. Dom ier, A.J.H. D onne, J.C. van Gorkom, N.C. Luhmann Jr., L arge a n d sm all scale
M H D m ode studies at TEXTOR. Proceedings o f the 12th Joint W orkshop on Electron
Cyclotron Em ission and Electron Cyclotron Heating (EC -12). W orld Scientific, pp.2152 0 ,(2 0 0 3 )
[5]. S.J. Kim, D.H . Edgeil, J.M. Greene, E.J. Strait, M .S. Chance. M HD m ode
identification o f tokam ak plasm as from M im o v signals. Plasm a Physics & Controlled
Fusion, vol.41, n o .11, N ov. 1999, pp.1399-420, (1999).
[6]. P.C. D e Vries, G. Waidmann, A.J.H. Donne, F.C. Schuller, M H D -m ode stabilization
by plasm a rotation in TEXTOR. Plasma Physics & Controlled Fusion, v o l.38, no.4, April
1996, pp.467-76,(1996).
[7]. Y. Nagayam a, A. Ejiri, K. Kawahata, E. Fredrickson, A. Janos, K. McGuire, G.
Taylor, ECE im age reconstruction o f M H D m ode structure on fu sion plasm as. EC-9.
Proceedings o f the Ninth Joint Workshop on Electron Cyclotron E m ission and Electron
Cyclotron Heating. W orld Scientific, pp.455-8, (1999).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
136
[8]. B.H. D eng, C.W. Dom ier, N.C. Luhmann, D .L. Brower, G. Cima, A.J.H. D onne, T.
Oyevaar, M J .
van de Pol, E C E im aging o f electron tem perature and electron
tem perature fluctuations (invited). R eview o f Scientific Instruments, vol.72, n o .l, pt.1-2,
pp.301-6, (2001).
[9]. S. Von Goeler, W. Stodiek, N. Southoff, Studies o f Internal D isru ption s a n d m = l
O scillations in Tokamak D ischarges w ith Soft X -ray Techniques, Phys. Rev. Lett., 33,
1201 (1974).
[10]. B.B . Kadomtsev, D isruptive Instability in Tokamaks, Sov. J. Plasm a Phys., 1, 389
(1975).
[11]. H. Soltw isch, Saw teeth, Fusion Technology, 29, 62 (1996).
[12]. T. Munsat, E. M azzucato, H. Park, C.W . Dom ier, M. Johnson, N .C . Luhmann, Jr., J.
Wang, Z. Xia, I.G.J. Classen, A.J.H. Donne, and M.J. van de Pol, 2-D Im aging o f
Electron Tem perature in Tokamak P lasm as. IEEE Transact, on Plasm a Sci. 33, 466
(2005).
[13]. H. Park, E. M azzucato, T. Munsat, C.W . Dom ier, M. Johnson, N.C. Luhmann, Jr., J.
W ang, Z. Xia, I.G.J. Classen, A.J.H. Donne, and M.J. van de Pol, Sim ultaneous
M icrow ave Imaging System f o r D ensity an d Tem perature F luctuation M easurem ents,
Rev. Sci. Instrum. 75, 3787 (2004).
[14]. T. Munsat, E. M azzucato, H. Park, B.H. D eng, C.W. Dom ier, N .C . Luhmann, J.
Wang, Z.G. Xia, A.J.H. Donne, M.J. van de Pol, M icrow ave im aging reflectom eter f o r
TEXTOR (invited). R eview o f Scientific Instruments, vol.74, no.3, pp. 1426-32, (2003)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
137
[15]. T. Munsat, E. M azzucato, H. Park, C.W . Dom ier, N.C . Luhmann, A.J.H. Donne,
M.J. van de Pol, L aboratory C haracterization o f an Im aging R eflectom eter System.
Plasma Phys. Control. Fusion 45 (April 2003) 469-487, (2003)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
138
Chapter VI
ECEI/MIR Optical Designs for other Tokamaks
6.1 DIII-D ECEI Optical System Design
A com bined ECEI/M IR system for DIII-D has been proposed by UC D avis. M y
work was focused on the preliminary ECE Imaging Optical System D esign.
6.1.1
Optical System Considerations
The optimal frequency range for ECEI on DIII-D extends from 90 to 127 GHz,
which exceeds the tunable bandwidth o f the dual dipole antenna em ployed in the current
systems. A solution to this problem is to fabricate two arrays, each covering half o f the
desired bandwidth and to separate the two frequency bands.
120
ate H-mode, w
100
IT
80
X
o
60
40
20
°0
0.2
0.4
0.6
0.8
1
r/a
Fig. 6.1 Electron cyclotron radiation frequencies o f the tw o low est harmonics in
Dm-D. Plotted together are the early H -m ode and the late H -m ode cases.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
139
6.1.2 Optical System Design
Optical sim ulations for a 20 channel system have been conducted based on the
measured dual dipole array pattern at 105 GHz (wavelength 2857142nm ).
The parameters o f the dual dipole array are as follow s. The E-plane spacing is 85
mil and the H-plane spacing is 40 mil. The receiving angles o f the half bandwidth o f the
1/e electric field are 15.5 degrees outside o f the substrate lens and 24 degrees inside the
substrate lens. [1]
The DIII-D ECEI Optical system uses tw o large mirrors which are tilted
horizontally. One focus lens and one substrate lens are used to tune the beam. The size o f
the w indow is assumed 42cm by 15 cm. A ll CO DEV parameters o f the optical system are
shown in Figure 6.2. Figures 6.3 and 6.4 show the view s o f the optical design.
S urface #
S urface
N am e
S urface
Type
Y R adius
X R ad iu s
T h ic k n e s s
G la s s
R efract
M ode
Y
O bject
S p h e re
Infinity
Infinity
0 .0 0 0 0
1
S p h ere
Infinity
Infinity
5 0 .0 0 0 0
Refract
8 0 .0 0 0 0 0
8 0 .0 0 0 0 °
2
S p h ere
-100.0000
-1 0 0 .0 0 0 0
160 .0 0 0 0
R efract
8 0 .0 0 0 0 0
0 0 .0 0 0 0 °
S to p
S p h ere
Infinity
Infinity
9 1 .8 0 0 0
Refract
8 0 .0 0 0 0 0
8 0 .0 0 0 0 0
EF2
S p h ere
Infinity
Infinity
100.0000
R efract
150.0000 0
1 1 5 .0 0 0 0 0
-200.0000
-2 0 0 .0 0 0 0
H -plane mirr
C ylinder
Infinity
-389 0 .0 0 0 0
4
Conic
5
B
R efract
X
I
| S em i-A p ertu re S em i-A p ertu re
....... " 0
0
5 2 3 0 0 0 .6 0 0
5 2 3 0 0 0 .6 0 0
5 2 0 .0 0 0 0
-5 0 0 .0 0 0 0 v
7
E -p lan e mirr
Cylinder
27 00.0000
Infinity
115 1 .0 0 0 0
8
W indow
S p h ere
Infinity
Infinity
3 0 .0 0 0 0
9
S p h ere
Infinity
Infinity
Im age
S p h ere
Infinity
Infinity
R efract
150.0000 0
1 1 5 ,0 0 0 0 0
Reflect
3 2 0 .0 0 0 0 0
2 2 0 .0 0 0 0 0
2 0 0 .0 0 0 0 0
R eflect
4 0 0 .0 0 0 0 0
R efract
210 .0 0 0 0 s
7 5 .0 0 0 0 0
1 212.0000
Refract
2 1 0 .0 0 0 0 s
1 5 0 .0 0 0 0 0
0 .0 0 0 0
Refract
2 0 0 .0 0 0 0 s
1 0 0 .0 0 0 0 0
9 6 0 0 0 0 .6 0 0
End O f D ata
Fig. 6.2 Screen shot o f Lens Data Manager W indow.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Im a g e
W in d o w
Mirror H
39 6 .8 3
MH
Fig. 6.3 Side V iew o f the ECEI Optical System . The sightlines are slightly
expanding to provide larger plasma coverage.
M irro r H
le n s
3 9 6 .8 3
HH
xz
Fig. 6.4 Top V iew o f the ECEI Optical System.
6.1.3 Gaussian Beam Trace
Figure 6.5 shows the Gaussian calculation of the optics. The beam waist o f the Eplane is 12.0 mm at the plasma region and the beam waist o f the H -plane is 16.4mm. The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
141
color outputs o f the Gaussian beam simulation are shown in Figs. 6.6 and 6.7. The 3-D
view of the com plete optical system is shown in Fig. 6.8.
