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Microwave Transmissivity of Sub-Wavelength Metallic Structures

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Microwave Diagnostics for
Magnetic Fusion Devices
By
LIUBING YU
B.S. (University of Science and Technology of China) 2008
DISSERTATION
Submitted in partial satisfaction of the requirements for the degree of
DOCTOR OF PHILOSOPHY
in
Applied Science
in the
OFFICE OF GRADUATE STUDIES
of the
UNIVERSITY OF CALIFORNIA DAVIS
Approved:
_______________________________
David Q. Hwang
_______________________________
Jonathan P. Heritage
_______________________________
Neville C. Luhmann, Jr. (Committee Chair)
Committee in Charge
2014
UMI Number: 3627320
All rights reserved
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UMI 3627320
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To my parents, sisters and those whom I love and who
love me
Acknowledgements
First of all, Professor Neville C. Luhmann, Jr., who is such a hard-working,
nice, tolerant people, is definitely my lifesaver. I have been wondering that why he
could tolerant such an arrogant, lazy, and immature me in 2008 and gave me this
excellent opportunity to work under his direction. It is not just the methods of the
microwave diagnostics, but also the methods of the past pain diagnostics and gain
achievement from the suffering; it is not just the knowledge of the plasma physics
that he taught me, but also the knowledge to the physical world that I am facing
currently; it is not just the Far-Inferred light that he teaches us to handle, but he
also shows me the light that brightens our future way. I want to express my true
appreciations to him, without his help, I could not imagine what kind of life I live
now. I also want to thank all the kind help and valuable comments from my
doctoral committee, Professor Jonathan P. Heritage, and Professor David Q.
Hwang.
Special thanks go to Dr. Calvin Domier for his hardworking and patience to
tutor me. I still remember those days that he helped me to test the EAST ECEI
optics day and night, and those times that he explained the RF and IF boards to me
hours and hours. Furthermore, I also want to thank Lynette Lombardo, our
program manager; without her help, I could not travel to Princeton nor San Diego
for the long-term physics studies. Additionally, I would also like to thank Dr.
Benjamin Tobias, who helped me survive in DIII-D and taught me step by step
how to turn on ECEI system and research mode. Likewise, I want to thank several
Professor Roberts Kaita, Craig Petty, for hosting me at PPPL and DIII-D. I also
want to thank Professor Max Austin and Professor EJ Strait for sharing their
equipment and valuable discussions.
I want to thank Mike Johnson and Mike Banducci for all the excellent
engineering works that supporting the diagnostics. And thanks go to the former
apprentices, Dr. Xiangyu Kong, Dr. Tianran Liang, Dr. Huan Liao, Dr. Christopher
Muscatello and Dr. Wen-Ching Tsai for their guidance. I want to thank lots of
friends and colleagues who make my life more colorful, like Jiali Lai, Shao Che,
Danqing Fu, Qi Jiang, Xiaoxin Ren, Xing Hu, Chen Luo, Bingxi Gao, Bing Cao,
Kaifu Gan, Hong Gao, Feng Wang, Zhenqian Li, Jie Zhang, Lang Cui.
In the end, I want to thank for my parents who are supporting me all the
times, they are so selfless that they have never asked anything back for rising me
up. Also, I feel so lucky to have one older sister and one younger sister who are
growing with me together.
Abstract
To tackle the energy shortage problems that we are facing, many scientists are trying to
achieve controlled fusion to provide clean and sustainable energy. Many large Tokamaks, which
is the most promising device concept, have been built worldwide and three of them (DIII-D,
NSTX, C-Mod) are currently in operation in the U.S. To understand the details of magnetic
fusion plasma physics, a variety of microwave diagnostics are applied to measure the plasma
properties from the millions of degrees plasma in a nonperturbative fashion. Our research group,
the Plasma Diagnostics Group, under the Davis MM-Wave Research Center (DMRC), focuses
on developing advanced microwave diagnostic tools. The Electron Cyclotron Emission Imaging
(ECEI) diagnostic, a passive radiometric microwave diagnostic, is an extremely useful imaging
tool invented in this group to study electron temperature and its fluctuations. The Microwave
Imaging Reflectometry (MIR) technique is also another imaging tool pioneered in this group,
and its purpose is to study electron density fluctuations using an imaging radar approach. Finally,
the Far Infrared Tangential Interferometry/ Polarimetry (FIReTIP) system is a density and
magnetic field diagnostic tool. This dissertation introduces the principles, structure, recent
technology advances, and some physical studies concerning these three systems.
The combined ECEI and MIR systems on the DIII-D (located at General Atomics in San
Diego) provide simultaneous electron temperature and density fluctuation imaging at the same
plasma volume. The ECEI system consists of two major parts: the optical and array system,
which images and downconverts the millimeter wave ECE radiation, and the electronics, which
detects the radiation power in each designed band. This dissertation concerns two recent
upgrades made by our group: one is the use of the zero bias Schottky detectors in the IF
electronics which has greatly decreased the noise level, and the other is the expanded radial
coverage which doubles the radial view in the plasma. For the MIR system, the synthetic
diagnostic modeling has guided the very successful optic and array design; some details
concerning the transmitter, receiver, and electronics are presented. In this dissertation, several
methods for the ECEI/MIR time calibration were conceived, applied, and compared; in addition,
the ECEI and MIR systems are also time calibrated with respect to two other important
diagnostics, the ECE radiometer and magnetic fluctuation diagnostic systems.
Intense bursts of mm-wave emission with durations of 5-10 μs have been observed on
DIII-D by both ECE radiometer and ECEI systems during edge localized modes, Quiet H-mode
(QH) modes, and the precursor before disruptions. Both the ECE radiometer system and the
ECEI system employ heterodyne detection methods and have overlapping intermediate
frequency (IF) bands. A new RF spectrometer, spanning this IF frequency range of
approximately 2-10 GHz, has been installed on the DIII-D tokamak in order to more fully
characterize the frequency, intensity, and localization of these bursts. Herein, the data for the H
mode case and QH-mode case will be discussed and scrutinized in order to constrain the needed
model to explain the bursts. As a trial model, the Cyclotron AutoResonance Maser (CARM) and
Gyro-BWO models are proposed to explain these bursts, which require further theory,
experimental, and simulation support.
The multichannel FIReTIP system provides line-integrated plasma density and magnetic
information from multiple viewing chords on the midplane of the NSTX device. Extremely wide
bandwidth phase comparator electronics for the FIReTIP system were developed and installed on
the NSTX device in 2009. This allows the system video bandwidth, previously limited to ~250
kHz, to extend out to ~500 kHz when operated as a simultaneous interferometer/polarimeter
system and as high as 4 MHz when operated in an interferometry-only configuration. The new
electronics provides simultaneous interferometer phase measurement data using two distinct
phase comparator methods. The first is a digital fringe counter (FC) approach limited to a video
bandwidth of ~500 kHz, while the second is an analog demodulator or in-phase and quadrature
(IQ) approach that achieves the full 4 MHz video bandwidth. New algorithms have been
developed to process the FIReTIP data for both regular (post-shot) and real-time density
calculations, with reliability checks conducted using laser Thompson Scattering data where
available.
Outline
Acknowledgements .......................................................................................................... iii
Abstract.............................................................................................................................. v
Outline............................................................................................................................. viii
Chapter 1 Introduction to Millimeter Wave/ THz Diagnostics .................................... 1
1.1 Motivation and Tokamaks .................................................................................................. 1
1.1.1 The Energy Problems and Nuclear Fusion ..................................................................... 1
1.1.2 Controlled Nuclear Fusion on Earth ............................................................................... 2
1.1.3 Major Tokamaks in US .................................................................................................. 3
1.2 Introduction to Microwave Diagnostics............................................................................. 5
1.2.1 Passive Microwave Diagnostics and ECE ...................................................................... 6
1.2.2 Active Microwave Diagnostics ...................................................................................... 8
1.2.3 Reflectometry, Interferometry and Polarimetry ........................................................... 11
1.3 Microwave Diagnostic Techniques ................................................................................... 13
1.3.1 Microwave Imaging (ECEI/MIR) ................................................................................ 13
1.3.2 Overall Profile Measurement (FIReTIP) ...................................................................... 16
1.4 Dissertation Overview ....................................................................................................... 16
Chapter 2 Combined ECEI and MIR Diagnostic Systems on DIII-D ..................... 23
2.1 ECEI Diagnostic System ................................................................................................... 23
2.1.1 Optical and Array System ............................................................................................ 25
2.1.2 Overview of ECEI Electronics ..................................................................................... 29
2.1.3 Automated ECEI Electronics Testing and Results ....................................................... 32
2.2 Recent ECEI Diagnostic Upgrade .................................................................................... 37
2.3 MIR Diagnostic System ..................................................................................................... 42
2.3.1 Optical and Array System, and Synthetic Diagnostic Modeling .................................. 44
2.3.2 Transmitter, Receiver, and Electronics ........................................................................ 47
2.3.3 Quadrature Method and Data Processing Method........................................................ 50
2.3.4 Video Frequency Response of the MIR Electronic ...................................................... 52
2.4 Simultaneously Imaging of MIR and ECEI, and Time Calibration of Multiple Diagnostic
Systems...................................................................................................................................... 55
2.4.1 Time Calibration for MIR and ECEI in the Laboratory ............................................... 56
2.4.2 Time Calibration for the ECE and Magnetic System in the Laboratory ...................... 59
2.4.3 Time Calibration Using the 3/2 NTM .......................................................................... 60
2.4.4 Time Calibrated Data of the 3/2 NTM Responses ....................................................... 65
2.4.5 Phase Difference Temporal Evolution ......................................................................... 67
Chapter 3 RF Spectrometer Design and Lab Characterization of Millimeter-wave Bursts
........................................................................................................................................... 72
3.1 RF Spectrometer Design ................................................................................................... 72
3.1.1 ECE Diagnostic System Introduction and IF Frequency Response ............................. 72
3.2.2 IF Electronics Modification and Its Frequency Response ............................................ 78
3.1.3 RF Spectrometer and Application ................................................................................ 81
3.2 Millimeter Wave Bursts in H mode ................................................................................. 85
3.2.1 Introduction to Millimeter Wave bursts in H mode ..................................................... 85
3.2.2 RF Interference Elimination ......................................................................................... 87
3.2.3 Intensity Characterization ............................................................................................. 89
3.2.4 Imaging ......................................................................................................................... 91
3.3 Millimeter Wave Bursts on QH-mode ............................................................................. 95
3.3.1 Introduction to Millimeter Wave Bursts in QH-mode ................................................. 95
3.3.3 QH-mode Burst Emission Mechanism ....................................................................... 101
3.3.4 EHO Structures ........................................................................................................... 105
3.3.5 Burst and Burst Stops with n=2 Dominant EHO ....................................................... 110
3.4 Model For Millimeter Wave Bursts ............................................................................... 113
Chapter 4 Data Correction for FIReTIP System ....................................................... 120
4.1 FireTIP System Introduction.......................................................................................... 120
4.1.1 System Overview of FIReTIP .................................................................................... 120
4.1.2 Laser Wavelength Selection ....................................................................................... 122
4.1.3 Implementation of FIReTIP ....................................................................................... 125
4.1.4 FIReTIP IF Electronics .............................................................................................. 127
4.1.5 System Phase Noise .................................................................................................... 128
4.2 Phase Measurement Electronics and Data Correction Methods ................................ 130
4.2.1 Phase Measurement Electronics ................................................................................. 130
4.2.2 Fringe Jump Error ...................................................................................................... 133
4.2.3 Data Process for Fringe Counter Method ................................................................... 136
4.2.4 Data Process for the IQ Method ................................................................................. 140
4.3 Real Time Feedback Control .......................................................................................... 144
4.3.1 Real Time Density Feedback Control Possibilities ................................................... 144
4.3.2 Real time Density Feedback Control Realization ..................................................... 147
4.4 Future Work..................................................................................................................... 149
4.4.1 Signal Power Upgrade ............................................................................................... 149
4.4.2 Electronics Upgrade .................................................................................................. 150
4.4.3 Two Color Interferometry System.............................................................................. 154
4.4.4 New Layout For Polarimetry ...................................................................................... 157
Chapter 5 Conclusions and Future System Upgrade ................................................ 162
5.1 Conclusions ....................................................................................................................... 162
5.2 System Upgrade ............................................................................................................... 165
5.2.1 ECEI System .............................................................................................................. 165
5.2.2 MIR System ................................................................................................................ 170
Chapter 1
Introduction to Millimeter Wave/ THz Diagnostics
1.1 Motivation and Tokamaks
1.1.1 The Energy Problems and Nuclear Fusion
After the industrial revolution, the World energy demand is increasing rapidly each year as
shown in Fig. 1.1[1].
Figure 1.1 World Consumption of Energy (U.S. Physical Units), 1985-2006, (data are taken
from Energy Information Administration, DOE, US)
Currently, there exist three major energy sources: Oil (35%), Coal (25%), and Natural gas
(21%)[1]. However, they are non-renewable. The reserves are limited while the production keeps
increasing; consequently, these energy sources will disappear someday. The reserve-toproduction ratio (RPR) is characterized as the lasting time. These three natural sources will
expire within less than two centuries if we maintain the consumption speed of the 2005 annual
usage[1]. Consequently, people are looking for renewable or high efficiency energy sources.
Fuel
Unit of measure
Reserves
Annual Usage (2005)
RPR (years)
Oil
trillions of barrels
1.2-2
0.03
40-80
998
6370
6
108
164
59
Coal
billions of tons
Natural gas quads
Table1: Estimated RPR of Oil, Coal and Natural gas (data are taken from Energy Information
Administration, DOE, US)
Nuclear energy provides an attractive solution to the energy crisis. Nuclear power is a
sustainable energy source that reduces carbon emissions. Nuclear power produces much less
conventional air pollution, such as greenhouse gases and smog, in contrast to the chief viable
alternative of fossil fuel.
However, controlled nuclear fission has several problems related to the environment and safety.
These include radioactive nuclear waste, the risk of nuclear weapons proliferation, and terrorism.
In addition, there have been serious nuclear accidents since 1952, which have resulted in more
than $10 billion in property damage and caused serious pollution to the environment [2]. In
contrast, controlled nuclear fusion is not a chain reaction, and it avoids many of these problems
and has achieved considerable advancement in its development over the last 5 decades [3].
1.1.2 Controlled Nuclear Fusion on Earth
In order to generate power from fusion or at least to be self-sustainable, the loss of energy
should be recovered by the fusion power [3], which is
.
In the above, is the plasma density, is the cross-section for the reaction, is the speed of the
ions, is the energy released per reaction, and is the energy confinement time.
This leads to the Lawson Criterion [3].
In order to satisfy the criterion, the cross section needs to be sufficiently large; the most
promising fusion reaction is the D-T fusion reaction around 10 keV-100 keV. For the D-T
reactions, the Lawson Criterion becomes:
There are three types of confinements suitable for obtaining fusion: gravitational, inertial,
and magnetic confinement. Only the stars can generate sufficient gravity to provide sufficient
gravitational confinement leaving the other two approaches as potential energy sources. Of these
two, magnetic fusion is more compatible with continuous energy production and is feasible to
operate.
Tokamaks are the most promising magnetic fusion device concept and are slated for a successful
demonstration with the completion of the International Thermonuclear Experimental Reactor
(ITER) [4] that is designed to generate about 500 MW power. It will be followed by the
DEMOnstration Power Plant (DEMO) which is planned to generate 2-4 GW power and which
will be a bridge to the future fusion power plants[5].
1.1.3 Major Tokamaks in US
Three major tokamaks are in commission currently: DIII-D[6], National Spherical Torus
Experiment (NSTX) [7] (followed by NSTX-U) and C-MOD[8].
The DIII-D National Fusion Facility sits at General Atomics, which has been conducting
magnetic fusion research since the 1960s and has been a pioneer in the non-circular cross-section
tokamak approach including Doublet II and Doublet III and today with DIII-D. As the largest
tokamak commissioned in the US, it has a major radius of 1.7 m, minor radius of 0.57 m, is a
large aspect ratio tokamak of 3, and has about 500 researchers from worldwide supporting it. It
has considerable experimental flexibility and extensive diagnostic instrumentation. Existing
capabilities of DIII-D include a highly flexible 2D shaping coil system to produce a wide variety
of plasma shapes, flexible heating and current drive systems, three arrays of 3D-field
perturbation coils located both inside and outside the vacuum vessel, multiple disruption quench
systems, over 50 state-of- the-art diagnostic systems to examine plasma parameters, and an
advanced digital control system for feedback control of the plasma[9]. Extensive diagnostic
instruments cover many aspects of plasma parameters diagnostics including electron temperature
and density, ion temperature and velocity, impurity concentration, radiated power, fueling,
divertor diagnostics, magnetic properties, plasma edge/ wall, fluctuations/wave activities,
particle diagnostics, and plasma current profiles. These has enabled several significant
discoveries including the importance of plasma shape on performance, using non-axisymmetric
coils to suppress ELM, and sustained operation near the ideal wall stability limit.
The National Spherical Torus Experiment (NSTX) is sited at the U.S. Department of Energy’s
Princeton Plasma Physics Laboratory (PPPL), which is managed by Princeton University. PPPL
has been the leading pioneer in plasma studies and fusion research since its establishment on
1961, and whose fusion plasma studies range from the stellerator, tokamak, magnetic
reconnection experiment, and spherical torus. NSTX was commissioned from 1999 to 2011;
currently, it is being upgraded to NSTX-U[10] to provide access to a widened parameter space.
The major upgrade includes a new center-stack capable of doubling the toroidal field, a second
more tangentially oriented NBI to double the plasma heating and external current drive, and
structural enhancements to enable a doubling of the plasma current. NSTX has a major radius
0.86 m, an aspect ratio greater than 1.3, plasma current of 1 MA, and toroidal field of 0.5 T;
NSTX-U has a major radius of 0.94 m, an aspect ratio greater than 1.5, plasma current of 2 MA,
and toroidal field of 1 T. Both of these are low aspect ratio tokamaks, which provides many
fusion advantages and scientific opportunities such as stable access to high plasma beta and more
efficient plasma heating.
Alcator C-Mod is located at the MIT Plasma Science and Fusion Center (PSFC), which leads the
high magnetic tokamak research in the world. Alcator is an acronym for Italian Alto Campo
Toro, which means "high-field torus". Starting from Alcator A in 1968, followed by Alcator B in
1975 and Alcator C in 1978, the Alcator C-Mod means "modification" to Alcator C, which reused some of the power supplies from Alcator C, and which has operated from 1991-2013. As
the world’s highest magnetic field tokamak plasma confinement experiment, C-Mod has a
toroidal magnetic field from 3-8 T, with major radius of 0.68 and minor radius 0.22 m, and
typical 0.4-2.0 MA plasma current.
1.2 Introduction to Microwave Diagnostics
Within the tokamak, generally, the plasma pressure, density, temperature, and current density
profiles are centrally peaked with radial gradients in tokamak plasma equilibrium. This will
provide two basic destabilizing forces sources: current gradients and pressure gradients
combined with adverse magnetic field curvature. A variety of magneto-hydro-dynamic (MHD)
fluctuations and macroscopic turbulence will be driven which challenge the confinement and
stability. The MHD instabilities use the fluid model to deal with the instability with the
wavelengths comparable to the minor radius of a tokamak (~ 0.5 m). The micro-instabilities deal
with wavelengths comparable to the ion Larmor radius (~ 2 mm)(e.g. the ion temperature
gradient mode) or the electron Larmor radius (e.g. the electron temperature gradient mode)
including finite Larmor radius and kinetic dissipation effects. More accurate understanding and
analysis is needed to avoid disadvantages or even facilitate active control if useful for transport.
This relies on physics understanding, including theory development, simulation matching, and
experimental verification. In the case of experimental verification, the microwave/millimeter
wave (MMW) portion of the electromagnetic spectrum is ideally suited for performing a variety
of measurements of magnetic fusion plasma equilibrium parameters and their fluctuations [11].
Usually there are many state-of-the-art continuous wave components (lasers, Gunn-oscillators,
Backward Oscillators), which help measure equilibrium and fluctuation properties with high
temporal resolution. Frequency sweeping technology has received extensive development
attention in order to measure equilibrium profiles faster Also advanced spectral analysis
techniques are finding ever increasing roles including their use for enhanced spatial resolution.
The techniques are broadly divided into passive microwave/millimeter wave diagnostics and
active microwave/millimeter wave diagnostics. Passive technology directly detects the natural
radiations from the objects or reflections from the environment. Active technology requires
some millimeter sources to illuminate the plasma, and then detect the transmitted portion, or
scattered part, or reflected part of the probe wave.
1.2.1 Passive Microwave Diagnostics and ECE
In a plasma, there are two major naturally occurring microwave/millimeter wave radiations, one
is the electron cyclotron radiation [12], and the other is the ion cyclotron radiation [13, 14]. For
the electron cyclotron radiation detection, when the plasma density cutoff frequency goes below
the electron cyclotron harmonic frequency, Electron Cyclotron Emission (ECE) is used, and
Electron Cyclotron Emission Imaging (ECEI) [15, 16] is applied to provide two dimensional
imaging; when the plasma frequency exceeds the cyclotron frequency, electrostatic Bernstein
Wave (EBWs) [17-19] can propagate across the magnetic field and then can be detected. ECE is
applied on many major tokamak around the world, including DIII-D, JET, TEXTOR, EAST, KSTAR, and JT-60[20-22], and is used to measure the plasma temperature and its fluctuations.
The recently developed UCD ECEI technique has also found numerous applications around the
world, including TEXTOR, ASDEX-U, DIII-D, K-STAR, EAST, and HL-2A[15,23-26]. EBW
emission (EBE) is mainly applied on overdense devices such as Wendelstein-7AS stellarator
(W7-AS), Mega Amp Spherical Torus (MAST), and NSTX. For the ion cyclotron radiation
detection, the ion cyclotron emission has been applied on both JET and TFTR [27, 28].
In this dissertation, the ECEI system will be described which employs the ECE
technology. In a magnetized plasma, the gyro motion of electrons results in plasma radiation at
the electron cyclotron frequency ωce = eB / γ me and its harmonics nωce (n is an integer). Here, B is
the magnetic field strength, e is the electron charge, me is the kinetic electron mass, and γ is the
Lorentz relativistic factor. When the plasma density and temperature are sufficiently high, the
plasma becomes optically thick to some harmonics of the electron cyclotron emission (ECE),
usually, the first harmonic ordinary mode and the second harmonic (n=2) extraordinary mode.
Emission from plasmas of magnetic fusion interest is in the Rayleigh-Jeans limit ( ω kTe ) so
that the radiation intensity of optically thick ECE harmonics reaches that of black body radiation,
i.e.,
I (ω ) = ω 2 kTe (8π 3c 2 )
Therefore, the plasma electron temperature and its fluctuations can be determined by
measuring the intensity of ECE. In a typical tokamak device, the toroidal magnetic field is
inversely proportional to the radial position, i.e. Bφ ∝ 1/ R . Thus, there is essentially a one to one
mapping between frequency and radial position. In most current designs, the second harmonic
frequency curve is utilized because of its higher frequency and wide radial coverage across the
plasma. Higher harmonics are not practical to be measured due to two main reasons: first, the 3rd
harmonic or higher harmonics has too high a frequency (usually higher than 150 GHz) to be
readily down converted due to the lack of suitable local oscillators with high enough output
power; for another, for higher harmonics, the plasma can usually not be considered as optically
thick.
1.2.2 Active Microwave Diagnostics
Active microwave plasma diagnostics utilize the plasma response to the launching wave to
diagnose the plasma. It has fewer limitations on the plasma conditions and has broader
applications. Major diagnostics include Reflectometry [29], Interferometry [30], Polarimetry
[31], Collective Thomson Scattering[32], Doppler backscattering[33], and Fast Alfvén Wave
Interferometry[34]. Reflectometry is a radar technique to measure the electron density profile
and its fluctuations from the reflection of electromagnetic waves at the plasma cutoff layer.
Interferometry is a standard density measurement method to obtain the line-intergraded density.
Polarimetry measures the line-intergraded magnetic times density. Collective Thomson
Scattering can probe the ρe scale ( ) localized electron turbulence as well as the
ρi scale. Doppler backscattering measures the intermediate wavenumber ( )
density fluctuations and propagation velocity of turbulent structures. Fast Wave Interferometry
obtains information concerning magnetic field, ion density, and the ion charge and mass, where
ion mass is of particular interest. In this dissertation, reflectometry, and interferometry as well as
polarimetry are of particular interest and their theory will be introduced below.
The normal (principal) modes in a cold, magnetized plasma include the ordinary wave,
extraordinary wave, and R, L waves in the high frequency limit (i.e., for frequencies much higher
than the ion gyro-frequency and plasma frequency, ω>> ωci and ωp). The definitions and the
corresponding refractive indices are described in the following.
Waves that propagate perpendicular to the magnetic field (kBT)
Ordinary wave: the electron vector of the incident wave is polarized parallel to the toroidal
magnetic field (E // BT). The index of refraction is
1/ 2
⎛ ω2 ⎞
μo = ⎜⎜1 − p2 ⎟⎟
⎝ ω ⎠
(
where ω p = ne2 ε 0 me
1/2
)
,
is the plasma frequency with an electron density n. The wave
propagates for ω > ω p . In the high frequency limit (ω>> ωci and ω p), the formula becomes:
2
1 ω
μo = 1 − × p2
2 ω
Extraordinary wave: the electric field direction is perpendicular to the toroidal magnetic field
(EBT) and thus the X-mode is elliptically polarized in the plasma. The electric field component
could be in the direction of the axis of propagation as well as normal to it. With the electron
cyclotron frequency ωc = eB me , the index of refraction is
⎡ ⎛ ⎞2
ω
ω 2 − ω 2p
μ x = ⎢1− ⎜⎜ p ⎟⎟ 2
⎢
ω ω − ω 2p + ω c2
⎣ ⎝ ⎠
(
1/2
)
⎤
⎥
⎥
⎦
With μo ≠ μ x (Bz≠0), the plasma is briefringent giving rise to the Cotton-Mouton effect. If we
ω p2
assume the high frequency limit (ω>> ωci and ω p), and Taylor expand it to the first order of 2 :
ω
1/2
⎡ ⎛ ω p ⎞2 ⎤
μ x = ⎢1 − ⎜ ⎟ ⎥
⎢⎣ ⎝ ω ⎠ ⎥⎦
2
1 ωp
= 1 − × 2 = μo
2 ω
Waves that propagate parallel to the magnetic field (k // BT)
R, L waves: a linearly polarized wave (EBT) has left-hand (L) and right-hand (R) circular
components with different refractive indices µR,L , and wave number kR,L,
1/2
μR,L
⎛
⎞
ω p2
= ⎜1 −
⎜ ω (ω ± ω ) ⎟⎟
c ⎠
⎝
1/ 2
⎞
⎛
⎞
ω p2
ω p2
⎟
⎟ , and k L = ω ⎜1 −
1−
kR =
⎜
⎟
c ⎝ ω (ω − ωce ) ⎠
c ⎜⎝ ω (ω + ω ce ) ⎟⎠
ω ⎛⎜
1/ 2
In the high frequency limit (ω>> ωci and ω p), the first order term becomes:
1/2
μR,L
⎡ ⎛ ω p ⎞2 ⎤
= ⎢1 − ⎜
⎟ ⎥
⎢⎣ ⎝ ω ⎠ ⎥⎦
2
1 ωp
= 1 − × 2 = μo
2 ω
Both circular waves can propagate for frequencies higher than the R-hand wave cut-off
frequency, but at different speeds. Therefore, the plane of polarization rotates as the wave
propagates along BT (see Figure 1.2). This is called Faraday rotation.
The total electric field can be expressed as the sum of the R-hand and L-hand circularly polarized
components,
[(
)]
) (
E = xˆ Eˆ R e −ikR z + Eˆ L e −ikL z + iyˆ Eˆ R e −ikR z − Eˆ L e −ikL z e iωt
The ratio of the x and y components of the field is,
Ex
1 + (ExL / ExR )ei ( k L − k R ) z
= −i
Ey
1 − (ExL / ExR )ei ( k L − k R ) z
For ExL/ ExR = 1, this equation reduces to
Ex
k −k
= cot L R z = cot ϕ
Ey
2
The angle in the cotangent function is called the Faraday rotation angle and is a function of
plasma density and magnetic field strength.