G A U S S I A N
B E A M
P R O P A G A T I O N
E CE I _ M i r r o r _ W a n g
WAVELENGTH
PROPAGATION
DISTA NC E TO
2
3
4
5
=********
BEAM RA DIU S
SUR NEXT SURFACE
OBJ
1
ON SURFACE
X
y
0.0000
5 0 .0 0 0 0
160 .0 0 0 0
1 .9 5 0 0
1 .9 5 0 0
15 .6 5 9 2
9 1.8 00 0
100 .0 0 0 0
5 2 0 .0 0 0 0
7 7 .7 0 9 0
1 1 3 .3 7 9 6
1 39.2 7 2 8
1 8 4.7872
153.0523
6 -5 0 0 .0 0 0 0
7 1151.0 0 0 0
8
3 0 .0 0 0 0
9 1212.0 0 0 0
IMG
PO SIT IO N
69.8 1 3 6
6 8 .9 7 3 6
1 6 .4 4 0 0
1 .9 5 0 0
1 .95 0 0
1 5.6 5 9 2
7 7 .7090
1 1 3 .3 7 9 6
1 3 9 .2 7 2 8
1 6 0 .0 3 0 4
180 .0 4 2 3
93 .39 93
9 2 .2 2 7 6
1 2 .0 3 1 0
NM
DI M EN SI O NS
= M IL L IM E T E R S
BEAM
WAVEFRONT RADIUS
PHASE
ORIE NT A TI ON
OF CURVATURE
O R IE N T A T I O N
(DEGREES)
BEFORE REFRA CTIO N
(DE GREES)
X
Y
0 .0
0 .0
0 .0
INF
INF
-5 0 .7 8 7 6
IN F
IN F
-5 0 .7 8 7 6
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
-2 0 0 .0 1 6 2
-2 9 1 .7 5 9 1
-5 3 7 .8 5 6 8
-4 0 0 2 .8 7 8
-2 4 1 4 .6 5 2
-2 0 0 .0 1 6 2
-2 9 1 .7 5 9 1
-5 3 7 .8 5 6 8
-4 0 0 2 .8 7 8
4 4 9 3 .9 1 6 2
0
0
0
0
0
0
0 .0
0 .0
0 .0
1298.5 1 0 8
2 4 6 4 .1 1 0 6
-7 8 5 3 2 .8 1
1245 .7 7 4 9
2 3 6 1 .6 1 9 5
-1 0 0 4 6 .9 8
0 .0
0 .0
0 .0
.0
.0
.0
.0
.0
.0
1
FIELD PO SIT IO N «
( 0 .0 0 ,
W AI ST RA DI US
BEFORE
REFRACTION
Y
X
WAIST TO SURFA
X
Y
1 .9 5 0 0
1 .9 5 0 0
1 .9 5 0 0
2 .3 3 9 8
2 .3 3 9 8
2 .3 3 9 8
22 . 5 2 2 0
1 6.4 39 9
1 6.4399
1 6 .4 3 9 9
1 6 .4 3 9 9
1 .9500
1 .9 5 0 0
1 .9 5 0 0
2 .3 3 9 8
2 .3 3 9 8
2 .3 3 9 8
2 2 .5 2 2 0
22 .5 2 2 0
1 2 .0 2 9 4
12 . 0 2 9 4
1 2 .0 2 9 4
0 .0 0 )
DISTA NC E FROM
0 .0 0 0 0
0 .0 00 0
5 0.0 00 0
1 9 9 .8 3 4 8
0 .0 0
0 .0 0
2 9 1 .6 3 4 8
5 3 7 .7 0 5 0
3 9 2 3 .5 9 4 1
50 .0 0
1 9 9 .8 3
2 9 1 .63
5 3 7 .7 0
39 2 3 .5 9
2 3 7 7 .5 0 5 5
-1 2 2 6 .5 0 6
- 2 3 2 4 . 122
1 .1 2 4 6
-4 4 2 3 .5
-1225.
-2 3 2 1 .4
2 .5 2
Fig. 6.5 Gaussian Beam calculation o f the central Channel.
ECEI_M irrotr_W ang
Fig. 6.6 Color output o f Gaussian Beam Trace o f the Side V iew .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
142
362.32
E C E I _ M i r r o r Wang
S c a le :
HH
XZ
0.07
Fig. 6.7 Color output o f Gaussian Beam Trace o f the Top V iew .
Fig. 6.8 3-D view o f the com plete system. Only the center channel and two edge
channels are shown.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
143
6.1.4 Ray Trace Calculation
The ray trace calculation in Fig. 6.9 gives the slope o f the chosen sight line.
Column Y is the position o f the sightline on every surface. Figure 6.9 only show s the
results o f the top channel.
RSI S O . .1 0
OBJ
1
2
3TO
4
S
6
7
8
9
IMG
W1 F3 0 0 3
EC E I_M irror_W ang
P o sitio n
1 , W a v e l e n g t h = * * * * * * * * NM
Z
X
Y
0.00000
0 .5 0 8 0 0
20.51000
0 .5 0 8 0 0
20.51000
0.00000
0.49317
19.9 1 1 1 4
-2 .00 3 5 5
0 .0 0 0 0 0
0 .00000
0.0 000 0
0.00000
-0 .2 7 9 4 6
-1 1 .2 8 2 7 4
-0 .9 3 8 7 5
-0 .4 7 9 5 4
-1 9 .3 6 0 9 6
-1 .6 5 4 9 6
-5 7 .8 7 2 7 0
-0 .0 0 0 3 5
-9 4 .6 5 7 1 2
1.65976
-1 .2 5 8 8 8
-1 0 9 .5 2 8 6 0
0 .00000
0.3 6415
0.00000
0.37264
- 1 0 9 .7 3 090
0.00000
1 .03141
-1 2 5 .4 1 8 7 1
OPD =
0 . 0 0 0 W a v es
TANY
-0 .0 1 8 7 3
- 0 . 0 1 2 48
-0 .1 2 2 9 1
-0 .1 2 2 9 1
-0 .0 8 1 5 5
-0 .0 7 3 8 1
0 .08528
-0 .0 1 4 9 4
-0 .0 0 6 7 4
-0 .0 1 2 9 4
-0 .0 1 2 9 4
TANX
-0 .0 0 0 4 6
-0 .0 0 0 3 1
-0 .0 0 3 0 4
-0 .0 0 3 0 4
-0 .0 0 2 0 2
-0 .0 0 1 8 3
0.57865
-0 .5 7 6 6 3
0.00028
0.00054
0.00054
LENGTH
0 .0 0 0 0 0
48.00018
163.22331
92.49118
99.39029
523.18615
499 .72 019
1149 .0 2 9 5 7
30.00068
1212.10170
Fig. 6.9 Ray Trace o f the top channel.
6.1.5 M odulation transfer function (MTF)
ECE I _ M i r t o t _ W a n g
( 0 .0 0 0 ,0 .0 0 0 )
DBG
D E F O C U S IN G 0 . 0 0 0 0 0
S P A T IA L
FR EQU EN CY
(C Y C L E S /H H )
Fig. 6.10 M TF A nalysis o f the design. M TF o f different channels are very near to
the diffraction lim it. They are a little worse perhaps due to the diffraction at the edge of
optical com ponents. The system is sensitive to k<3.2cm "\
k = — = 2 ^ x 1 0 x 0 .0 5 « 3.14cm -1
A
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
144
6.1.6 Point Spread Function
Figure 6.11 show s the center field Point Spread Function. The spot diameter o f
the beam at the resonance surface is 2-3 cm at the E-plane and 3 cm at the H-plane.
POINT SPREAD FUNCTION
ECEI M i r r o r _ W a n g
Field - ( 0.000/ 0.000) Degrees
Defocusing = 0.000000 mm
Fig.6.11 Point Spread Function o f the Center Channel.
6.2 NSTX MIR Optical System Design
M icrowave Imaging Reflectom etry for N ST X has been proposed by UC D avis. M y
work consisted of the preliminary 1-D and 2-D MIR optical system designs.