φ=∫
1/2
1/2
2
⎛ ω p2
ω ⎞
ω ⎞ ⎫⎪
kR − kL
1 ω ⎧⎪⎛ ω p
⋅ dz = ∫ ⎨⎜1 − 2 (1 + ce ) ⎟ − ⎜1 − 2 (1 − ce ) ⎟ ⎬ ⋅ dz
⎜ ω
ω ⎟⎠
ω ⎟⎠ ⎪
2
2 c ⎪⎜⎝ ω
⎝
⎩
⎭
2
=
1 ω ω p ωce
1
1
e3
ω 2ω ⋅ dz =
ne Bz ⋅ dz
⋅ dz =
2
2 ∫ p ce
∫
2 cω ω
2cω
2me 2ε 0 c ω 2 ∫
2ϕ
ϕ
Figure 1.2 Diagram for Faraday rotation
1.2.3 Reflectometry, Interferometry, and Polarimetry
Reflectometry is a radar technique for the detection of plasma fluctuations from the reflection
of microwaves from the plasma cut-off surfaces. Here, electromagnetic waves are reflected at the
plasma cutoff layer, when the refractive index goes to zero for the particular wave frequency. For
the case of O-mode reflectometry, its cutoff layer is only related to density; however, for the case
of X-mode reflectometry, its cutoff layer is also related to the magnetic field. Cutoff location
determination is based on the measurement of the time delay between the incident and the
reflected waves. If one measures this time delay for a series of frequencies ranging from those
reflecting at the plasma edge to the ones reflecting at a given depth, the corresponding density
profile can be derived.
Polarimetry measures the phase difference between the plasma and vacuum to determine the
density. In the high frequency limit, the first order term of µ is the same as we derived above. A
wave traveling through the plasma with a local density distribution ne(z) along the path z
undergoes a phase shift φ ,
ω
φ = ∫ (1− μ ) dz =
c
∫
2
1 ωp ω
e2
• 2 • dz =
λ ∫ ne dz = 2.8 ×10−15 λ ∫ ne dz
2
2 ω c
2ε0 mc
By spanning a sufficient number of chords over the mid-plane of the plasma, the interferometry
data can be viewed as temporally and radially resolved plasma density ne (r , t ) .
ne =
∫ n dz
e
2L
L = 2 × R 2 − RT2
The line-averaged density ne can be calculated by dividing the line-integrated density
∫ n dz by the double path distance 2L. Here, the single beam path L is obtained by the
e
Pythagorean law, where R represents the tokamak major radius and RT represents the tangency
radius.
The polarimetry approach measures its Faraday rotation angle to obtain magnetic information.
The Faraday rotation can be used to determine the toroidal magnetic field in Tokamaks by
launching the R-hand and L-hand circularly polarized waves. Since the fields and densities are
path-dependent in the plasma, the Faraday rotation angle is a line integrated value of the product
of ne and Bz and is proportional to the probing wavelength squared,
e3
1
2.35 ×104
ϕ= 2 2
n B ⋅ dz =
ne Bz ⋅ dz = 2.6 ×10−13 λ 2 ∫ ne Bz ⋅ dz
2 ∫ e z
2
∫
8π me ε 0c f
f
With the use of a fan beam configuration, the polarimetry data can be inverted to yield the time
dependent toroidal magnetic field Bz (r , t ) .
1.3 Microwave Diagnostic Techniques
1.3.1 Microwave Imaging (ECEI/MIR)
Microturbulence and large fluctuations in plasmas have very complicated patterns and are
extremely difficult, if not impossible, to be adequately described by 1-D measurements. High
spatial and temporal resolution visualization diagnostics of 2-D and 3-D structures are therefore
required to properly observe the instabilities. The UC Davis plasma diagnostics group has
pioneered the development of two 2-D plasma imaging techniques: (a) Electron Cyclotron
Emission (ECE) Imaging (ECEI) which provides a measurement of electron temperature and its
fluctuations; and (b) the radar-based Microwave Imaging Reflectometry (MIR) [35-43]
technique which measures the electron density profile and its fluctuations, in collaboration with
Princeton Plasma Physics Laboratory (PPPL) researchers, Drs E. Mazzucato, B. J. Tobias, and
G. Kramer, as well as researchers including Dr. A.J.H. Donné, from the FOM-Instituut voor
Plasmafysica Rijnhuizen, the Netherlands. Very recently, UCD has developed and installed a
combined ECEI and MIR system on DIII-D, which can view the same plasma volume
simultaneously, which will greatly extend the physical understanding of many phenomena.
ECE Imaging is a very effective plasma visualization technique employed to investigate the
dynamics of electron temperature Te and its fluctuations. Figure1.3 contains a schematic picture
to show the way to realize the measurement. This ECEI system collects ECE radiation from the
hot plasma through optical lenses, and the radiation will be received by a planar antenna mixer
array. Before that, a notch filter is used for filtering out stray ECRH radiation to protect the
mixing diode from saturating and prevent distorting the output signal; and the dichroic plate is a
metal plate with a periodic array of holes in it and works as a high pass filter, which makes single
band mixing possible with the local oscillator thereby providing higher resolution. The received
signal (RF) contains information including the radiation intensity and frequency, and enables us
to calculate the local plasma electron temperature and its corresponding position, and then to
form a 2-D temperature profile measurement. The high frequency RF signal will be mixed with a
local oscillator to down convert it to a much lower frequency called the intermediate frequency
(IF). The IF signal range in the current ECEI system is from 2 to 9.2 GHz. Finally, the
electronics circuits are able to divide the IF signal by means of a power divider into 8 discrete
frequency bands. Each band corresponds to a different radial position in the plasma. A mixer
array (20 vertical channels) is used to acquire the local temperature information on 20 different
vertical positions. With 8 radial positions in each vertical position, we can obtain a 2-D 20x8
electron temperature profile simultaneously. By taking advantage of novel technologies, such as
broadband IF electronics and fast data collection, it is also possible to obtain real-time plasma
temperature fluctuation measurements and images.
Figure 1.3 Experiment optical arrangement of 2-D ECEI system
Microwave reflectometry has proven to be an extremely useful and sensitive tool for
measuring electron density profiles and low level density fluctuations in some circumstances;
however, this technique has been shown to have limited viability for 2-D turbulence common in
tokamaks. In the presence of two-dimensional (2D) turbulent fluctuations, the interpretation of
reflectometry becomes considerably more complex. Thus, to capture multi-dimensional images of
plasma density fluctuations, the microwave imaging reflectometry (MIR) concept was developed
by UC Davis and collaborators. The following two pictures illustrate the layout of a typical MIR
system:
Figure 1.4 Conceptual schematic layout of a typical MIR system
Left: illumination part; Right: detection part
Figure 1.4 schematically describes the basic imaging scheme, where the probing microwave
(blue) and reflected wave (green) launches and exits the tokamak through the same window, and
shares a set of basic optical elements. The beam splitter is used to separate the reflected beam
from the probing beam. The reflected beam is detected by an antenna array as done in the case of
ECEI. The shared primary optical elements have two major functions: first, they are used for
shaping the wave front of the probing wave to match the shape of the cutoff surface, thus making
the wave rays impinge perpendicularly upon the cutoff surface so as to minimize the deleterious
effect of plasma refraction on the spectrum of probing wave numbers. Since any small deviation
in the radial position of the cutoff layer causes large deviation of the reflected beam, if the
curvature matching between the probing wave and plasma cutoff layer is not well performed;
second, for the reflected wave, the primary optics serves to create an image of the virtual cutoff
(shown in Figure 1.4 right) onto the array of detectors. In addition, additional lenses may be used
to adjust different focal positions, and de-magnify the image as much as possible to overcome
the power limitation of the probing wave.
1.3.2 Overall Profile Measurement (FIReTIP)
In plasma diagnostics, absolute measurement is very important, for example the plasma electron
density and temperature measurement will determine whether the Lawson Criterion are reached
or not. The UC Davis plasma diagnostics group also has extensive research on profile diagnostic.
The UCD developed Far Infrared Tangential Interferometry/ Polarimetry (FIReTIP) system had
been in commission in NSTX from 2002-2011. The Interferometer measures the line integrated
density, while the Polarimeter measures the line integrated density multiplied by the magnetic
field, and since they are measured over the same chord, it is possible to separate the magnetic
field information out, especially its fluctuation information. By this approach, one is able to
measure the density and magnetic field fluctuations at the same chord simultaneously. In
addition, by forming a fan structure over the mid-plane plasma of up to 6 chords, it is possible to
obtain the density profiles.
1.4 Dissertation Overview
This dissertation will mainly present two microwave imaging diagnostics (ECEI and MIR), and
FIReTIP for the density and magnetic diagnostic. ECEI provides temperature fluctuation
imaging and MIR provides density fluctuation imaging; by combining them on the DIII-D
Tokamak, it is possible to reveal new physics insight and advances. Millimeter wave bursts [4749] are an interesting phenomenon observed on both the ECE and ECEI systems which warrant
further characterization, physical models and experimental verifications. Lastly, the FIReTIP
system was introduced and the data are processed with newly developed algorithms for both
regular (post-shot) and real-time density calculations.
Chapter 2 describes the combined ECEI and MIR systems on DIII-D which provide
simultaneous electron temperature and density imaging at the same plasma volume. The ECEI
system consists of two major parts, the optical and array system, which rectifies, images, and
downconverts the ECE radiation, and the electronics, which detects the radiation, power in each
microwave band. Two recent upgrades, one is the use of the zero bias detectors which has
greatly decrease the noise level, and the other which is the expanded radial coverage which
doubles the radial view in the plasma, the system has been significantly improved. For the MIR
system, synthetic diagnostic modeling was used for the optic and array design; some details
about the transmitter, receiver, and electronics will also be presented. In addition, several
methods for the ECEI/MIR time calibration are conceived, applied, and compared; in addition,
these methods are applied to calibrate two additional key diagnostics systems, the ECE
radiometer and magnetic fluctuation diagnostic systems.
Chapter 3 will introduce the observed intense bursts of mm-wave emission by both the ECE
radiometer and ECEI systems during edge localized modes, Quiet H-mode (QH) modes, and the
precursor before disruptions. A new RF spectrometer with an IF frequency range of
approximately 2-10 GHz, designed to characterize the bursts, has been installed on the DIII-D
tokamak. Several characteristics of the bursts in H-mode will be firstly presented. Furthermore,
these bursts are also observed in the QH-mode [50] low collisionality plasma, and found to be
synchronized to the edge harmonic oscillation (EHO) and the rising edge of longer period
oscillations in filterscope data. Enhanced electron transport precedes bursting and we
hypothesize that this bursting is due to some of the resulting electron orbits being in resonance
with the 3D structure of the EHO. As a trial model, this dissertation offers the Cyclotron
AutoResonance Maser (CARM) and Gyro-BWO models to explain these bursts[51], which need
further verification from more targeted experimental data and simulation results.
Chapter 4 will introduce the multichannel FIReTIP system that provides line-integrated plasma
density and magnetic information from multiple viewing chords on the midplane of the NSTX
device. Extremely wide bandwidth phase comparator electronics that were developed and
installed on NSTX device in 2009 extend the bandwidth up to 4 MHz when operated in an
interferometry-only configuration. The new electronics provides simultaneous interferometer
phase measurement data using two distinct phase comparator methods, one is the FC approach,
and the other is the IQ approach. New algorithms have been developed to process the FIReTIP
data for both regular post-shot and real time calculations for both FC and IQ approaches, with
reliability checks conducted using Thompson Scattering data where available. Subsequently, the
possibilities check for real time density feedback control was conducted here using new
processed data; and the FC and IQ approaches are evaluated for different conditions. In the end,
this paper presents some possible upgrade plans to improve the signal strength, decrease the
noise level and cut the costs of the system.
Chapter 5 summarizes all the conclusions described in the previous chapters, followed by some
future research upgrades to those diagnostics systems at the end of this dissertation.
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Chapter 2
Combined ECEI and MIR Diagnostic Systems on DIII-D
2.1 ECEI Diagnostic System
Electron Cyclotron Emission (ECE) is a passive microwave radiometric diagnostic tool that is
widely used for electron temperature measurements [1]. Using a combination of focal plane
antennas, large aperture optics, and multichannel radiometric electronics, a 2-D imaging tool
ECE Imaging (ECEI) [2-9] has recently been developed to study diverse plasma phenomena by
electron temperature (Te) and fluctuation (δTe) measurements. It has been employed on devices
such as TEXTOR, RTP, and TEXT-U [2-4] and is presently being operated on the KSTAR,
EAST, DIII-D, ASDEX-UG, and HT-7 tokamaks [5-10].
The principle behind ECEI is to use large aperture optics and vertically-aligned antenna/mixer
arrays to collect ECE from multiple vertical locations within the plasma, and to use advanced
electronics to sample multiple ECE frequencies and thereby simultaneously measure multiple
radial locations to form 2-D Te profile and fluctuation images. The ECEI technique is illustrated
schematically in Figure 2.1. Fusion plasmas are often heated using electron cyclotron resonance
heating (ECRH); in these cases, a quasi-optical notch filter is inserted into the optical path to
protect the array from stray ECRH collected by the optics. A dichroic plate, consisting of
thousands of holes cut into a metallic plate, acts as a highpass filter to ensure single sideband
operation at frequencies above the dichroic plate cutoff frequency and above the local oscillator
(LO) frequency that pumps the array and which downconverts signals (using the heterodyne
method [1, 11]) to lower frequencies where it is more cost effective to amplify, divide, and
detect.
Figure 2.1. Typical heterodyne ECEI configuration.
In the 1st, 2nd, and 3rd generation electronics [12], each downconverted ECEI signal is divided
into 8 discrete frequency bands with each band corresponding to a different radial position in the
plasma [13]. The HT-7 and ASDEX-UG systems each consist of a single array with 16 vertical
channels to yield resolutions of 16×8; the DIII-D system uses dual arrays with 20 vertical
channels each to cover two separate radial regions with a total resolution of 20×16; finally, the
KSTAR ECEI system has similar dual arrays, but with 24 vertical channels to achieve a total
resolution of 24×16. The dual-array systems [6, 14] share the same tokamak port and window as
well as some of the large aperture plasma-facing optics; typically, one is employed for Low-field
Side (LFS) imaging and one for High-field Side (HFS) imaging although other arrangements are
possible [15]. In the 4th generation electronics [8,10], which has been applied in EAST, each
downconverted ECEI signal is divided into 16 discrete frequency bands. The EAST ECEI system
consists of a single array with 24 vertical channels to yield resolutions of 24×16.
2.1.1 Optical and Array System
The DIII-D ECEI system is installed at the 270° midplane port[16], shown in Figure 2.2. The
port is the largest one on DIII-D, which is the so-called man-hole port for providing access to the
inside of the tokamak. It is shared with the Michelson Interferometer and the ECH overpower
detection. A large fused silica window (60 cm vertical, 20 cm horizontal) is applied in the
interface, which accommodates the diffractive spreading. The radiation bounces from two 45°
mirrors (one in the vacuum) and then goes to the zoom lenses. The large zoom optics can be
remotely adjusted and provide variable vertical plasma coverage from 20 cm to 55 cm. Then, the
radiation is separated into the LFS and HFS portions by a dielectric beamsplitter, and each
objective lens system can be adjusted separately. Then, each of them gets detected and mixed in
the RF detector arrays. The local oscillator coupling is on the left side of the RF detector and is
concealed in this image.
Figure 2.2. DIII-D ECEI optical and array system. (Figure is reprinted from B. J. Tobias’ PHD Thesis
with permission)
The first of the DIII-D system innovations is the mini-lens application and its associated
technology development. Antennas are usually mounted on a substrate for ease of fabrication,
which therefore radiate significantly more power into the dielectric (or front-side) than into the
air. Because a flat substrate will generate substrate modes due to trapping waves, a large hemisphere or elliptical lens (around 17 cm diameters) with a similar dielectric constant to substrate is
usually applied. However, the large lens will cause the aberration for off-axis elements. The
miniaturized elliptical substrate lenses or mini-lens [17] (around 2 cm diameters) conception (see
Figure 2.2, a) was conceived to solve this problem. By using an array of closed arranged (see
Figure 2.2, b-c) miniature elliptical substrate lenses and placing the antenna at the focus, it is
possible to minimize the aberrations and significantly improve the antenna pattern with a narrow
main lobe and reduced side lobe. Since the mini-lens is designed to refract rays originating at its
focus to parallel rays, it enables the needed space for the front-side LO pumping which has been
implemented in previous and current ECEI systems. The front-side LO pumping makes the LO
and ECE optics separate and it is thus easier for the antenna to be simultaneously optimized for
both LO and ECE. It also makes the LO power get focused on each single antenna and resulting
in even distributions for different antennas. However, front side pumping requires the use of a
splitter to combine them, which will lose half of both the ECE and LO power. To use side
signals, staggered channels and a 3 dB dielectric film beam splitter are applied. It also doubles
the channels, avoids the use of a beam dump, and helps integration [18].
Figure 2.3 Antenna array boxes. a)picture; b) front view; c) side view; d) Top view.
Another key innovation is dual-array imaging, which make it possible to simultaneously image
different regions of the plasma. To save the limited space near the port and money, the vertical
zoom optics are shared. Then, by means of a carefully chosen dielectric thin film beamsplitter,
they are divided into HFS and LFS portions. Subsequently, by adjusting separate objective
lenses, they can be focused on different locations of the plasma. In the wide zoom configuration,
the LFS focus location covers from R=1.9 m to R=2.4 m, and the HFS focus location varies from
R=1.45 m to R=1.95 m. In the narrow zoom configuration, the LFS location covers the major
radius from 1.9 m to 2.2 m, and the HFS location covers from 1.6 to 1.9 m.
Examples of the region imaged with respect to the total poloidal cross-section of the plasma are
given in Figure 2.4. The radial position of each region can be changed remotely by a change in
LO frequency and adjustment of the objective lens. The vertical zoom also can be varied
remotely independently of the location. For large mode structures like NTM [19] and the
Sawtooth [20] precursor [21], usually wide coverage with low resolution will be chosen; for
small structure modes like Alfven Modes [22], high resolution with less coverage is usually
chosen. Vertical zoom is a common adjustment for both HFS and LFS, and the maximum
vertical zoom magnification is 2.1:1. The third feature is the radial spacing adjustment that is
accomplished in the electronics and will be discussed in detail in the next section. The IF spacing
may be adjusted to be either 600 MHz or 900 MHz, which results in a radial zoom ratio of 1.5:1.
It should be noted that since the switch is on a module-to-module basis, the radial spacing can be
adjusted independently for HFS and LFS.
Figure 2.4 Both wide and narrow coverage configurations for the DIII-D ECEI system are
shown compared to an example of plasma equilibrium. (Figure is reprinted from B. J. Tobias’
PHD Thesis with permission)
2.1.2 Overview of ECEI Electronics
The electronics sits in the Michelson Lab. One reason is to avoid the RF noise in the pit, another
is to save the space in the pit, and the third reason is that the relative constant temperature helps
the electronics maintain heat equilibrium which helps reduce the noise and prolong the lifetime,
and it also make the shot-by-shot adjustment easier. For illustrative purpose, the figure below
shows the actual situation of the ECEI electronic system together with the RF and IF circuit
boards. There are two racks, one for low field side measurement and the other for high field side
measurement, each consisting of 20 modules which correspond to 20 vertically spaced antennas
on two sets of arrays. The input signals come from the pit to the Michelson Lab through the low
loss SMA cables. Right figures are the RF and IF board of each module.
Figure 2.5 DIII-D ECEI electronic system (left), RF(top right) and IF(bottom right) circuit boards
The electronics consists of two printed circuit boards: an RF board and an IF board [13]. In the
RF board (see Figure 2.6), the signal passes through a low noise amplifier and a 0-31.5 dB digital
attenuator, and is then split into 8 parts by three stages of wideband 2-way Wilkinson power
dividers. Each part is mixed with a distinct Voltage Controlled Oscillator (VCO), and then
lowpass filtered to effectively select a relatively narrow band of frequencies around each VCO
frequency. Frequency spacing of the VCOs is user-selectable between 600 MHz (narrow zoom
operation) and 900 MHz (wide zoom operation) to fit the diagnostic needs for a particular
plasma discharge.
Figure 2.6. Schematic layout for the 3rd generation ECEI RF board.
The resultant signals from the RF board are passed on to the IF board (see Figure 2.7) where
each signal is further amplified and then rectified by a diode detector. IF board pre-detection
attenuators provide up to 15 dB of gain control to compensate for any channel-to-channel
variations. The detected or video signal is amplified and lowpass filtered by a 10th order variable
frequency filter which sets the video bandwidth to 50, 100, 200, or 400 kHz. Finally, each signal
is level-shifted and amplified such that the outputs fall into the range of -2.5 to 2.5 V (-1.0 to
+1.0 V on selected plasma devices) to match the available digitizer input voltage range and thus
maximize the effective resolution of the ECEI signals.
Figure 2.7. Schematic layout for a single channel of an ECEI IF board.
2.1.3 Automated ECEI Electronics Testing and Results
Each ECEI system consists of two printed circuits boards. There are which has more than 200
components on each board, so there is high probability for a malfunction after the soldering and
assembling process. Furthermore, all the plug-in components in the boards need to be soldered
manually. For each module, these components are 9 attenuator controllers, 1 SMA connector (RF
inputs), 8 lemo connectors (digital outputs), 8 trimpots (output zero adjustment), and two power
inputs. Some modification after the fabrication will increase the manual processing. Finally,
each one consists of hundreds of channels, which requires considerable debugging, testing, and
characterization work. To save the time and energy, one automatic system is applied in the lab
and is illustrated below in Figure 2.8.
Figure 2.8. Schematic layout (top) and one actual example (bottom) for Automated Electronics
Testing
Firstly, the Labview program in computer controls the sources to generate the desired test signal.
Here, the typical sources are sweep oscillators and frequency synthesizers, which do not
havemany flexible features. However, they can be controlled by GPIB ports to adjust the power
on/off, the power level, and the frequencies. Then, the generated signal go to a power divider;
one goes through signal monitor and gives the feedback to the computer; another goes through
the device under test, and then give the output to an analog to digital converter, and then goes
back to the computer. The signal monitors several digital components in the lab, including the
frequency counter, power meter, and spectrum analyzer. Several different interfaces are designed
for the testing of separate boards, for example, the power divider port for the input of the IF
boards. The RF and IF boards can be tested separately or in combination, which greatly benefits
the debugging process and helps facilitate future improvements. Here, the digitizers are high
sampling rate units, the National Instruments USB-6351, which can provide 16 channels at 1
MHz sampling simultaneously. The video bandwidth is less than 400 kHz, so this digitizer is
good enough to be utilized in the noise spectrum testing.
Several features are characterized by this system, and can be found in Doctor Xiangyu Kong’s
Ph.D dissertation [23]. Figure 2.9 is one example, which is the IF frequency response for wide
and narrow zoom of the electronics. The frequency response test is conducted by a frequency
sweep from 2-20 GHz (since the band width of the preamplifier has a bandwidth of 2-20 GHz).
This is to ensure there is a one to one coupling between each channel and the radial position in
tokamak. Since only the single sideband signal is detected, the mapping from radial position to
the RF frequency signal is one to one, so to achieve one to one mapping in position to channel, it
is required that there be a one to one map from the RF frequency band to the video signal at each
channel. As seen from the picture below, the wide zoom operation can provide excellent one to
one mapping for frequency to channel; the spurious bumper around 5 GHz in Ch 1 are 23 dB
lower than the main lobe and the other channels’ spurious signal level is about the same as the
background noise.
Figure 2.9 Frequency response for wide and narrow zoom
To ensure there is a one-to-one frequency mapping, the dichroic plate needs to be chosen very
carefully in the actual plasma operations. Dichroic plates act as high pass filters (HPF), and their
cutoff frequencies are fixed and the optional values are 72 GHz, 77 GHz, 81 GHz, 85 GHz, 90
GHz, 95 GHz, 100 GHz, 110 GHz, 115 GHz, 120 GHz, and 125 GHz. Take the wide zoom as an
example; the IF pass band can be simplified as 2-10 GHz. After the LO frequencies are chosen
for each plasma condition, the dichroic plates in the radiation path need to be in between LO±2
GHz in order to ensure it will suppress the RF-IF part of the signal, as shown in Figure 2.10.
Another issue is that due to the possibility of stray rays, the HFS LO might come to the LFS
arrays Although it is small compared to the LO power level, it might be comparable to the
radiation power level from the plasma. Consequently, the mixed signal cannot sit in the passband
of the electronics, so the HFS LO can be 10 GHz above the LFS LO, or 3.05 GHz, 3.95 GHz,
4.85 GHz, 5.75 GHz, 6.55 GHz, 7.45 GHz, and 8.35 GHz. Here, 6.55 GHz is very good option,
which can provide continuous radial coverage, since the spacing between HFS radial Channel 1
and LFS radial Channel 8 is 1.15 GHz which is very close to the regular 900 MHz space.
Figure 2.10. Schematic drawing of choosing the dichroic plate frequency
2.2 Recent ECEI Diagnostic Upgrade
2.2.1 Use of Zero Bias Detectors
Early ECEI systems employed biased or barrier detector Schottky diodes for good linearity at
low power levels. Unfortunately, this linearity came at the expense of significant voltage drift in
our differential diode comparison circuits. Figure 2.11 shows that it takes about 60 sec from the
initial turn-on of the ECEI electronics to stabilize, and that the output voltage drift during this
time is ~80 mV. Switching to zero bias detector diodes has greatly alleviated this problem, with
turn-on drifts reduced to < 5 mV and stabilization times reduced to < 6 sec. Figure 2.12 shows
the measured background noise and its spectrum for one of the new zero bias ECEI modules, at
the highest video bandwidth setting to illustrate the noisiest situation. The peak to peak value is
23.7 mV, with a root mean square value of 2.80 mV. The measured spectrum is < -40 dBV/Hz,
and it is very flat out to ~300 kHz with good response out to the bandwidth limit of 400 kHz.
Figure 2.11. Turn-on drift comparison between barrier diodes and zero bias diodes, acquired
with a 50 kHz noise bandwidth setting.
Figure 2.12. Output noise (top) and spectra (bottom) of a zero bias ECEI module, channel #8,
acquired with a 400 kHz noise bandwidth setting.
The strong voltage drift reduction is particularly important in the study of plasma edge
fluctuations, in which the electron temperatures are quite low and large voltage drifts can
significantly affect the accuracy of the ECEI measurements. Physics areas that have greatly
benefited from this performance improvement include Edge Localized Modes (ELMs), Alfvén
Eigenmodes (AEs), and the Edge Harmonic Oscillation (EHO).
2.2.2 Expanded Radial View ECEI Electronics
As an alternative to using dual imaging arrays to provide wide radial views of tokamak plasmas,
UC Davis is developing new system architectures with greatly expanded RF bandwidths. This
technology is currently only applied in EAST ECEI system [8, 23], but will have good potential
to expand its use to other ECEI systems especially the DIII-D ECEI system in future. Tabulated
in Table 2.1 are the instantaneous RF bandwidth restrictions broken down by ECEI system
components. It is clear that the greatest limitation to achieving a wide RF bandwidth is the ECEI
electronics module that has been limited to an IF range of 2-9.2 GHz. Two approaches are under
investigation to this end. One converts higher frequency IF signals (10.8 to 18.0 GHz) to lower
frequencies and then input these signals to existing ECEI modules; the other is to develop new
higher frequency modules that work directly with the higher frequency IF signals. This
dissertation will focus on the second approach. Recent advances in surface mount components
above 9 GHz including VCOs, power amplifiers, filters, and mixers now make it possible to
perform mixing in the 9-18 GHz region at reasonable cost.
ECEI System
Component
Possible RF/IF
Range
Dichroic plate
2-25 GHz
Antenna
DC-40 GHz
Schottky Diode Mixer
DC-40 GHz
Balun
2-40 GHz
Low Noise Amplifier
2-20 GHz
ECEI Electronics
Module
2-9.2 GHz
Table 2.1 RF frequency limit for each component in the ECEI system
The approach is shown schematically in Figure 2.13. A wideband power divider splits the
wideband input into two parts, with one part continuing on to a conventional or low frequency
ECEI module with the second part connecting to new, higher frequency electronics. Similar to
the conventional module, the signal is amplified, and split into 8 parts each of which is mixed
with an LO signal. The LO signals are spaced 900 MHz apart, starting at 9.7 GHz. When
coupled to a conventional ECEI module set to the 900 MHz spacing (i.e. wide horizontal zoom),
this provides continuous coverage from 2 to 16.5 GHz. After promising results were obtained
with prototype test circuits, this approach was chosen to realize the wideband 24×16 EAST ECEI
imaging system.
9.7 GHz
7.15 GHz
HPF
Input Signal
2-16.4 GHz
18 dB
10.6 GHz
11.5 GHz
External
Control
0-31 dB
12.4 GHz
18 dB
13.3 GHz
18 dB
14.2 GHz
7.15 GHz
HPF
15.1 GHz
16.0 GHz
Figure 2.13. Schematic diagram of method to frequency extend ECEI electronics (left), and
actual RF board implementation (right).
A plot of the EAST extender module power linearity is provided in Figure 2.14, which
demonstrates that the output voltage is directly proportional to the ECE radiation power over the
EAST digitizer voltage range of -1 to 1 V with a worst-case fit error of < 5%. A typical
frequency response is plotted in Figure 2.15, revealing that the eight frequency bands are highly
localized with steep band edges. The measured crosstalk between adjacent channels is less than 30 dB, so this guarantees excellent one-one mapping with the capability of performing
correlation measurements with the ECEI data.