6.2.1 Optical System Considerations
Plotted in Fig. (6.12) are the plasma frequency (f0), which is the cutoff frequency
for O -m ode propagation, as well as the right hand cutoff frequency (A) and left hand
cutoff frequency (A) for X -m ode propagation. The definition o f these quantities can be
found in [2]. They are calculated by assuming a parabolic density profile with the central
densities indicated in the figure. For the conditions shown in Fig. 6.12, the fundamental
and the second harmonic electron cyclotron radiation from 0.5 m <R < 1.4 m cannot
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
145
propagate out o f the plasm a to the low field side due to the cu toff at the plasma
frequency. Thus, ECE im aging is not feasible for the N S T X device.
NSTX freq u en cies
120
100
80
40
ce
0.2
0/4
0.6
1.0
1.2
1.4
R [m ]
Fig. 6.12 Electron cyclotron radiation frequencies o f the two low est harmonics in
N ST X with a central magnetic field o f 0.4 T. Plotted together are the plasm a frequency
(f0), right hand cutoff frequency (/«) and left hand cutoff frequency (/l) for a parabolic
density profile with the central densities shown in the figure.
6.2.2 O ne-D im ensional MIR Optical System D esign
The size o f the window assigned to the 1-D MIR system is 42cm x 15 cm. The
distance between the window and the center o f the plasma is R = 1800 mm. The design
frequency is 45 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
146
O
45GHz
45G H z
cubic fi
cubic
1.44
1 .4 2
4a
1.34
1 .3 2
3 .5
4 .5
5 .5
X 10
X 1 0 19
(a) Radius o f curvature vs. central density
19
(b) Front location vs. central density
Fig. 6.13 Left picture (a) show s the relationship between the curvature radius of
the cutoff surface (at 45 G Hz) and the central density o f the plasma. The right picture (b)
shows the relationship between the location of the cutoff surface (at 45 GHz) and the
central density o f the plasma. (Courtesy o f Lu Yang)
1 4 0 mi l s
1
1 j
------------- r
------------- L
'
=' .
y
1
1 j i
1
1
1
1
1
j '
P 1 0 0 mi l s
Fig. 6.14 1-D Antenna Array for the N ST X MIR system. The spacings o f the
antenna array are 140 m ils (E plane) and 100 m ils (H-plane), respectively. The half angle
o f the antenna is 15.5 degrees out o f the substrate lens.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
147
S urface
N am e
S u rface #
S u rfa c e
Type
Y R ad iu s
X R ad iu s
S p h e re
Infinity
Infinity
0 .0 0 0 0
S p h e re
Infinity
Infinity
9 0 .0 0 0 0
2
S p h e re
-9 0.0 0 0 0
-90.0000
3 0 .0 0 0 0
S to p
C ylinder
Infinity
Infinity
7 0 .0 0 0 0
S p h e re
Infinity
Infinity
80 0000
-1 80.0 0 0 0
-180.0000
Infinity
O b jec t
1
4
S u b s tra te Lens
F o c u s L ens
5
C onic
T h ic k n e s s
G la s s
R efract
M ode
R efract
Y
X
S em i-A p e rtu r S em i-A p ertu r
.................
m
m
90.0000 0
9 0 .0 0 0 0 °
R efract
9 0 .0 0 0 0 0
9 0 .0 0 0 0 °
R efract
45 0000 ®
4 5 .0 0 0 0 0
R efract
1 0 0 .0 0 0 0 0
8 0 .0 0 0 0 ®
4 0 0 .0 0 0 0
R efract
1 0 0 .0 0 0 0 ®
8 0 .0 0 0 0 ®
Infinity
4 0 0 .0 0 0 0
R efract
2 0 0 ,0 0 0 0 0
1 8 0 .0 0 0 0 ®1
'HD'
'HD 1
R efract
6
B e a m S p litter
S p h e re
7
Mirror H
C ylinder
Infinity
-2 3 0 0 .0 0 0 0
-4 0 0 .0 0 0 0
R eflect
3 2 0 .0 0 0 0 ®
2 5 0 .0 0 0 0 ®
8
Mirror E
C ylinder
11 00.0 0 0 0
Infinity
8 4 0 .0 0 0 0
R eflect
4 0 0 .0 0 0 0 ®
2 2 0 .0 0 0 0 ® t
9
W indow
S p h e re
Infinity
Infinity
1 0 .0 0 0 0
R efract
2 1 0 .0 0 0 0 0
1 5 0 .0 0 0 0 ®
10
S p h e re
Infinity
Infinity
4 0 0 .0 0 0 0
R efract
2 1 0 .0 0 0 0 ®
1 5 0 .0 0 0 0 D
Im age
Y Toroid
52 0.00 0 0
1 4 0 0 .0 0 0 0
0 .0 0 0 0
R efract
2 0 0 .0 0 0 0 ®
1 5 0 .0 0 0 0 ®
96000
Fig. 6.15 Screen shot o f Lens Data Manager W indow o f the N S T X 1-D MIR
system.
Table 6.1 Field points in CODEV which is defined in Lens> System data>
Fields/Vignetting. A 17-Channel array can be used in this system.
Ch 1
Ch 5
Ch 9
Ch 13
Ch 17
Position
X(mm)
1.27
1.27
0
-1.27
-1.27
Position
Y(mm)
28.45
14.22
0
-14.22
-28.45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
148
NSTX
Fig. 6.16 Side V iew o f MIR optical design for N STX .
G A U S S I A N
B E A M
P R O P A G A T I O N
NSTX
PO SIT IO N
o
o
0 .0
0.0
0.0
o o
o o
0 .0
o
o
o
o
IN F
INF
-9 3 .0 1 1 1
-1 2 2 .8 6 8 6
-1 9 0 .9 1 8 6
-3 6 9 .1 0 5 1
-1 1 8 2 .7 0 6
-1 5 6 8 .0 2 4
195 9.43 85
4 6 7 .8241
8 8 8 .5588
3 7 8 .6 0 5 0
o
o
0 .0
0 .0
0 .0
0 .0
INF
INF
-9 3 .0 1 1 1
-1 2 2 .8 6 8 6
-1 9 0 .9 1 8 6
-3 6 9 .1 0 5 1
-1 1 8 2 .7 0 6
-1 5 6 8 .0 2 4
-1 3 0 5 .8 1 1
609.68 95
1 165.6223
-1 1 2 2 3 .4 9
o
o
0 .0
o
o
4.7 7 0 0
4.7 7 0 0
2 6.5107
3 4.9936
5 5.0904
70.306 2
105 .552 6
1 41.4 755
1 77.6 650
62 .751 7
62.0530
1 5 .9553
o o o o
o o o o
4.7700
4.7700
2 6 .5 1 0 7
3 4.9936
5 5.0904
70.3 062
149 .2740
2 00.0 766
15 2.9289
41.8848
4 1.5277
24.7065
BEAM
WAVEFRONT RADIUS
PHASE
OR IENT AT ION
OF CURVATURE
OR IE NTATION
(DEGREES)
BEFORE REFRACTION
(DEGREES)
X
Y
o
o
OBJ
0.0000
1
90 .0 0 0 0
2
30 .0 0 0 0
3
70 .0 0 0 0
4
80 .0 0 0 0
5
400.0000
6
400.0000
7 -4 0 0 .0 0 0 0
8
8 4 0.0000
9
10.0000
10
400.0000
IMG
BEAM RADIUS
ON SURFACE
X
Y
DIMENSIONS * MILLIMETERS
o
o
PROPAGATION
DISTANCE TO
SUR NEXT SURFACE
= * * * * * * * * NM
o
o
WAVELENGTH
1
FIELD PO SIT IO N *
( 0 .0 0 ,
WAIST RADIUS
BEFORE
REFRACTION
X
Y
DISTANCE FROM
WAIST TO SURFACE
Y
X
4 .7 7 0 0
4 .7 7 0 0
4 .7 7 0 0
7 .2 17 8
7 .2 1 7 8
7 .2 1 7 8
22.9753
22.9753
24.6982
24.6982
24.6982
24.6982
4 .7 7 0 0
4 .7 7 0 0
4 .7 7 0 0
7 .2 1 7 8
7 .2 1 7 8
7 .2 1 7 8
22 . 9 7 5 3
22 . 9 7 5 3
2 2.9753
1 5.1960
I S . 1960
15.1960
0.0 0 0 0
0.0 0 0 0
9 0.0000
11 7 .6 4 1 3
18 7 .6 4 1 3
3 6 5 .2148
1126 .670 4
1526 .670 4
123 7.69 31
-3 9 7 .6 9 3 1
-7 5 3 .3 2 1 0
7.5 1 6 9
0.00)
0 .0 0 0 0
0 .0 0 0 0
9 0.0000
117.6413
187 .6413
3 6 5.2148
112 6.6 704
1 5 2 6 .6704
-1 9 2 6 .6 7
-4 4 0 .3 9 0 0
-8 3 5 .2 7 2 2
-3 5 .1 8 0 0
Fig.6.17 Gaussian Beam calculation o f the central channel. Beam W aist o f the Eplane is 15.2 mm. Beam W aist o f the H-plane is 24.7 mm. At the w indow , the radius o f
the beam is 42 mm (H-plane) and 63m m (E-plane).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
149
N STX
S c a le :
0 .0 9
2 6 -Ju n -0 5
Fig. 6.18 Color output o f the Gaussian Beam Trace o f Side V iew .