Figure 2.14. Power linearity measurement of the ECEI extender module.
Figure 2.15. Frequency response of the ECEI extender module.
It should be noted that the good results obtained with the ECEI extender modules does not mean
that there is no further development work required. For example, the extremely small signal pads
on the high frequency VCOs led to impedance matching problems that were difficult to
overcome (the VCOs were designed to be placed on high dielectric constant substrates, and not
on the low dielectric constant substrates employed here). Large channel-to-channel variations in
signal amplitude were observed in all modules which, although compensated for by using the IF
board gain control switches, were consistent among all modules and need to be identified and
eliminated. The source of these amplitude variations is still under investigation, but is thought to
be the result of either the surface mount amplifier’s power-frequency response, a narrow power
divider response, or increased mixer conversion loss on those channels with poor coupling
between the mixers and the on-board VCOs. A new board layout has since been drawn up that is
expected to alleviate much of these concerns, with new results expected shortly.
2.3 MIR Diagnostic System
The principle behind MIR is to use large aperture optics and vertically-aligned antenna/mixer
arrays to collect reflected microwave from multiple vertical locations within the plasma, and to
use advanced transmitters as well as receivers to sample multiple cutoff layer and thereby
simultaneously measure multiple radial locations to form 2-D ne fluctuation images [24-32]. The
MIR technique is illustrated schematically in Figure 2.16. The transmitter illuminates an
extended region of the cutoff layer, and the illumination beam matches the cutoff curvature to
achieve a robustness of the signal and eliminate the stray reflection from other layers. Due to the
refraction of the beam when the microwave gets closer to the cutoff, there exists a virtual cutoff
point behind actual cutoff location [24], where ray asymptotes arrive at a common focal position.
The virtual cutoff layer needs to be imaged into the mini-lens detector to collect high order
reflected signals. The notch filter and dichroic plate are similar to the ones in the ECEI system.
In the DIII-D system [31-32], the notch filters provide 70 dB insertion loss to the ECRH
frequencies; the dichroic plate has a fixed frequency, which acts like a bandpass filter whose
passband is 54-81 GHz which is slightly wider than the MIR operational V band. Another local
oscillator (LO) frequency pumps the array and which downconverts signals to lower frequencies
(the LO also downconverts the split transmitter signal to be a reference signal which is not
shown in the schematic figure) where it is more cost effective to amplify and detect.
Figure 2.16. Typical in-phase quadrature heterodyne MIR configuration. (Credit to: C.M.
Muscatello)
Each downconverted signal and reference are detected in the electronics to provide the amplitude
and phase information. The original TEXTOR MIR system [24-28] consists of an array with 16
vertical channels and only one probe frequency to yield resolutions of 16×1; the KSTAR MIR
system [33-34] applied the legacy UCD 16-element TEXTOR imaging array and collected data
at two simultaneous, fixed illumination frequencies which provide 16×2 resolution [28]; the
DIII-D MIR system [35-36] uses an array with 12 vertical channels and 4 simultaneously fast
step tunable transmitter signals with a total resolution of 12×4. Both systems share the same
tokamak port and window as well as some of the large aperture plasma-facing optics with the
ECEI system, thereby providing the capability of simultaneous temperature and density
fluctuation measurements over exactly the same plasma region.
2.3.1 Optical and Array System, and Synthetic Diagnostic Modeling
The DIII-D MIR system, as shown in Fig. 2.17 (a), is utilizing the 270° mid-plane port where a
large aperture fused window accommodates diffractive spreading. MIR is sharing this port and
large aperture zoom optics with ECEI system. One significant result is that the ECEI and MIR
systems can view the same volume of plasma simultaneously such that plasma density and
temperature fluctuations may be diagnosed simultaneously at the same position, which will leads
to new physical views of the tokamak plasmas. This zoom optics are configurable to provide
variable vertical plasma coverage of up to 55 cm for the ECEI system, and up to 20 cm for the
MIR system. Since ECEI is mainly operated in E-band and MIR is in V-band, a thin-film
dielectric beamsplitter with high insertion pass in low frequency is designed and applied to
separate the two systems. After another beamsplitter, it goes to the illumination and receiver
objective lens systems, which control the focusing of illumination and receiving. The signal is
received at vertically separated antenna arrays, and then is mixed with the LO frequency to
provide the 1-10 GHz IF signals. This IF signals are amplified and then sent to remotely located
IF electronics.
Figure 2.17: a) Top view of the ECEI/MIR layout; b) Sketch layout of the MIR systems (Credit
to C.M. Muscatello)
The biggest innovation is independently controlled, dedicated focusing lenses and advanced
receiver optic systems. By applying these independently fabricated lenses, firstly it is easier to
remove the malfunctioning units, and more importantly, this helps to decrease the aberrations
due to the optics, which is very helpful for the optic design for different imaging configurations.
By applying these focusing lenses, the optics system is designed and its three focus
configurations are shown in Fig 2.18. The top of the figure shows the edge focus, narrow channel
spacing cases, which requires both shared lenses to be as close as possible to the port (this will
put ECEI into narrow zoom as well) and is best for imaging strongly shaped cutoff layers; the
middle part of the figure shows the edge focus, wide channel spacing, which requires one shared
lens as close as possible to the port and the other shared lens a large distance from the port (ECEI
into wide zoom as well) and is best for imaging weakly shaped cutoff layers; the bottom part of
the figure show the core focus , in this case, wide zoom is chosen for smaller major radius focus;
its limitation is that off-midplane channels will be difficult to couple to core cutoff layers.
Figure 2.18 Receiver accommodates a variety of poloidal and radial coverage (Credit to: C.M.
Muscatello)
Another diagnostic advancement is the synthetic diagnostic modeling for the evaluation of the
current optics design. Outside the plasma, an optical algorithm that has Gaussian beam and
Fourier beam propagation capabilities is used for the optics properties; inside the plasma, a fullwave reflectometer code, FWR2D (as well as advanced FWR3D), are used to evaluate DIII-D
relevant conditions. By this method, a wide range of fluctuation parameters can be evaluated and
achieved, so that the fluctuation working range and limitation of specific optics systems can be
obtained. Figure 2.19 shows two examples (left and right) of the working cases with different
density fluctuation levels. The top part shows the cutoff fluctuation in the real plasma (red) and
the measured phase at the receiver (blue), and they match well and the correlation is more than
0.95. The bottom shows the IQ plot of the measured signal over time; each black dot means one
IQ point in time, and blue is the reference. It shows that they formed a nice circle instead of
filling the region, which means the amplitude modulation is small and the focus is good for these
cases.
Figure 2.19 Receiver accommodates a variety of poloidal and radial coverage (Credit to C.M.
Muscatello & X. Ren)
2.3.2 Transmitter, Receiver, and Electronics
The detector section of the DIII-D MIR diagnostic is comprised of a 12 vertical *4 radial =48
channel array. Figure 2.20 shows a schematic diagram of two probing signals. To expand to a 4
channel system, it is only required to add one more IF signal with different frequencies, and by
increasing more frequencies it will be possible to achieve up to 16 radial channels which is the
ultimate goal. In the transmitting system, a double sideband up-converting mixer, which
combines the LO source from the mechanically tunable frequency Gunn Oscillator which is
fixed at 65 GHz and the IF source from two USB-controllable, fast step tunable Pronghorn
sources of 0.5-9 GHz variable frequencies and -15 to +10 dBm power, four illumination signals
are obtained with frequencies of 56-74 GHz. A 36 dB power amplifier after this mixer l ensures
that the power level is above 1 dBm for each illumination signal, which is much higher than the
leakage LO power of -20 dBm. These frequencies and power levels can be adjusted on a shot-toshot basis currently. After a future upgrade, the frequencies will be varied during a single shot to
provide a radial scan of the right-hand cutoff layer; and the power level may be modulated to
reduce the background noise.
In the receiving system, the receiver LO source is a voltage controllable Gunn-oscillator with a
tunable range of 64-65.6 GHz. With a phase lock loop, these two Gunn-oscillators are phase
locked with each other with an LO frequency 370 MHz above the transmitter LO, and this 370
MHz signal serves as one local oscillator (LO1) in the final electronics. Another Pronghorn
source is separated from the IF source in the transmitting system by 510 MHz what serves as
another local oscillator (LO2). The reflected signal is imaged by 12 vertical antenna arrays, and
is mixed with the Gunn LO source by Schottky diode mixers to obtain the first down-conversion.
Then, it is down-converted again mixing with the Pronghorn sources. After the double downconversion, the fGUNN-fIF signal is converted to 810 MHz, and the fGUNN+fIF signal is converted to
140 MHz. In addition, there is a programmable controlled variable attenuator from 0-31.5 dB
and RF switches, which adds to the flexibilities of power level control and background noise
calibrations.
Fig 2.20 Transmitting and receiving system of MIR
The MIR electronics consists of power divider modules and the IF board modules shown in Fig
2.21. In the power divider modules, the 510 MHz LO and 370 MHz LO are mixed with each
other and generate the 880 MHz and 140 MHz signals; after the bandpass filter each are divided
into 12 parts and then go to each board and serve as the LO for the IQ mixer. Here, extensive
bandpass filters are applied for each signal to reduce possible sidebands and noise. In the IF
board modules, the signal is amplified by a low noise amplifier, separated into two parts, which
each pass through a 0-31.5 dB digital attenuator controlled by a Labview program which
facilitates remote adjustments. Then, the 880 MHz and 140 MHz bandpass filters provide the
correct signal for each of the IQ mixers. After the IQ mixer, each of them pass through a 1.5
MHz lowpass filter and are then amplified by the same wideband dual-channel amplifier in order
to maintain the relative amplitude and phase information. Finally, they are digitized by a 14 bit 1
MHz digitizer.
Fig 2.21 MIR electronics
2.3.3 Quadrature Approach and Data Processing Method
The key component required to obtain the amplitude and phase information is the IQ
demodulator (or IQ mixer), whose operating principle is shown in Fig 2.22. Assuming the input
of the RF and LO signals are:
The In-phase and Quadrature signals are then given by :
Considering the offset of the two signal (E1, E2), amplitude unbalance (AU) and phase
unbalance (PU) are introduced into the signal; they will become:
Fig. 2.22 The left part of the figure shows the operating principle of the IQ mixer. The LO signal is divided into two
parts which are 90° out of phase, and the RF is divided with same phase, and then they are modulated together.
Then, they pass through the Low Pass Filter to obtain the In-phase part (I) and quadrature signals (Q). The right part
of the figure shows the polar plot of the I- and Q-signals, which will be a perfect circle while varying the phase.
Two types of surface mounted IQ mixers are applied in the MIR electronics: Mini-Circuits JCIQ176D for 140 MHz signal processing and SYIQ-895D+ for 880 MHz. The 140 MHz mixer has
very small error resulting from offsets and unbalances; however, for the 880 MHz mixer,
because of the high frequency, the errors are very large. The maximum offset is 0.2 V which is
very large compared with a typical 1 V signal; the amplitude unbalance is huge as well so that
the ratio of the IQ signals goes as high as 1.3; the phase unbalance goes up to π/20. In Fig 5, the
blue dashed line represents the original IQ, the left is the polar IQ plot, and the right is the
measured phase change versus the real phase change. In order to obtain calibrated, two
continuous waves with slight frequency differences (ωDF), are input into the IQ mixer as RF and
LO. These offsets are the means of each signal over integers of the output signal period; the
amplitude unbalance is the ratio of the range of Q and I. Then, they are calibrated to
Next, to fix the phase unbalances, we rotate the axis to the IQ eclipse axis.
By dividing tan(π/4+PU/2) of the new I component, it comes to the final balanced IQ signals.
The corrected data are shown in red in Fig 2.23, which shows that the phase linearity has
improved dramatically over the original data.
Fig 2.23 Original (blue dotted) and corrected data (red solid) for polar IQ plot (left) and phase linearity (right)
2.3.4 Video Frequency Response of the MIR Electronic
To test the video frequency response of the MIR electronics, a Frequency Modulated signal with
10 MHz modulation needs to be generated in the input signal. Here, the Agilent Technology
N5183A MXG Microwave Analog Signal Generator, which gets the Amplitude Modulation,
Frequency Modulation, and Phase Modulation function over the carrier frequency range from
100 kHz to 20 GHz, is used. The LOs are set to the required optimum setting, Source 1 set to 4
GHz at +3 dBM, Source 3 are set to 4.51 GHz at +3 dB, and the 370 MHz LO is provide by the
Pronghorn Sources as well, which is -7 dBm. All of them are synchronized by the 10 MHz clock
signal output of the signal generator. The signal generator is set to 3.63 GHz, an amplitude of -33
dBm, and the 10 MHz FM in 0.4 Hz. As shown in Fig.2.24, the top is the original data and the
bottom is the spectra of the data. It is clear that there is an amplitude change in the raw signals,
and the modulation signal produces a very clear line in the spectrum. At time 3610 ms, the RF
matches with the LO frequency, the amplitude goes to maximum in the raw data, and in the
spectrum, the digitized signal has about zero frequency. As time progresses, the frequency
increases; when the time reaches 3785 ms, the frequency of this mode reaches its maximum
value of 500 kHz, which is limited by the digitizer’s of 1 MHz sampling rate. Then the frequency
decreases as the time passes 3785 ms. When it reaches 3860 ms, the signal amplitude drops to its
first dip, and in the frequency spectrum, it shows about 0 Hz frequency. The reason is that the
digitizer drops the 1 MHz signal to 0 Hz. Then, the signal repeats this circle.
Fig 2.24 Frequency Modulation of the input signal, the top is the original data; the bottom is the spectra of the data.
At time 3610 ms, the RF matches with the LO frequency.
From these data, the frequency response can be easily obtained as shown in Fig 2.25. The video
frequency can be calculated from the time or the spectrum; the amplitude response is just the raw
data signal amplitude. It is noted that the response is quite similar to a sinh(x)=sin(x)/x function;
the reason is the digitization method applied in MIR. In MIR, the signal is digitized at 8 MHz
and then by averaging over 8 points, the 1 MHz sampling data are obtained, and then stored in
the MDS-Plus trees. This average will act as a sinh(πf/fs)/f frequency filter to the original data,
and here fs=1 MHz, which matches the result. The built-in filter in the MIR electronics is a single
Coilcraft, Inc. 7th order elliptical filter with the cutoff at 1.5 MHz. Consequently, the average
Amplitude (a.u.)
filtering, with a lower cutoff frequency, has the dominant effect on the signals.