Fig. 6.19 3-D view ing o f the com plete N ST X 1-D MIR system. Only the center
channel and the two edge channels are shown.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
150
POINT SPREAD FUNCTION
F i e M * < 1 . 0 0 0 , (1 .0 3 0 ) D e y r« « n
D w f o c u s in g « 0 .3 0 0 0 3 3 mm
Fig.6.20 shows the Point Spread Function of the center channel. The spot
diameter of the beam at the resonance surface is 2-3 cm at the E-plane and 4.4 cm at the
H-plane.
6.2.3 Tw o-D im ensional MIR Optical System Design
The size of the W indow assigned to the 2-D M IR system is 42 cm x 30 cm. The
distance between the W indow and the center of the NSTX plasm a is R = 1800 mm. The
design frequency is 50 GHz.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
151
280 mils
“ 200mils
Fig. 6.21 2-D A ntenna Array for the NSTX M IR System. T he spacings o f the
antenna array are 280 mils (E plane) and 200 mils (H-plane), respectively. The half angle
of the antenna is 15.5 degrees out of the substrate lens.
S u rface
N am e
S u rfa c e #
O b jec t
I
S u rfa c e
I
T ype
|
Y R ad iu s
X R a d iu s
|
T h ic k n e s s
S p h e re
Infinity
Infinity
0 .0 0 0 0
S p h e re
Infinity
Infinity
9 0 .0 0 0 0
2
S p h e re
-9 0.0 0 0 0
-9 0 .0 0 0 0
S to p
Cylinder
Infinity
Infinity
S p h e re
Infinity
Infinity
8 0 .0 0 0 0
-150.0000
-1 5 0 .0 0 0 0
5 5 0 .0 0 0 0
1
4
S u b s tr a te L ens
F o c u s L ens
5
C o n ic
| G la s s
I R etract I
Y
I
X
I
I M ode |S em i-A p e rtu r|S em i-A p ertu r|
m
[3
R efract
R efract
9 0 .0 0 0 0 0
9 0 .0 0 0 0 °
3 0 .0 0 0 0
R efract
9 0 .0 0 0 0 °
9 0 .0 0 0 0 °
7 0 .0 0 0 0
R efract
4 5 .0 0 0 0 °
4 5 .0 0 0 0 0
R efract
1 0 0 .0 0 0 0 °
8 0 .0 0 0 0 0
R efracl
1 0 0 .0 0 0 0 °
8 0 .0 0 0 0 °
'HD'
'HD'
6
B e a m S plitter
S p h e re
Infinity
Infinity
4 0 0 .0 0 0 0
R efract
2 0 0 .0 0 0 0 ®
1 8 0 .0 0 0 0 ®
7
M irror H
Cylinder
Infinity
-2 5 0 0 .0 0 0 0
-4 0 0 .0 0 0 0
R eflect
3 2 0 .0 0 0 0 °
2 5 0 .0 0 0 0 °
8
M irror E
C ylinder
| 1000.0000
Infinity
3 0 0 .0 0 0 0
R eflect
4 0 0 .0 0 0 0
9
W in d o w
S p h e re
Infinity
Infinity
1 0 .0 0 0 0
R efract
2 1 0 .0 0 0 0 °
1 5 0 .0 0 0 0 ®
10
S p h e re
Infinity
Infinity
6 3 0 .0 0 0 0
R efract
2 1 0 .0 0 0 0 ®
1 5 0 .0 0 0 0 °
Im age
V Toroid
430.0 0 0 0
1 1 7 0 .0 0 0 0
0 .0 0 0 0
R efract
2 0 0 .0 0 0 0 13
1 5 0 .0 0 0 0 °
96000
m
2 2 0 .0 0 0 0 °
E n d O f D ata
Fig. 6.22 Screen shot of Lens D ata M anager W indow of the N STX 2-D MIR
system.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
152
Table 6.2 Field points in CODEV which is defined in Lens> System data>
Fields/Vignetting. An 8x4 Array is designed.
Ch 1
Ch 2
Ch 3
Ch 4
ChO
Ch 5
Ch 6
Ch 7
Ch 8
Position
X(mm)
7.62
7.62
2.6
2.6
0
-2.6
-2.6
-7.62
-7.62
Position
Y(mm)
26.7
19.6
12.5
5.4
0
-5.4
-12.5
-19.6
-26.7
28 4 .0 9
NSTX
S cale:
0.09
MM
1 5 -A p r-0 5
Fig. 6.23 Side View of the NSTX M IR Optical Design.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
153
G A U S S I A N
BEAM
P R O P A G A T I O N
POSITION
NSTX
WAVELENGTH
PROPAGATION
DISTANCE TO
SUR NEXT SURFACE
********* NH
BEAM RADIUS
ON SURFACE
X
Y
OBJ
0 .0 0 0 0
4 .2 9 0 0
4.2900
1
9 0 .0 0 0 0
4.2900
4.2900
2
3 0 .0 0 0 0 2 6 .7 0 6 7 2 6 .7 0 6 7
3
7 0 .0 0 0 0 3 5 .3 2 4 9 3 5 . 3 2 4 9
4
8 0 .0 0 0 0 5 5 .6 7 8 1 5 5 . 6 7 8 1
5 5 5 0 .0 0 00 7 1 .0 6 5 5 7 1 .0 6 5 5
6 4 0 0 .0 0 0 0 1 3 8 .1 38 7 9 7 . 6 7 8 8
7 - 4 0 0 . 0 0 0 0 1 6 6 .7 1 9 9 1 1 7 .8 8 8 8
8 3 0 0 .0 0 0 0 1 2 0 .5 0 57 1 3 8 .4 6 5 7
9
1 0.00 00
61.3 273
9 5 .3 3 9 1
10 6 30 .0 0 0 0 6 0.92 17 9 4 .5 9 2 4
IMG
2 3 .0 5 7 4
1 3 .4 3 1 8
DIMENSIONS - MILLIMETERS
BEAM
WAVEFRONT RADIUS
PHASE
ORIENTATION
OF CURVATURE
ORIENTATION
(DEGREES)
BEFORE REFRACTION (DEGREES)
X
Y
0.0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
INF
INF
-9 2.3838
-1 22.2658
-190.7267
-369.0415
-1 958.444
-2308.693
-1054.028
787.2801
1 5 0 2 .6 9 3 9
1 7 3 3 .2 8 7 9
INF
INF
-92.3838
-122.2658
-190.7267
-369.0415
-1958.444
-2308.693
2 6 7 4 .8 7 8 8
665.2162
12 66.9942
4 9 9 .1 4 3 8
0 .0
0 .0
0.0
0.0
0.0
0.0
0 .0
0 .0
0.0
0 .0
0 .0
0 .0
1
FIELD POSITION -
(
WAIST RADIUS
BEFORE
REFRACTION
Y
X
DISTANCE FROM
WAIST 'TO SURFACE
Y
X
4.2900
4.2900
4.2900
6 .4 9 7 6
6 .4 9 7 6
6.4976
35.6508
3 5 .6 5 0 8
22.7657
2 2 .7 6 5 7
22 .7657
22.7657
4 . 2 900
4 . 2 900
4.2 9 0 0
6.4976
6.4976
6 .4 9 7 6
35.6 5 0 8
35.6 5 0 8
35.6 5 0 8
13 . 1975
1 3 .1 9 7 5
1 3 .1 9 7 5
0 .0 0 , 0.00)
0.0000
0.0000
9 0 .0 0 0 0
118.1292
188.1292
3 6 5 .9 5 6 4
1697.5 5 8 9
2 0 9 7 .5 5 8 9
9 7 8 .7 9 2 1
-678.7921
-1292.854
-43.5820
0.0000
0.0000
90.0000
11 8.12 92
18 8.12 92
3 6 5 .9 5 6 4
1 6 9 7 .5 5 8 9
2 0 9 7 .5 5 8 9
-2 497.559
-652.4693
-1 242.331
-17.2592
Fig.6.24 Gaussian Beam Trace. The radius of the beam w aist is 13.2 mm (Eplane), the radius of the beam waist 22.7 m m (H-plane). At the window , the radius of the
beam is 61 mm (H-plane) and 95mm (E-plane).
NSTX
Fig. 6.25 Color output of Gaussian Beam Trace of the Side View. Only 5
channels are shown here.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
154
Fig. 6.26 3-D viewing of the com plete NSTX M IR system.
6.3 KSTAR Tokamak ECEI Optical System Design
A 2-D ECEI/M IR detection system is proposed for the K STAR Tokam ak. Figure
6.27 shows the K STAR Tokam ak which is located in K orea and is in the final
construction phase. The goal of the Korea Superconducting Tokam ak Advanced
Research (KSTAR) project is to serve as a demonstration and prototype of the ITER
device. Figure 6.28 shows some electron cyclotron radiation frequencies o f the Tokamak.
M y work concentrated on the preliminary optical design for the ECE Imaging system.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
155
Fig. 6.27 The picture shows the K STA R Tokamak. The main radius is 1.8 meter.
The m inor radius is 0.5 meter, (http://ww w .knfp.net/english/)
30 0
250
200
o 150
100
50
-0.5
0 .5
r /a
Fig. 6.28 Electron cyclotron radiation frequencies o f the three lowest harm onics
in KSTAR with a central magnetic field o f 3.5 T. Plotted together are the plasm a
frequency (f0) and left hand cutoff frequency (ft) for a parabolic density profile with the
central density neo = 1 .5 x l0 20 ir f 3.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
156
Fig. 6.29 Conceptual D esign of KSTAR ECEI system. Tw o large plasm a facing
mirrors are placed within the vacuum vessel. They are a poloidally (vertically) curved
cylindrical mirror and a toroidally (horizontally) curved cylindrical mirror. The output
signals pass through a relatively small output window.
Optical sim ulations for 40 channels have been conducted based on our m easured
dual dipole array pattern at 170 GHz (the wavelength is 1764706 nm).
The param eters of the dual dipole array are as follows. The E-plane spacing is 85
mils and the H-plane spacing is 40 mils. The receiving angles o f the half bandwidth of
1/e electric field are 15.5 degrees outside of the substrate lens. [1]
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
157
Mirrors
Array
Lenses
Focal plane
W indow
ECEI plasm a coverage: 50 cm (vertical)
Fig. 6.30 KSTAR ECEI Imaging O ptics configuration.
Surface
N am e
Surface #
I Surface
I
Type
I
|
Y R adius
|
X R adius
|
T h ick n ess
G lass
I
|
Refract
Mode
O bject
S phere
Infinity
Infinity
0.0 0 0 0
Refract
1
S phere
Infinity
Infinity
1580.0000
Refract
I
Y
I
X
I S em i-A perture|S em i- A perture
la
m
:
250.0000 °
60.0000 0
2
Mirror E
Cylinder
-2700.0000
Infinity
-590.0000
R eflect
480.0000 0
60.0000 0
3
Mirror H
Cylinder
Infinity
3200.0000
1500.0000
Reflect
450.0000 0
80.0000 0
4
Cylinder
-2500.0000
Infinity
-800.0000
R eflect
4 50.0000 0
8 0 .0 0 0 0 ®
5
Cylinder
1600.0000
Infinity
895.0000
R eflect
4 5 0 .0 0 0 0 0
80.0000 0
S phere
Infinity
Infinity
30.0000
7
S phere
Infinity
Infinity
100.0000
S top
S phere
Infinity
Infinity
400.0000
9
Cylinder
450.0000
Infinity
160.0000
10
Cylinder
-1000.0000
Infinity
120.0000
11
Cylinder
240.0000
Infinity
120.0000
S
W indow
:
9 60000.600
523000.600
:
Refract
1 6 5 .0000®
75.0000 0
Refract
150.0000 0
80.0000 0
Refract
10 0 .0 0 0 0 ®
60.0000 0
Refract
300.0000 0
50.0000 0
Refract
3 00.0000 0
50.0000 0
523000.600
Refract
300.0000 0
50.0000 0
Refract
300.0000 0
50.0000 0
5 23000.600
R efract
1 0 0 .0 0 0 0 °
1 0 0 .0 0 0 0 °
12
Cylinder
Infinity
-300.0000
2 00.0000 v
13
S phere
240.0000
240.0000
7 0.0000
14
Sphere
Infinity
Infinity
0,0000
Refract
1 0 0 .0 0 0 0 °
1 0 0 .0 0 0 0 °
Image
S phere
Infinity
Infinity
0.0000
Refract
30.0000 0
20.0000 0
End Of Data
Fig. 6.31 Screen shot of Lens D ata M anager W indow for the K STAR ECEI
system.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
158
Fig. 6.32 Side View o f the ECEI Optical Design for KSTAR. The spacing
between the edge channels in the plasm a is 500 mm.
Fig. 6.33 Top View o f ECEI Optical Design for KSTAR.
4 5 4 .5 5
ECEI_ M IR R O R S
Scale:
0.05
JW
HM
2 6 -Jul-05
Fig. 6.34 Color output of Gaussian Beam Trace of the Side View. Only 5
channels are shown here.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
159
6.4 JT-60 Tokamak ECEI Optical System Design
6.4.1 Optical System Design
A 2-D ECEI system for JT-60 has been proposed by UC Davis. M y w ork was
focused on the prelim inary EC E Imaging Optical System Design.
The optimal frequency range for ECEI on JT-60 extends from 176 to 200 GHz.
Optical simulations for a 24 channel system have been conducted at 180 GHz
(wavelength 1666667nm).
The param eters o f the dual dipole array are as follows. The E-plane spacing is 85
mil and the H-plane spacing is 40 mil. The receiving angles of the half bandw idth of the
1/e electric field are 15.5 degrees outside of the substrate lens and 24 degrees inside the
substrate lens.
The JT-60 2-D EC EI optical system uses two large m irrors which are tilted
horizontally. One focus lens and one substrate lens are used to tune the beam. The size of
the window is assumed 45cm by 15 cm. All CODEV param eters of the optical system is
shown in Fig. 6.35. Figure 6.36 shows the side view of the optical design. Figure 6.37 is
the 3-D view of the com plete optics.
S urface #
S urface
N am e
S urface
Type
Y R adius
X R adius
T h ic k n e ss
G la s s
R efract
M ode
O bject
S p h ere
Infinity
Infinity
0 .0 0 0 0
1
S p h ere
Infinity
Infinity
50.0 0 0 0
Refract
8 0 .0 0 0 0 0
8 0 .0 0 0 0 °
2
S p h ere
-100.0000
-100.0000
160.0000
Refract
8 0 .0 0 0 0 °
8 0 .0 0 0 0 °
Stop
S p h ere
Infinity
Infinity
91.8 0 0 0
Refract
8 0 .0 0 0 0
S p h ere
Infinity
Infinity
100.0000
Refract
150 .0 0 0 0 s
115.0000
-200.0000
-200.0000
520.0 0 0 0
Refract
150 .0 0 0 0 B
115.0000 0
4
EF 2
5
Conic
Refract
Y
X
S em i-A p ertu re S em i-A perture
O
o
'HD'
'HD'
a
m
m
8 0 .0 0 0 0 0
m
2 2 0 .0 0 0 0 0
R eflect
3 2 0 .0 0 0 0
R eflect
4 0 0 .0 0 0 0
R efract
2 2 5 .0 0 0 0 0
9 0 .0 0 0 0 0
1530.0000
R efract
2 2 5 .0 0 0 0 0
9 0 .0 0 0 0 0
0.0000
Refract
2 0 0 .0 0 0 0 0
100.0000 0
6
H -plane mirr
Cylinder
Infinity
-4100.0000
7
E -plane mirr
Cylinder
2700.0000
Infinity
-500.0000 v
500.0 0 0 0
a
W indow
S p h ere
Infinity
Infinity
30.0000
9
S p h ere
Infinity
Infinity
Im age
S p h ere
Infinity
Infinity
9 6 0 0 0 0 .6 0 0
E n d O f D ata
Fig. 6.35 Screen shot of Lens D ata M anager W indow.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
2 0 0 .0 0 0 0 0
160
ECEI_Mirror_Wang
Fig. 6.36 Side View o f the ECEI Optical System. The sightlines are slightly
expanding to obtain w ider plasm a coverage.