Frequency (kHz)
Fig 2.24 Video Frequency response of the MIR electronics.
2.4 Simultaneous Imaging of MIR and ECEI, and Time Calibration of Multiple
Diagnostic Systems
Tokamaks are complex systems, and multiple plasma properties need to be diagnosed in order to
obtain the requisite information for the successful understanding of magnetic fusion physics.
Magnetic field, electron temperature, electron density, ion temperature, ion density, and other
internal profiles are required for a detailed reconstruction of the plasma equilibrium. To provide
the required accuracy, all of these systems need to be time calibrated to obtain the right
combined information. In particular, to employ multiple diagnostic systems to characterize high
frequency MHD modes such as Alfven modes and tearing modes, these systems need to be
synchronized to within a few microseconds. In this section, the Electron Cyclotron Emission
Imaging (ECEI), Microwave Imaging Reflectometry (MIR) systems, the ECE radiometer, and 3D magnetic diagnostic are discussed and calibrated. On the DIII-D tokamak, the ECE[37] system
measures the absolute temperature over the mid-plane, with 40 channels and 50 GHz coverage.
The 3-D Magnetic diagnostic system [38] measures the magnetic fluctuations and accumulated
magnetic field over the poloidal, radial, and toroidal directions. As a subset, toroidal arrays in
midplane will be discussed in this dissertation, which reside at different toroidal locations of 97,
137, 157, 277, 307, 322, and 340 degrees.
2.4.1 Time Calibration for MIR and ECEI in the Laboratory
In DIII-D, the ECEI and MIR systems share the same 270° man-hole port and the zoom lens in
the optics. The MIR and ECEI data acquisition systems are housed in the DIII-D Michelson Lab,
and they share a common IF frequency band; ECEI has 2-9.2 GHz pass bands, while MIR has 110 GHz pass bands. The ECEI system measures its IF power level, while MIR measures the
quadrature IF signals (both its amplitude and phase). Consequently, the input signals are chosen
to be purely amplitude modulated (the power versus time is a sinusoidal function); ECEI will
yield a sinusoid output, MIR’s amplitude square will also result in sinusoid output. The input
signal is chosen to be 2.63 GHz, the AM amplitude is set to 80%. The AM frequency varies from
1.3 to 364 kHz for different shots. Table 2.2 lists the AM frequencies, the calculated phase
difference, and time delay from ECEI to MIR system. The time delay is calculated to be between
5.92 to 6.35 μs (the first value is not accurate since the phase delay is too small), which matches
the expected data calculated from the filter’s group delay data.
Phase difference from
ECEI to MIR (rad)
1.3
-0.040
5.3
-0.19
12.3
-0.47
43.3
-1.72
114.3
-4.51
164.3
-6.46
214.3
-8.35
264.3
-10.1
314.3
-12.0
364.3
-13.9
Table 2.2: Time delay measurement by the phase delay
Frequency (kHz)
Time Delay from ECEI
to MIR (μs)
4.92
5.92
6.09
6.35
6.28
6.25
6.20
6.14
6.09
6.08
Suppose the initial phase difference of those two systems is unknown, and then a linear fit will
resolve the problem. For this case, the linear fit is phase difference=-0.0383*frequency-0.050 as
shown in Fig. 2.25. First, the intersection -0.05 is true phase differences, which is calculated to
be very close to zero compared with the π phase. Second, the slope gives us the -2πt value; we
can divide by -2π to obtain the time delay from the ECEI system to that of the MIR system,
which is 0.383*1000/(2* π ) =6.09 μs.
Phase Difference (rad)
Frequency (kHz)
Fig.2.25: Calculated phase difference from the ECEI system to the MIR system versus the
amplitude modulated frequency. The red dotted line is the linear fit.
The ECEI and MIR systems both use the same type of digitizer and the same trigger signal.
Consequently, their time delay is mainly associated with the signal processing sections. The
ECEI system uses three stages of low pass filtering. The first stage is a fixed 7th order, 650 kHz
linear phase filter (manufacturer; Linear Technology Corporation, model LTC1069-7) which has
a group delay of 1.3-1.5 μs; another one is an adjustable 10th order, tunable linear phase filter
(LTC1569-7) which has a group delay of 3.7-4 μs as the cutoff frequency is set to 400 kHz. The
last stage is two 1st order RC filters, which gives a combined time delay of 1.75 μs. Therefore,
there will be a total delay of 6.75-7.25 μs to the signal. In the case of MIR, a single Coilcraft,
Inc. 7th order elliptical filter is used which results in about 0.5 μs signal delay. Consequently,
ECEI should be retarded from MIR by approximately 6.25-6.75 μs.
2.4.2 Time Calibration for the ECE and Magnetic Systems in the Laboratory
The ECE and magnetic systems employ different types of digitizers and triggers, which provide
the major contribution to the timing difference between the two systems. Specifically, the ECE
system uses a 500 kHz sampling rate digitizer with a -50 ms trigger (with respect to plasma start
up). The magnetic system can vary the sampling rate (from 50 to 1000 kHz) and trigger signals;
in this dissertation it uses a 200 kHz sampling rate digitizer with a-115 ms trigger. Fortunately,
there is a fiber-optic system that connects the ECE lab with the annex where the magnetic
digitizers are located, so this provides a direct method of measuring the time delay for both
systems. One simple calibration approach is to input a square wave to both systems and then
compare the phase delay of the harmonics of the input frequency to obtain the time delay.
First, the signals are down-sampled to 100 kHz in digitized data to provide the same time bases.
The Greatest Common Divisor (GCD) of the sampling frequency and the input signal frequency
determine its valid digitized cycle; to obtain an accurate phase, this cycle needs to be sufficiently
long to ensure that different parts of the signal are sampled. Consequently, their GCD needs to
be smaller than the input signal frequency; however, it cannot be too small because that would
require too many data points to perform the analysis. Therefore, in the analysis, the input
frequencies are chosen to be 110 Hz. Therefore, compared to both digitized frequencies, its valid
cycle frequency is 10 Hz, which gives 100 ms valid time. In addition, the square wave is chosen
to give some harmonic frequencies to analyze the phase, and its harmonic amplitude decreases
linearly with respect to its harmonic number; since the digitizer has 14 bit resolution, this results
in a harmonic coverage up to 250. Note that the time delay for the fundamental harmonic is not
accurate since the phase delay is too small which results in significant inaccuracy in the time
delay result. From its 11th harmonic frequency to its 251st harmonic frequency, a linear fit for
these harmonics is obtained and shown in Fig. 2.26 The linear fit is the phase difference=0.0943*frequency-0.036. First, the intersection is very close to zero compared with the π phase.
Phase Difference (rad)
Second, the slope gives the time delay from the ECE to magnetic data, which is 15.0 μs.
Frequency (kHz)
Fig. 2.26: Calculated phase delay at this frequency versus input’s harmonic frequency. The red dot is the linear fit;
the intersection point reveals the error bar to be zero, and the slope gives the 2π times the time delay from the
magnetic data to the ECE data.
2.4.3 Time Calibration Using the 3/2 NTM
To determine the time delay for all four systems, the response to the same MHD events need to
be measured. In particular, the 3/2 NTM [39] is an excellent candidate for the time calibration.
First, the frequency range is relatively large; it ranges from about 40 kHz to around zero in
locked mode, but to ensure accurate phase information, 40-10 kHz is used in the data analysis.
Secondly, it is very stable during a plasma discharge. They can easily last for 4 seconds or so in
DIII-D, which makes them quite suitable for the phase analysis. Last, but not least, NTMs cover
at least 14 cm continuously in radial extent. Therefore, the mode might be observed on 7-8
channels in ECE continuously; of which 4-5 continuous channels have a constant phase inside
the islands, which greatly simplifies the phase measurement for the ECE and ECEI systems. In
addition, the core 3/2 NTM has stable coupled boundary perturbations, which makes the MIR
and magnetic system phase measurements possible.
In the actual case, the ECE, ECEI, and MIR systems do not have magnetic probes at the same
toroidal angle. However, the ECEI and MIR systems are sharing the same toroidal angle;
therefore, their time calibration will be introduced firstly. The first step is to choose the times
when the 3/2 NTM amplitude is stable in the two systems, which usually means several
milliseconds away from the ELM time. Then, we find the 3/2 NTM frequencies on the two
systems, and determine whether they match with each other. The next step is to determine the
correct radial location in the midplane for the ECEI and MIR systems.
In the shot 153732, there was a very strong and stable 3/2 NTM lasting from 2 to 3 s. Also,
during this time the ECEI HFS1302 stay inside and very close to the 3/2 surface, and there are
about 30 Type-I ELM events during this time which still give sufficient time in between for
phase analysis. MIR07P3 is the calculated phase from the vertical channel 7 and radial channel 3
in the pedestal’s midplane. Over time during this shot, the plasma rotation speed will change,
which will result in the evolution of the 3/2 NTM mode frequency. Therefore, difference phases
between ECEI and MIR data will be obtained for different frequencies. The phase differences
between ECEI channel HFS1302 and MIR channel MIR07P3 are plotted versus the NTM mode
frequency in Fig. 2.27. From the plot, it is clear they satisfy a linear relation, and the linear fit is
phase difference= -0.0386*frequency-0.0033. It gives a time delay of 0.0386*1000/(2* π)= 6.15
μs between ECEI and MIR, which is in good agreement with the laboratory result of 6.09 μs.
Phase Difference (ECEI-MIR)
The intersection point is very close to zero.
Frequency (kHz)
Fig. 2.27: Phase difference from ECE to MIR versus mode frequency. Solid line is the evolution with time; dotted
line is the linear fit of the data.
However, the magnetic probe system has many toroidal sets, so it is possible to calculate the
magnetic fluctuation at the ECE or ECEI toroidal locations. Similar to the above, we chose the
right times and right radial channels for the ECE and ECEI systems. Then, we calculate the
phase of these toroidal sets, and plot their phases at their toroidal locations. Following the
preceding, a linear fit for the magnetic fluctuation data is obtained and tested to determine
whether it is an n=2 mode. Finally, the phase difference between the fitted line and its point is
calculated.
As an example, the original data of Fig. 2.28 are taken between 2144 to 2149 ms, when the NTM
is stable and is 25 kHz in all three systems. Both ECE CH10 and ECEI HFS1301 stay inside and
very close to the 3/2 surface. Figure 2.28 shows the calculated relative phase of the magnetic
data, ECE and ECEI data to 97° magnetic data. The asterisks correspond to the magnetic data,
and the line is the fitted data based on it, which proves that it is an n=2 mode. The diamonds are
the ECE data with triangles indicating the ECEI data. Then, the phase differences for ECE and
Relative Phase (rad)
ECEI to the same toroidal angle can be calculated as shown in the dashed line in Fig. 2.28.
ECEI
ECE
Toroidal Phase (rad)
Fig.2.28: The relative phase to 97° magnetic data at the 3/2 NTM mode frequency versus toroidal angle. The
asterisks correspond to the magnetic data, and the line is the fitted data based on it; the diamonds are the ECE data
with triangles the ECEI data. Using this method, it is possible to calculate the phase difference between the ECE
and ECEI signals and the magnetic fluctuation data at the same toroidal locations, as shown in each dotted line.
The phase difference between ECE channel 10 and the magnetic fluctuation is plotted in Fig.
2.29. From the plot, it is clear there exists a linear relation, and the linear fit is the phase
difference=-0.0854*frequency-1.56841. It gives a time delay of 0.0854*1000/(2* π)=13.6 μs
between the ECE and magnetic data. This result is very close to the 15 μs obtained from the
Phase Difference (rad)
laboratory calibration result.
Frequency ( kHz )
Fig. 2.29: Phase difference from ECE to magnetic versus mode frequency. Solid line is the evolution with time;
dotted line is the linear fit of the data.
The phase difference between ECEI channel HFS1302 and the magnetic fluctuation is plotted in
Fig. 2.30. From the plot, it is clear that a linear relation exists, and the linear fit is phase
difference= -0.0958*frequency-1.602. It give a time delay of 0.0958*1000/(2* π )= 15.2 μs from
ECEI to magnetic data.
Phase Difference (rad)
Frequency ( kHz )
Fig. 2.30: Phase difference from ECEI to magnetic versus mode frequency. Solid line is the evolution with time;
dotted line is the linear fit of the data.
2.4.4 Time Calibrated Data of the 3/2 NTM Responses
Now all four systems are time calibrated, to the ECEI system, magnetics is in advance by 15.2
μs, the MIR system is in advanced by 6 μs, and the ECE system is in advance by only 1.6 μs. A
stable 3/2 NTM time 2866-2876 ms, where the NTM frequency is 14.2 kHz, are chosen for
study. ECEI HFS1302, MIR 07P3, ECE Ch10 are chosen for same reasons, magnetic fluctuation
data are chosen to be 277° which is closest to ECEI toroidal angle. First, they are time calibrated.
Then, the poloidal magnetic fluctuation data are converted to the poloidal magnetic field data.
The magnetic fluctuation data are taken from -3.115 s (relative to plasma startup) when the
poloidal magnetic field is close to zero, so it can be converted into the absolute magnetic filed
data by simply integrating the signal. And there is a corresponding low sampling rate absolute
magnetic field data, which shows good match. Then, the phases for the ECE system and
magnetic field data are adjusted respectively to the ECEI system due to their toroidal angle
difference. In the case of 3/2 NTM, the magnetic field phases are adjusted by 2*(277-270)/360
*(2* π), and the ECE phase has 2*(81-270)/360*(2* π) adjustment. Then, the frequency is
chosen near the 3/2 NTM, and the time chosen when all the amplitudes of four systems are
ECE
Bp
MIR
ECEI
stable. One example is plotted in Fig. 2.31.
Time (ms)
Fig. 2.31: Time calibrated data of ECEI, MIR, poloidal magnetic field, and ECE. Black line with pluses is the ECEI
data; orange line with asterisks is the MIR data; green line with diamonds is poloidal magnetic data; blue line with
triangles is ECE data.
From Fig. 2.31, the temperature inside the island, the density in the pedestal, and the poloidal
magnetic field outside the plasma are in phase. This observation verified a recent 3/2 NTM mode
study [40], in which 3/2 NTMs are identified to be a combination of the global kink response and
a local tearing response. At the O-point, inside the island, the temperature will reach its
minimum value due to the temperature flatness of the magnetic island. Due to the in-going
magnetic line, the magnetic data will reach their absolute minimum, both toroidal and poloidal
magnetic field; and at the edge, the density will drop to a minimum with the magnetic field.
Under the circumstance of regular Ip like shot 153732, poloidal magnetic field is positive, so its
absolute minimum is its minimum. Consequently, the magnetic field, the plasma density, and the
electron temperature perturbations are in phase.
2.4.5 Phase Difference Temporal Evolution
Below is an example of the simultaneous imaging of the NTM. Figure 2.32 shows its relative
position on the equilibrium. The ECEI system is a dual-array system; the HFS ECEI is its high
frequency array set and sits inside the 3/2 surface, while the LFS ECEI is its low frequency array
and sits near the edge. MIR is on the pedestal of the plasma.
Figure 2.32: Plasma equilibrium and the diagnostic coverage block diagram. Blue solid line is the q surface,
dashed line is the rho surface. Red rectangles are ECEI location, the left one is the HFS ECEI, and the right one is
the LFS ECEI; Green rectangle is the MIR location.
Figure 2.33 shows the time evolution of the NTM mode; each picture is spaced by π /4 phase of
the NTM mode. Inside the island, it is clear that there are two peaks on the HFS ECEI’s radial
direction. It is believed that this response is an overlap of one kink-like mode and the tearing
mode near 3/2 surface [40], which introduces the double peaks at two radial locations. On the
LFS ECEI, there is a ‘ghost channel’ [41], which is caused by the density fluctuation and its
effect on the re-absorption of the ECE radiation. This ghost channel shows exactly where the
Last Closed Flux Surface is located on the imaging. For the MIR system, which measures the
right-hand X-mode cutoff surface drift, positive phase means that either the density or magnetic
field is increasing. Here, it is clear that the phases of the temperature inside the 3/2 surface, the
temperature perturbation in the pedestal, and the density fluctuation in the pedestal are all three
in good agreement.
Figure 2.33: Time evolution of the 3/2 NTM perturbation observed on the HFS ECEI (figure a), the LFS ECEI
(figure b) and MIR (figure c).
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Chapter 3
RF Spectrometer Design and Laboratory Characterization of
Millimeter-wave Bursts
Intense bursts of mm-wave emission with durations of 5-10 μs have been observed by both
Electron Cyclotron Emission (ECE) radiometer [1, 2] and Electron Cyclotron Emission Imaging
(ECEI) systems [3] during edge localized modes, Quiet H-mode (QH) modes, and the precursor
before disruptions. Both the ECE radiometer system and the ECEI system employ heterodyne
detection methods and have overlapping intermediate frequency (IF) bands. A new RF
spectrometer, spanning this IF frequency range of approximately 2-10 GHz, has been installed
on the DIII-D tokamak in order to more fully characterize the frequency, intensity, and
localization of these bursts, which will be introduced firstly in Section 3.1. Subsequently, the
data for the H mode case and QH-mode case will be discussed in the following sections. The
needed model to explain the bursts is presented in Section 3.4, followed by a trial model
proposed by the author.
3.1 RF Spectrometer Design
3.1.1 ECE Diagnostic System Introduction and IF Frequency Response
On the DIII-D tokamak, an ECE radiometer, a 40 channel system in year 2012[4], (there was a
recent addition of 8 channels in 2013 which is not in the content of this dissertation) is the most
important and accurate means for determining central electron temperatures of many discharges.
The Michelson Interferometer, a standard diagnostic for measuring electron cyclotron
emission[5], is used to determine the absolute temperature measured from the ECE
radiometer[6]. The ECE radiometer applies heterodyne methods to measure the radiation power,
and it employs only a single down conversion and detection for ease of calibration. To help
analyze the IF interference, the IF frequency response of its electronics are tested.
A fast-scanning Michelson Interferometer (FSMI), a twin of the instrument employed on
TFTR[6], has been operating at DIII-D since 1987 for the diagnostics of Electron Cyclotron
Emission. The FSMI is configured as a Martin-Puplett polarizing type [7]. It provides frequency
resolution of 4 GHz and a frequency range of 50-300 GHz that covers the current ECE
radiometer range of 83-131 GHz. The scanning motor is typically run at 20 Hz, giving an
integration time for each scan of ~6 ms, and the calibration error is 5%.
Below is a simple schematic illustrating the heterodyne method of detecting the ECE radiation
power. The ECE radiation from the plasma goes to the ECE system through a WR-10
waveguide; it first passes through the 110 GHz notch filter which protects the system from stray
ECRH power, and then it passes through two 3 dB couplers and is then divided into three parts.
Each one is mixed with separate 81 GHz, 96 GHz, and 112 GHz LOs after going through their
corresponding high pass filters. Then each signal goes through a 35 dB amplifier followed by a
0-59 dB adjustable thumbwheel attenuator for amplitude adjustment, and then goes to each
corresponding card. Card I and Card II, which were originally in the system, had a very similar
design. They divided the signal into 16 channels, and the signal at each channel has a different
bandpass filter. These filters have a 500 MHz bandwidth with center frequencies ranging from
2.5 to 17.5 GHz at 1 GHz steps; in Card I, they are labeled from ECE1 to ECE16 in this order
and in Card II are labeled ECE17 to ECE32. Card III is an upgraded card, and has 8 channels,
with 1 GHz bandwidth with center frequency from 3-17 GHz in 2 GHz steps, and they are
labeled ECE33-ECE40 in this order. Here, one very unique design is that the CH16 and CH17
channels are about in the same band, which extends from 98.25 to 98.75 GHz. Making use of
this overlap, calibration of the total system is facilitated since the absolute temperature should be
very close, and it helps reveal possible abnormal mixer activities, which will be discussed in the
following Section 3.2.
Figure
F
3.1. Schematic of the DIII-D ECE radiometer.
In the frequency response test, an Agilent Technology N5183A MXG Microwave Analog Signal
Generator, which can provide a signal sweep from 100 kHz to 20 GHz, is used. The same trigger
(-50 ms to plasma start-up) is used in the signal generator and digitizer, and the sweep output is
also digitized. In testing, a signal, with -60 dB, 1-20 GHz linear frequency sweep in 8 seconds
with 3 ms dwell time, is input to each card for the frequency response test.
Figure 3.2 is the frequency response for Card I, of which the left part corresponds to ECE1ECE8 while the right part is ECE9-ECE16. Figure 3.3 is the frequency response for Card II, of
which the left part corresponds to ECE17-ECE24 while the right part is ECE25-ECE32. One
minor issue is that it does not have larger attenuator over the stop band for Card I and II. For
example, for the ECE6 which is the sixth channel from left to right in Figure 3.2 left, its pass
band is 7.25 to 7.75 GHz with a 500 MHz bandwidth, however the signal level from 2-3 GHz is
about 10 dB lower than the signal level at the peak of the pass band, so it only approximately
gets as low as the 10 dB attenuator in the stop band. From the frequency response plot, it is noted
that ECE14 (Fig.3.2 right) has an unusual frequency response, the designed center frequency for
it is 15.5 GHz while the actual center is 15.15 GHz; but luckily this offset does not cause the
overlap of the pass band to the pass band of its adjacent channels. ECE28 (Fig.3.3 left) has a
wider bandwidth of 900 MHz rather than the regular 500 MHz. Card III has a better attenuation
over the stop band; it has at least 16 dB for all the channels.
Figure 3.2. Frequency Response of Card I. Left part is the lower 8 channels, and right part is the
higher 8 channels.
Figure 3.3. Frequency Response of Card II. Left part is the lower 8 channels, and right part is
the higher 8 channels.
Figure 3.4. Frequency Response of Card III.
As discussed earlier, the ECE16 and ECE17 channels have an overlapped frequency band;
Fig.3.5 is their total frequency response assuming that the mixer has a flat frequency response in
their band. Here, the correlation is calculated to be 0.93.
Amplitude (a.u.)
ECE16 (Solid
with Diamond)
.
ECE17 (Dashed
with Triangle)
Frequency (GHz)
Figure 3.5. Overlap of ECE16 and ECE17 channels.
3.2.2 IF Electronics Modification and Its Frequency Response
The ECEI system has a different IF response from the ECE system; it has 700 MHz video
bandwidth, and 600 MHz / 900 MHz spacing for narrow/ wide zoom. The first step is to match
with the video bandwidth. The common one in the ECE electronics is 500 MHz for Cards I&II,
and corresponds to the majority of the cases where the bursts occur. Figure 3.6 displays the IF
response of the IF board. The original (in blue) is the current setting with two 370 MHz LPFs
(manufacturer: Mini-Circuits, model LFCN225); the green line is the modification to LPF160
(LFCN160, cutoff 250 MHz). The yellow line is the modification to LPF160‘ the pink line is the
modification to LPF120 (LFCN120, cutoff 200 MHz)’ and the red line is the modification to two
LPF120s. The total bandwidth of the ECEI electronics is twice its IF bandwidth due to double
mixing in the second down conversion of the signal. Consequently, changing one original LPF to
LPF160 will result in 250 MHz bandwidth in the IF board and 500 MHz in total.
Amplitude (a.u)
1
Original
0.9
One LPF160
0.8
Two LPF 160
0.7
One LPF 120
Two LPF 120
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.05
0.1
0.15
0.2
0.25
Frequency (GHz)
0.3
0.35
0.4
0.45
Figure 3.6. Frequency Response of the IF board in the ECEI modules when utilizing different LPFs.
It is then necessary to change the center frequency to 1GHz steps. In Table 3.1, the VCOs used
to generate the LO for each channels of the ECEI system are listed. The VCO CVCO55BE2560-3200 is manufactured by Crystek Microwave, while the others are by Hittite Microwave
Corporation. Without changing the VCOs, the tuning voltage can be varied to obtain a center
frequency from 2.5-8.5 GHz with 1 GHz steps, with Channel 5 not used.
Ch
1
VCO Model
CVCO55BE-
Tuning
Frequency setting
Frequency setting for
frequency
in narrow/ wide
RF spectrometer
range (GHz)
zoom (GHz)
(GHz)
2.4-3.4
3.4 / 2.5
2.5
2560-3200
2
HMC390LP4
3.4-4.0
4.0 / 3.4
3.5
3
HMC429LP4
4.2-5.1
4.6 / 4.3
4.5
4
HMC430LP4
4.6-5.6
5.2 / 5.2
5.5
5
HMC431LP4
5.8-6.9
5.8 / 6.1
6
6
HMC505LP4
6.3-7.8
6.4 / 7.0
6.5
7
HMC532LP4
6.5-8.2
7.0 / 7.9
7.5
8
HMC506LP4
7.5-8.9
7.9 / 8.8
8.5
Table 3.1
VCO model and frequency range for each of the channels. The center frequency
in the ECEI and RF spectrometer systems are listed as well.
The modified ECEI module has better stop band response as shown in Fig.3.7, where the
smallest attenuator in the stop band is the second harmonic of Ch1 at 5 GHz, which is 23 dB
lower than the main lobe. After the above modifications, the frequency responses of these
electronics are very similar to the ECE channels; Table 3.2 is the calculated correlation to ECE1
to ECE7, in which the diagonal is very close to unity, and other parts are close to zero. Figure 3.8
is the frequency response for the modified ECEI CH4, ECE4, and ECE20; they show good
agreement over the pass band.
Amplitude (a.u.)
Frequency (GHz)
Figure 3.7
Modified
The frequency response for the modified ECEI module (without Ch5).
CH 1
CH 2
CH 3
CH 4
CH6
CH 7
CH 8
ECE1
0.963548
-0.0587102
-0.0623275
-0.0675792
-0.0684078
-0.0695962
-0.0700324
ECE2
-0.0443931
0.856673
-0.0568272
-0.066872
-0.0686214
-0.0707792
-0.0706619
ECE3
-0.0475142
-0.051469
0.943829
-0.0678272
-0.0691843
-0.0712521
-0.0716013
ECE4
-0.0407185
-0.046853
-0.0581231
0.957614
-0.0699782
-0.0765882
-0.0769803
ECE5
-0.0424018
-0.0486787
-0.0598832
-0.0736863
0.936709
-0.078223
-0.0786552
ECE6
-0.0281007
-0.0379813
-0.0569491
-0.0798907
-0.0826663
0.931337
-0.0864848
ECE7
-0.037188
-0.0449541
-0.0589167
-0.0761752
-0.0776034
-0.0810531
0.919488
ECEI CH
Table 3.2
Correlation Between modified ECEI modules to the first 7 channels of the ECE
system. Red data are the corresponding channels in the diagonal, which is close to 1; others are
close to zero.
Amplitude (a.u.)
Modified ECEI 4
ECE4
ECE20
Frequency (GHz)
Figure 3.8 The frequency response for Ch4 of the modified ECEI module (black solid line with
diamonds), ECE4 (yellow dot-dashed line with plus), and ECE20 (blue dashed line with
triangles).
3.1.3 RF Spectrometer and Application
The RF spectrometer was mainly designed for the RF interference, so it needs to obtain the RF
signal from the plasma directly, as shown in the blue part in Fig. 3.9a. A slotted antenna, with 19 GHz frequency bandwidth, is positioned near the 270-degree port as shown in Fig 3.9b. There
is an elliptical lens with a diameter of 70 mm attached in the dielectric side, which is for
improved signal detection. This application will be discussed more in the following Sections 3.2
and 3.3.
Figure 3.9 a) Schematic of the RF Spectrometer. b) Slotted antenna and elliptical lens.
The lens and antenna can also be replaced by a regular down-converted signal from the antenna
arrays; usually, the signal is chosen to be the central channels of ECEI, as shown in the green
part of Fig. 3.9. Following this, there is a power divider, which separates the signal into two
parts; one goes to the regular ECEI module, and the other goes to the modified ECEI modules.
For the regular ECEI module, some additional attenuators (1-50 dB variable) can be added for
measurement of the power level of the intense emission. Its 8 channels are labeled as RFSP01RFSP08 (Radio Frequency SPectrometer) for short. For the modified ECEI module, it can
provide 7 contiguous ECE channels; its 8 channels are labeled RFSP09-RFSP15 after the regular
ECEI module. This modified ECEI module is useful for the temperature calibration using the
ECE system, which is less relevant to the burst study and will be discussed in the following.