Fig. 6.37 3-D view o f the complete system. Only the center channel and two edge
channels are shown.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
161
6.4.2 Gaussian Beam Trace
Fig. 6.38 shows the Gaussian calculation o f the optics. The beam waist of the Eplane is 6.7 mm at the plasm a region and the beam waist o f the H -plane is 8.9 mm. The
color outputs of the Gaussian beam sim ulation are shown in Figure 6.39 and 6.40.
G A U S S I A N
B E A M
P R O P A G A T I O N
POSITIO N
E c !^ _ M ir r o E _ tJ a n g
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
INF
INF
-5 0 .2 7 6 4
-1 9 9 .6 4 3 9
-2 9 1 .4 2 4 0
-5 4 3 .8 2 6 5
-5 8 9 9 .3 9 1
-2 0 4 1 .7 8 3
1 5 4 5 .3600
2 9 3 6 .4 1 2 7
-1 517.694
INF
INF
-5 0 .2 7 6 4
-1 9 9 .6 4 3 9
-2 9 1 .4 2 4 0
- 5 4 3 . 8 2 65
-5 8 9 9 .3 9 1
6390 .7 6 6 4
1562.8427
296 9 .7 6 8 2
563.1 8 0 2
0 .0
0 .0
0 .0
o
o
1.1380
1.1380
15.3470
77.0873
112.5352
1 3 7.8905
1 5 1.2065
164.0313
124.2623
123 . 0 1 9 5
6.7392
o
o
OBJ
0 .0 0 0 0
1 .1380
1
50.0000
1 .1380
2
160.0 0 0 0
15.3470
3
91.8000
77.0 8 7 3
4
1 0 0 .0 0 0 0 112.5352
5
5 2 0 .0 0 0 0 13 7 .8905
6 - 5 0 0 .0 0 0 0 1 7 4.5983
7
5 0 0 .0 0 0 0 140.2380
8
30.0 0 0 0
9 1 .7 3 4 6
9 1530.0000
9 0 .8 0 6 8
IMG
8.9387
BEAM
WAVEFRONT RADIUS
PHASE
ORIENTATION
OF CURVATURE
ORIENTATION
(DEGREES)
BEFORE REFRACTION
(DEGREES)
X
Y
o
o
BEAM RADIUS
ON SURFACE
X
Y
DIMENSIONS » MILLIMETERS
nm
0 .0
o o
o o
PROPAGATION
DISTANCE TO
SUR NEXT SURFACE
*********
0 .0
o
o
WAVELENGTH
1
FIELD PO SI TI O N -
( 0 .0 0 ,
WAIST RADIUS
BEFORE
REFRACTION
X
Y
DISTANCE FROM
WAIST TO SURFACE
X
Y
1 .1 3 8 0
1.1380
1 .1 3 8 0
1.3 7 3 7
1.3 7 3 7
1.3 7 3 7
20.5071
8 .8 9 5 0
8 .8 9 5 0
8 .8 9 5 0
8 .8 9 5 0
0 .0 0 )
1 .1 3 8 0
0.0000
0 .0 0 0 0
1 .1 3 8 0
0.0000
0 .0 0 0 0
1 .1 3 8 0
50.0000
50.0000
1 .3 7 3 7
1 9 9 .5 8 0 5
199.5805
1 .3 7 3 7
291.3805
2 9 1 .3 8 0 5
543.7725
1 .3 7 3 7
543.7725
2 0 .5 0 7 1 5 7 9 0 .8 7 9 7 5790 .8 7 9 7
2 0 .5 0 7 1 2 0 3 0 .8 3 0 5
-6 2 9 0 .8 8
6.6627
-1 5 3 0 .8 3
-1 5 5 8 .3 5
6. 6627 - 2 9 0 8 . 2 3 7 - 2 9 6 1 . 0 5 7
6 .6 6 2 7
14.7 9 9 6
-1 2 .7 1 9 6
Fig. 6.38 Gaussian beam trace of the center channel.
ECEl_Mirror_Wang
Fig. 6.39 Color output of Gaussian Beam Trace of the Side View.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
162
320.51
ECEl_Mi r ro r_Wa ng
S cale:
0.08
JW
MM
XZ
23-Aug-05
Fig. 6.40 C olor output of Gaussian Beam Trace of the Top View.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
163
References:
[1] Zhengang Xia, The investigation o f dual dipole antenna im aging array and
developm ent o fS ch o ttky diode fabrication, M aster D issertation, UCD, 2002.
[2]. F.F. Chen, Introduction to Plasma Physics, New York, Plenum Press (1974).
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
164
CHAPTER VII
SUMMARY AND FUTURE DEVELOPMENTS
7.1 Summary
With the help of the recent advancements in m illim eter wave imaging array
technology [1,2], ECE Imaging [3-7] and M IR [5-8] systems were developed and applied
to the study of electron tem perature and density profiles and fluctuations in the TEXTO R
tokamak. These studies have significantly contributed to the advancem ent o f the
understanding of transport phenom ena, especially m icroturbulence and anomalous
transport phenom ena in tokam ak plasmas. O ur colleagues in FOM , TEX TO R , and PPPL
are currently conducting detailed investigation of these phenom ena.
In the new ECEI system installed on TEXTOR, a m ulti-frequency heterodyne
receiver is constructed for each of the im aging channels, so that 2-D maps of Te profiles
and fluctuations can be obtained in a single discharge. This new EC EI diagnostic
represents
a breakthrough
in
2-D
electron
tem perature
profile
and
fluctuation
measurements. One advantage of the new ECEI diagnostic is the capability to provide
two-dimensional local measurements over the plasma m inor cross-sections. W ith this
feature, true 2-D images of Te fluctuations of m = l oscillation (“saw teeth”) near the q ~ l
surface are obtained in TEXTOR, thereby permitting the detailed study of the physics of
magnetic reconnection phenom ena on a fast time scale. [Reference 6]
2-D imaging reflectom etry has been developed to m easure density fluctuations
over an extended plasm a region in the TEXTOR tokamak. This technique is made
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
165
possible by collecting an extended spectrum of reflected waves with large-aperture
imaging optics. D etails of the im aging reflectom etry concept, as well as technical details
of the TEXTO R instrum ent can be found in References 6-8.
7.2 Future Developments
7.2.1 ECEI diagnostic upgrades for TEXTOR
In collaboration with PPPL and FOM , we have planned a new upgrade of the
ECEI system to increase the vertical and horizontal plasm a coverage (now at 16 cm and 6
cm, respectively).
For vertical plasm a coverage, we plan to increase the intra-elem ent antenna
spacing from 70 mils to 100 mils, and then modify the optics system to transform the
ECEI viewing chords from parallel (current configuration) to expanding, such that the
intra-channel spacing increases as the ECEI system im age plane lies deeper into the
plasma. The combination of m odified optics and elem ent spacing is expected to increase
vertical coverage from 16 cm (current system) to 24 cm (upgraded system).
For horizontal plasm a coverage, the current system has a 3.0-7.0 GHz bandwidth,
with 300 M H z wide frequency channels spaced roughly 500 M H z apart; the upgraded
system will have a 2.5-12.0 GHz bandwidth, with 750 M Hz w ide frequency channels
spaced roughly 800 M Hz apart. The w ider bandwidth IF electronics will increase the
horizontal coverage from 6.4 cm (current system) to 10.0 cm (upgraded system).
Increasing the num ber of channels from 128 to 256 is also under consideration.
Upgrading the current electronics system requires new pow er dividers, gain equalizers,
baluns, broader band antennas, and IF amplifiers. For exam ple, a new W ilkinson Pow er
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
166
divider design is discussed in the following. Figure 7.1 shows the new design o f the 2way W ilkinson Pow er divider. Figure 7.2 shows the structure of the W ilkinson pow er
divider in the software Agilent ADS. Figure 7.3 is the layout o f Fig. 7.2. Figure 7.4
shows the sim ulated perform ance of the new design.