As discussed in Section 3.2, the modified ECEI modules have very similar RF frequency
response to that of the ECE system, and will have 7 contiguous channels. It is noted that the ECE
system is located at the toroidal 81° port, and the ECEI system is sitting at the 270° port. Since
there will be 7 channels in common with the ECE system, it is convenient to have 7 channels
calibrated for absolute temperature. This will help determine the toroidal mode number for fine
structure and the absolute temperature of the ECEI system. Below are some data from shot
153857. The RF spectrometer gets the power divided signal from HFS12, which is less than 1 cm
below the midplane. The HFS LO frequency is set to 89 GHz, so it will place the RF
spectrometer’s seven contiguous channel at 91.5, 92.5, 93.5, 94.5, 95.5, 96.5, and 97.5 GHz,
which correspond to the ECE09, 10, 11, 12, 13, 14, and 15 channels. Table 3.3 is the listed
correlation from data from the modified ECEI Channels to their corresponding channels. From
the table, most of the channels do have stronger correlation to their correspondents.
Modified
CH 1
CH 2
CH 3
CH 4
CH6
CH 7
CH 8
ECE9
0.972856
0.980345
0.961892
0.952077
0.930917
0.922386
0.912902
ECE10
0.967564
0.982579
0.972446
0.969537
0.954487
0.948056
0.939266
ECE11
0.9561
0.978246
0.976268
0.980374
0.971711
0.967584
0.959575
ECE12
0.938978
0.967932
0.973406
0.984937
0.983236
0.981625
0.974467
ECE13
0.918278
0.952769
0.964845
0.98339
0.988614
0.989776
0.983512
ECE14
0.901144
0.939259
0.954914
0.97816
0.988753
0.992858
0.987483
ECE15
0.892235
0.932364
0.948208
0.973822
0.987109
0.992744
0.988436
ECEI CH
Table 3.3 . Correlation between RF Spectrometer data and corresponding channels in the ECE
system. Red data are the corresponding channels in the diagonal, which also is maximum for
both in row and column, and it is very close to unity; one blue one is not the maximum in row or
column, but it is very close to unity; others are very close to unity, but smaller.
The time evolution of the plasma temperatures of the modified ECEI module Channel 8 and
ECE15 are shown in Figure 3.11. From the data, they have very similar shapes. However, since
the two systems are digitized with different frequencies, the noise levels are not the same.
Figure 3.10 The time evolution of the plasma temperatures of the modified ECEI module
Channel 8 and ECE15.
3.2 Millimeter Wave Bursts in H mode
3.2.1 Introduction to Millimeter Wave bursts in H mode
H-mode (high confinement) plasma operation is believed to be the advanced scenario for future
fusion operation because of its high density, high temperature, and good confinement [9]. Intense
bursts, which are observed in the ECEI and ECE radiometer systems, are a common
phenomenon in DIII-D [1-3] for H-mode discharges with edge-localized modes (ELMs). JET
and TFTR also reported similar ECE bursts [10-12] that are induced by ELMs. Several models
have attempted to explain the bursts [13-14], but they are not fully understood for the generation
mechanism up to now. More characteristics of these bursts at DIII-D have been examined in this
dissertation research to help discern their origin.
As an example, Shot 148762 shown in Fig. 3.11 is the ITER relevant collisionality (νe*≤0.15)
shot [15]. In this figure, a) is plasma current, b) is the toroidal magnetic field, c) is the α line
emission intensity; d) is the LFS1301 (frequency at 80.5 GHz), which is one of the ECEI
midplane channels outside of the plasma LCFS; and e) is the ECEVF01 (frequency at 83.5)
which is one of the ECE channels inside the plasma LCFS. This shot is a Neutral beam injection
(NBI) heated high beta plasma, which develops into H-mode around 0.8 s. This plasma has typeI ELMs appearing during 1.1-3.2 s and 3.8-5 s, and does not have ELMs during the time period
of 3.2-3.8 seconds because of the 4 kA RMP ELM suppression [15]. The bursts, observed on
both the ECEI and ECE channels, are highly correlated with the Dα signal, which is related to
the ELM temperature crashes. However, there is no direct amplitude relation between the
amplitude of the Dα signal and the ECE and ECEI signals. These bursts of radiation do not
precisely synchronize with the Dα emission; however, they begin at the earliest onset of the
magnetic perturbations, approximately 100 μs before the rise in Dα emission detected by
filterscopes viewing the divertor, and continue for another 100 μs afterwards [3].
Figure 3.11 Example of the H-mode bursts. A) is plasma current, b) is the toroidal magnetic
field, c) is the filter scope data; d) is the LFS1301 which is one of the ECEI channel; e) is the
ECEVF01 which is one of the ECE channels.
In 2D imaging studies by ECEI, spikes in emission appear at frequencies both above and below
the cold-resonance of the LCFS, and may vary in frequency by several GHz over the duration of
a single burst. The most intense spikes appear in a region of ±10 cm about the equatorial plane,
but may also be observed at the extreme vertical extent of the ECE-I view, which is ±25 cm for
the case shown [3]. Usually, the emission is only significantly high in one channel for either the
ECEI or ECE radiometer systems, so that the bandwidth is less than or equal to ECE’s one
channel bandwidth of 500 MHz[1]. The origin of the emission varies randomly in different
locations close to the ELM time, with multiple structures simultaneously appearing to propagate
in both co- and counter-directions with respect to the observed rotation of the core plasma in the
laboratory frame [3]. Under some conditions, the frequency of the burst appears to be
downshifted over time, but it is not a systematic feature; examples for frequency upshifts can
also be found[1].
Forward modeling [16] of the expected diagnostic response has been performed for the
perturbation to the thermal electron population, as well as for bi-Maxwellian populations with a
significant fraction of energetic tail electrons. It is found that the thermal distribution of the
electrons cannot explain the observed temperature [3]. In the case of the thermal distribution
with a bi-Maxwellian population, the observed temperature cannot be higher than 4 keV even
with a 1 MeV electron tail, which is in contradiction with the fact that it will go up to 10 MeV.
Secondly, radiation appears strictly at the downshifted frequency, which is in contradiction with
the fact that the bursts happen both inside and outside the LCFS. Finally, the highest energies
resonate below the accessible window, which contradicts the fact that the highest energies
propagate in the radial direction.
3.2.2 RF Interference Elimination
Both the ECE radiometer system and the ECEI system employ heterodyne detection methods
and have overlapping intermediate frequency (IF) bands (2-10 GHz), so, it is possible that the
bursts come from the IF bands and are sufficiently strong to cause noise in the two systems.
Consequently, the RF Spectrometer is installed near the tokamak 270° port and receives the IF
band directly.
In shot 150757, regular bursts are observed during 2.5 to 4.8 s for both the ECEI and ECE
systems. One example of the bursts at time 4.214 s is shown in Fig. 3.12. The red one is the RF
spectrometer CH1 data, which is the 2.5 GHz channel of the regular ECEI module. The blue
ones are the ECEI channels, and their IF channels are also 2.5 GHz. The channels from top to
bottom are also the vertical distribution in temperature imaging from top to bottom. From this
figure, there is no correlation with the amplitude with the RF spectrometer data with the bursts of
the ECEI data on its corresponding channels. It is therefore concluded that the RF interference
contributions to the bursts are very small compared with the true millimeter radiation.
Figure 3.12 Data of the RF spectrometer and bursts for ECEI. The red one is the RF
spectrometer CH1 data, which is the 2.5 GHz channel of the regular ECEI module. The blue
ones are the ECEI channels, and their IF channels are also 2.5 GHz. The channels from top to
bottom are also the vertical distribution in temperature imaging from top to bottom.
The bursts for the RF spectrometer and ECE data at the same time 4.214 s are shown in Fig. 3.12.
All the RF spectrometer data in this figure are from the modified ECEI module, which is
intended to mimic the ECE IF band frequency responses. Three pairs of data from the ECE
system and the RF spectrometer data are shown; the plot with the same color shares the same IF
center frequency and bandwidth. From this figure, there is no correlation with the amplitude with
the RF spectrometer data with the bursts of the ECE data on its corresponding channels.
Consequently, it is concluded that in the ECE data, the RF interference contributions to the
bursts are very small compared with the true millimeter radiation
Figure 3.13 Data of the RF spectrometer and bursts for ECE. A) is the ECE Ch1 of frequency
fLO+2.5 GHz, here fLO=81 GHz; b) is the ECEVF01’s corresponding IF channel with f=2.5 GHz.
c) is the ECE Ch4 of frequency fLO+5.5 GH; d) is the ECEVF04’s corresponding IF channel with
f=5.5 GHz; e) is the ECE Ch7 of frequency fLO+8.5 GH; d) is the ECEVF07’s corresponding IF
channel with f=8.5 GHz.
3.2.3 Intensity Characterization
The RF Spectrometer can also be used to characterize the intensity of the regular 2nd harmonic
ECE bursts. As shown in Fig. 3.14, a signal with some bursts is power divided into two parts;
one goes into the regular ECEI modules, while the other passes through another 20 dB attenuator
and then goes to the ECEI modules. Subsequently, they are first calibrated by some medium
bursts that do not saturate either module. Then, by the regular times of the regular ECEI
modules, it is possible to obtain the absolute temperature by comparison with the temperature
profiles near the plasma pedestal. Finally, the intensity of the bursts can be obtained by using this
approach.
Figure 3.14 Bursts intensity calibration using RF Spectrometer.
One example is shown in Fig.3.15. In 3.15 a), a medium burst near time 3.316 s generates a very
similar shape in both modules, and it reads 3.62 V in the regular module and 0.0265 V in the 20
dB+ECEI modules. Then, in part b) of this figure, from the regular module, we know its
background voltage is 0.02 V without the burst, and from the edge temperature profiles, it is
close to 1 keV. Finally, the strongest burst shown in the 20 dB+ECEI module gets a reading of
1.82 V. Therefore, the strongest burst temperature is
1 keV/0.02*(3.62/0.0265)*1.82=12,000 keV=12 MeV.
This high radiation temperature also proves that it cannot be a thermal effect.
Figure 3.15 Burst intensity calibration using the RF Spectrometer.
3.2.4 Imaging
Due to the fact that the bursts are so strong, 30 dB attenuators are added in the ECEI LFS array.
One example of a single burst in 4.5 s of shot 150757 is shown in Fig 3.16. Part a) is the time
trace of the LFS1202; and part b) is the imaging obtained from the ECEI LFS data. Part c) is the
imaging if only 10 dB attenuators are added; in this case, the channels will saturate (i.e. reaches
the maximum voltage of 5 V) if the signal reaches 0.05 V in the 30 dB cases. From part b) of this
figure, there is no clear radial or poloidal movement of this burst, but it is not a systematic
feature. From part c) of this figure, this burst changes its vertical spread with time, but it is not
stuck to a flux surface.
Figure 3.16 Temporal evolution of a single burst. Part a) Temporal evolution of Channel
LFS1202, its channel location is shown in red dots in frame (1) of part b) and part c). Part b),
imaging of ECEI LFS with 30 dB attenuators. Part c), imaging of ECEI LFS if with 10 dB
attenuators.
Another example of a single burst in 4.18 s of shot 150757 is shown in Fig 3.17. Part a) is the
time trace of the LFS1202; and part b) is the imaging obtained from the ECEI LFS data. From
part a), and frame (1-3) of part b), the channel LFS1202 is very close to the burst in frame (2),
but the burst is very localized and does not reach channels LFS1302. From frame (4) to frame
(13), another burst is generated. It moves outward radially and downward vertically firstly, and
then it moves inward and upward, and finally disappears.
Figure 3.17 Temporal evolution of a single burst. Part a) Temporal evolution of Channel
LFS1202, its channel location is shown in red dots in frame (1) of part b). Part b), imaging of
ECEI LFS with 30 dB attenuators.
The vertical and radial distributions of these bursts can also be obtained. From the vertical
distribution of the bursts shown in Fig. 3.18 a), it is clear that channels near the mid-plane have
strong bursts, especially those in a region ±10 cm about the equatorial plane. From the radial
distribution of the bursts shown in Fig. 3.18 b), the bursts are more likely to occur near the
LCFS, in a region ±2 GHz about the ECE radiation frequency in the LCFS in the equatorial
plane.
Figure 3.18 Burst distribution over the vertical and radial locations. Part a) Vertical distribution
of the burst, from top to bottom is also from top to bottom in ECEI temperature imaging; Part b),
Vertical distribution of the burst, from top to bottom, the frequency increases, and the radial
location decreases. Here, the LCFS frequency is approximately 85.9 GHz, which sits between Ch
2 and 3.
3.3 Millimeter Wave Bursts in QH-mode
3.3.1 Introduction to Millimeter Wave Bursts in QH-mode
For regular H-mode plasmas, the ELMs will dissipate large amounts of energy in a short time
and therefore introduce a huge challenge to the heat handling of the divertor[9]. In addition, they
can affect the β limit and reduce the core transport regions needed for advanced tokamak
operation. Quiescent H-mode (QH-mode) [17] plasma operation has been demonstrated to solve
these problems, which is ELM-free and yet has good density control. In QH-mode, the Edge
Harmonic Oscillation (EHO) plays an important role by driving particle flux into the divertor,
which helps the plasma to maintain constant density and radiated power levels.
As an example, Shot 146473 shown in Fig. 3.19 is a lower single-null plasma shape shot with
ITER relevant collisionality and pedestal beta [18]. This quiescent H-mode (QH-mode) is
sustained by magnetic torque from non-axisymmetric magnetic fields, which is a promising
operating mode for future burning plasmas. Using magnetic torque from n=3 fields to replace
counter-Ip torque from neutral beam injection (NBI), long duration, counter-rotating QH-mode
operation is achieved. In Fig.3.19, a) is the plasma current, b) is the toroidal magnetic field, c) is
the α line emission intensity; d) is the LFS1304 (frequency at 83.2 GHz), which is one of the
ECEI midplane channels located outside of the plasma LCFS; and e) is the ECEVF01 (frequency
at 83.5 GHz) which is one ECE channel close to the ECEI channel LFS1304. From the D-alpha
signal, the plasma reaches the H-mode around 1.1 s, and reaches QH-mode around 1.8 s and lasts
to the end of the shot. There are intense bursts during the time interval 2.4 to 4.0 s. Compared
with the regular ELMy bursts shown from 1.5 to 1.7 s, the bursts in QH-mode are more frequent.
Figure 3.19 Example of the QH-mode bursts. a) is plasma current, b) is the toroidal magnetic
field, c) is the filter scope data; d) is the LFS1304 which is one of the ECEI channel; e) is the
ECEVF01 which is one of the ECE channels.
It is found that there is a threshold level of the collisionality νei for ECE-EHO bursting [2]. In a
set of similar QH-mode discharges of 20 sequential DIII-D shots from 114933-114953, some
shots have the bursting mode while others do not. Comparing νei calculated at the start of the
EHO phase of the discharge and for the radius near the physical location of the mode indicates a
threshold of 17 ms-1 below which bursting occurs. Therefore, it is concluded that for bursts to
occur, a