T e rm
M Sub
■
VISUB
' M Subl
T e r m 2'
■Num=2
Z=50 O hm
<1
T erm
TermV
Nu m=)
Z=50 O h m
■ H=20.'0 mil ■
' E r= 3 05 ■ ■ '
+ Mur=t
• ■
. C ond=1 .OE+50 .
H u= 3.9e+ 034 mil
T = 1 .34 mil
' T anD = 0 ' '
■ R ough= 0'm it
D A jA O C t jplerl^urititiedZ
D A JW D C t u plerl
Sub'st="M: ub1" '
F = 4 '5 GHz
D eltaF =4 CiHi
Zo=5C Ohr
N=0
R m ax=0.1
D elfa= 0 mil
1
+ f
T p rrri
T e rm 3
N um = 3
Z - 5 0 Ohi
S tP A R A M E T E R S
S _ P a ra m
S P1
S tart= 1 0 G H z
3 to p = 15.0 GHz
Step=0.0.1 G H z .
Fig. 7.1 New W ilkinson Power D ivider Design.
Com pared with Sec. 4.1.1, the new version ADS provides better performance
design of the W ilkinson Pow er divider. The new design is a three-circle structure and the
design shown in Sec. 4.1.1 is a single circle structure. C om paring Fig. 7.4 with Fig. 4.6,
the change o f the S 21 is 0.22 dB in fig. 4.6 and 0.1 dB in Fig. 7.4, and 0.2 dB band is 3-7
GHz in Fig. 4.6 and 1.4-7.5 GHz in Fig. 7.4. Consequently, the new design has wider
bandwidth and sm aller insertion loss.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
167
Need Help? N iiv c * te I * wpropdafe » c * lg n O U d c '< ittrim « '
Fig. 7.2 Structure o f the Pow er D ivider Design in A gilent ADS.
Fig. 7.3 ADS layout of the W ilkinson D ivider whose center frequency is 4.5 GHz.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
168
-3 0 —
.m2
mf
r
- 3 . 1-
ml
freq= 1.660GHz
dB(S(2,1 ))=-3.10Q
- 3 .2 -
m2
freq=7.260GHz
dB(S(2,1))=-3-1Q1
c o .cnT
S S
mm
_33“
u ~c
- 3 .4 -
-3 5 —
-3
6
-
“i
i
i
1
r~
2
3
4
5
6
7
8
freq, GHz
Fig. 7.4 Sim ulation result of one W ilkinson D ivider. S 21 and S 31 are shown.
7.2.2 MIR upgrades for TEXTOR
In its present 1-D form, a single m illim eter-wave frequency is launched and
reflected from the target plasm a. By com bining the output o f several sources into a single
waveguide, and then launching the com bined output into the plasm a, radiation may be
simultaneously reflected and im aged from multiple cutoff layers. The low IF frequency
(-3 0 0 M Hz) array will be replaced with a broad IF bandw idth array and preamplifiers
similar to the present 2-D ECEI array. The single illum ination source will be replaced by
multiple sources, and the M IR electronics m odified to separate out and detect the
multiple downconverted M IR signals from each array element.
To
com pensate
for the increased
losses
caused
by
com bining
multiple
illumination sources, a quasi-optical diplexer will be developed to efficiently separate the
MIR and ECEI signals. This would replace the -5 0 %
reflection quasi-optical
beam splitter now installed, potentially increasing the M IR detected signal levels by as
much as
6
dB (3 dB on the illumination beam , 3 dB on the reflected beam).
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
169
A fixed frequency illumination source at 88 G Hz will be augm ented by a second
source mechanically-tunable from 81 to 89 GHz. A third source will be used (the first
two sources are already em ployed in the present 1-D system) with a fixed frequency of
90.0 GHz, to provide LO pow er to the M IR im aging array. This source com bination
results in a fixed IF frequency of 2.0 GHz from the dow nconversion o f the fixed
frequency R F source, and a variable IF frequency o f 2-8 G Hz from the mechanicallytunable RF source (tuning from 82.0 to 88.0 GHz). W ith the addition of this second RF
source, we will be able to sim ultaneously probe tw o distinct cutoff surfaces. The
separation betw een the two surfaces is controlled through the tunability of the second
source, and allow for detailed explorations of the radial correlation between poloidally
identical channels on the corresponding surfaces.
Four fixed frequency illumination sources will be employed. These sources will
be spaced 0.5 to 1.0 GHz apart, with the spacing to be determ ined at a later date from
TRA N SP (TRA N SP is a large com prehensive tim e-dependent tokam ak transport data
analysis code developed at PPPL. Reference 9-11) sim ulations of the TEXTO R plasm a
and by the radial correlation experiments. In order to m axim ize the illumination power,
relatively high pow er Gunn or IM P ATT oscillators will be pow er com bined in a custom
W R-10 m ultiplexer. The four frequency configuration will provide considerably greater
plasm a coverage and yield significantly m ore physics inform ation than the two frequency
configuration, such as the study of 2-D velocity flow speed structures across rational q
surfaces. The m ixer module is shown in Fig. 7.5 with four distinct frequencies. The result
of using a 16 channel imaging receiver array is a 16x4 m apping o f density fluctuations
over an extended volume of the TEXTOR plasma.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
170
L04
70 MHz
11 ,Q1
M ic r o w a v e
Amp
I2. Q2
I3 . Q 3
I4. Q4
Fig. 7.5 M ixer M odule. Four distinct frequencies are used. 16 m odules are needed
in the 2-D M IR system.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
171
References
[1] Zhengang Xia, The investigation o f dual dipole antenna im aging array and
developm ent o fS ch o ttky diode fabrication, M aster D issertation, UCD, 2002.
[2], Z. Xia, N. Akil, C.W. Domier, N.C. Luhm ann Jr, H. Park, Wide bandwidth p rinted
circuit imaging antenna arrays. Conference D igest o f the 2004 Joint 29th International
Conference on Infrared and M illim eter W aves and 12th International Conference on
Terahertz Electronics (IEEE Cat. No.04EX857). IEEE, pp.561-2, (2004)
[3]. T. M unsat, E. M azzucato, H. Park, C.W . Domier, M . Johnson, N.C. Luhm ann, Jr., J.
W ang, Z. Xia, I.G.J. Classen, A.J.H. Donne, and M .J. van de Pol, 2-D Imaging o f
Electron Temperature in Tokamak Plasmas. IEEE Transact, on Plasm a Sci. 33, 466
(2005).
[4] J. W ang et al., "Two-dimensional Electron Cyclotron Em ission Im aging Diagnostic
for TEXTOR," Rev. Sci. Instrum. 75, 3875 (2004).
[5] A.J.H. D onne, M.J. van de Pol, B.H. Deng, C.W. D om ier, N.C. Luhm ann Jr, E.
M azzucato, T. M unsat, H. Park, Com bined EC E/reflectom etry im aging at TEXTOR.
German-Polish Conference on Plasma Diagnostics for Fusion and A pplications Abstracts. M ax-Planck-Institut fur Plasmaphysik. pp.21.2002.
[6]. H. Park, E. M azzucato, T. Munsat, C.W . Domier, M. Johnson, N.C. Luhm ann, Jr., J.
W ang, Z. Xia, I.G.J. Classen, A.J.H. Donne, and M .J. van de Pol, Sim ultaneous
M icrowave Imaging System fo r Density and Temperature Fluctuation M easurements,
Rev. Sci. Instrum. 75, 3787 (2004).
[7], C.W. D om ier, B.H. Deng, J. Wang, X.P. Liang, H.J. Lu, Z.G. Xia, Y.P. Liang, C.C.
Chang, N.C. Luhmann Jr, T. M unsat, E. M azzucato, H.K. Park, M .J. van de Pol, A.J.H.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Ill
Donne, ECE and reflectom etric imaging on tokamak plasm as. IEEE Conference R ecord Abstracts. 2002 IEEE International Conference on Plasm a Science, IEEE. pp.285, (2002).
[8]. T. M unsat, E. M azzucato, H. Park, B.H. Deng, C.W . D om ier, N.C. Luhmann, J.
W ang, Z.G. Xia, A.J.H. Donne, M.J. van de Pol, M icrow ave im aging reflectom eter fo r
TEXTOR (invited). Review of Scientific Instruments, vol.74, no.3, pp. 1426-32, (2003).
[9]. J. Ongena, M. Evrard, D. M cCune, Num erical Transport Codes, in the Proceedings
of the Third Carolus M agnus Sum m er School on Plasm a Physics, (Spa, Belgium, Sept
1997), as published in Transactions of Fusion Technology, M arch, Vol. 33, No. 2T, pp.
181-191,(1998).
[10]. R. V. Budny, D. R. Ernst, T. S. Hahm, et al., L ocal transport in Joint European
Tokmak edge-localized, high confinem ent mode plasm as with H, D, D T,and T isotopes,
Physics of Plas 7, 5038, (2000).
[11]. A. Pankin, D. M cCune, R. Andre et al., The Tokam ak M onte Carlo Fast Ion M odule
N U BEAM in the N ational Transport Code Collaboration Library, Com puter Physics
Com m unications Vol. 159, No. 3, 157-184, (2004).
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
173
Appendix IID L ROUTINES
Program One
; NAME:
; sawjmovie
; PURPOSE:
; Plots ECEI 2-D picture by channel and frequency at given time range
; SYNTAX:
; saw_movie, shotnumber, timelimits
; REQUIRED PARAMETER:
; shotnumber, timelimits
; OPTIONAL PARAMETER
; RESTRICTIONS:
; Currently the routine accesses ECEI data that is stored locally in a CDF file.
; DEPENDENCIES:
; ncdfread_ecei.pro
; MODIFICATION HISTORY:
; Written by:
JIAN WANG, modified from routines by Tobin Munsat.
; Last Revision: JULY, 2004
PRO saw movie, sn, t=timelimits
; read data from ncdf file.
ncdfread_ecei, sn, data, timebase
tlo=timelimits(0)
thi=timelimits(l)
tlimits = [-0.01,6]
idx = where(timebase ge tlimits(O) and timebase le tlim its(l))
timebase = timebase(idx)
npts=n_elements(idx)
; FILTER is used.
f_low=0
f high=0.05
; High pass filter, frequency.
order=100
Coeff = DIGITAL_FILTER(f_low, f high, 50, order) ;To get coefficients.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
FORj=0,14 DO BEGIN
FOR k=0,7 DO BEGIN
plotdata=data(j,k,idx)
idata = CONVOL(reform(plotdata),Coeff)
data(j ,k,0:npts-1)=idata(0:npts-1)
ENDFOR
ENDFOR
startidx = min(where(timebase GE tlo))
endidx = max(where(timebase LE thi))
DimX = 350
DimY = 600
loadct,5
DEVICE, DECOMPOSED = 0
window, 0,xsize=DimX,ysize=DimY
;MPG stuff begins
mpegdir = 'D:/ECEI_idl/ecei_mpg/'
movietitle = string) sn)+'_'+string(tlo)+'_'+string(thi)
fb = mpegdir+movietitle+'.mpg'
b r= 104000000.0
mpegID = MPEG_Open([DimX, DimY], Filename=fh,bitrate=br,iframe_gap=15)
image24 = BytArr(3, DimX, DimY)
TVLCT, r, g, b ,/get
;MPG stuff ends (temporarily...)
n_timepoints = endidx-startidx+1
increm en ts
;Calibrate the data
time_ca=[3.0,4.0]
; Time for calibration
id_ca= where(timebase ge time ca(0) and timebase le time_ca(l))
n_ca=n_elements(id_ca)
y=[-7.5,-6.5,-5.5,-4.5,-3.5,-2.5,-1.5,-0.5,0.5,1.5,2.5,3.5,4.5,5.5,6.5]
x=[192.6,191.8,191,190.2,189.4,188.6,187.8,187]
;=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
;=[1,2,3,4,5,6,7,8]
levels_def=fltarr(500)
for p=0,499 DO BEGIN
levels_def(p)=0.8+p *0.001
ENDFOR
dataplot=fltarr(l 5,8)
FOR jj=startidx,endidx,increment DO BEGIN
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
175
FORj=0,14 DO BEGIN
FOR k=0,7 DO BEGIN
average_ca= double(total(data(j ,k,i d_ca))/double(n_ca))
dataplot(j ,k)=data(j ,k,jj)/average_ca
ENDFOR
ENDFOR
average_cal=double(total(data(8,2,id_ca))/double(n ca))
dataplot(l ,4)=0.25*(dataplot(0,4)+dataplot(2,4)+dataplot(l ,3)+dataplot(l ,5))
dataplot(5,7)=0.2*(dataplot(6,6)+dataplot(5,6)+dataplot(4,6)+dataplot(4,7)+dataplot(6,7))
; dataplot(5,3)=0.25*(dataplot(5,2)+dataplot(5,4)+dataplot(4,3)+dataplot(6,3))
; dataplot(8,4)=0.25*(dataplot(9,4)+dataplot(7,4)+dataplot(8,3)+dataplot(8,5))
dataplot(7,0)=0.2*(dataplot(8,0)+dataplot(8,l)+dataplot(7,l)+dataplot(6,0)+dataplot(6,l))
; dataplot(9,1)=0.2*(dataplot(9,2)+dataplot(9,0)+dataplot(l 0,2)+dataplot(l 0,1 )+dataplot(l 0,0))
dataplot(3,0)=0.2*(dataplot(2,0)+dataplot(2,1)+dataplot(3,1)+dataplot(4,1)+dataplot(4,0))
; dataplot(12,4)=0.25*(dataplot(l l,4)+dataplot(13,4)+dataplot(12,3)+dataplot(12,5))
dataplot(9,7)=0.2*(dataplot(9,6)+dataplot(10,6)+dataplot(8,6)+dataplot(8,7)+dataplot(10,7))
; dataplot(ll,6)=0.25*(dataplot(10,6)+dataplot(12,6)+dataplot(ll,7)+dataplot(l 1,5))
dataplot(7,3)=0.25*(dataplot(7,2)+dataplot(7,4)+dataplot(8,3)+dataplot(6,3))
!p.multi=[0,l,2]
posl =[0.19,0.82,0.95,0.95]
pos2 = [0.19,0.08,0.95,0.65]
west=0.2
east=0.95
south=0.7
north=south+0.015
width = east-west
title-S h o t '+strcompress(string(sn)+'_Filter Frequency='$
+string(400*f_high)+'kHz_'+'t='+string(tlo)+'-'+string(thi)+'s',/remove_all)
title 1 -S h o t '+strcompress(string(sn)+', Channel 9, Frequency 3')
; device,/PORTRAIT,/inches,xoffset=0.0,xsize=8,yoffset=1.0,ysize=10,filenarae=titlel
; device,/color
plot, timebase,data(8,2,*)/average_cal,xstyle=l,ystyle=l,xtitle='t
(s)',ytitle='A.U.',xrange=timelimits,$
title=titlel,charthick=2,charsize=1.0,position=posl
oplot,timebase(jj)*[l,l],1.0*[0.0,2.0],thick=2,color=100
contour,transpose(dataplot),x,y,xstyle= 1,ystyle= 1,xtitle-R(cm)',ytitle='Z
[cm]',/fill,levels=levels_def,$
title=title,charthick=2,charsize=1.0,position=pos2,/noerase
;draw color-bar legend
res = 256
nlab = 2
labels = ['Lo','Hi']
FOR i=0,res-l DO BEGIN
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
xs = west+float(i*width/res)+[0,0,width,width]/res
ys = [south,north,north,south]
polyfill, xs,ys, /normal, color=256*i/res
ENDFOR
xs = west+[0,0,width,width,0]
ys = [south,north,north,south,south]
plots,xs,ys,/normal
FOR i=0,nlab-l DO BEGIN
xyouts,west + width*float(i)/(nlab-l), north+.Ol ,labels(i),$
/normal,charsize=l .0,alignment=0.5,charthick=2
ENDFOR
;MPEG stuff begins
WSET, 0
screenDump = TVRd(/order,/true)
Device, Get_Visual_Depth=thisDepth
IF thisDepth GT 8 THEN BEGIN
Image24=screendump
ENDIF ELSE BEGIN
image24[0,*,*] = r(screendump)
image24[l,*,*] = g(screendump)
image24[2,*,*] = b(screendump)
ENDELSE
M P E G P ut, mpegID, Image=image24, Frame=jj-startidx,/color
;MPEG stuff ends (until after loop)
ENDFOR
MPEG Save, mpegID
MPEG Close, mpegID
print,'wrote file '+fti
END
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Документ
Категория
Без категории
Просмотров
0
Размер файла
4 714 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа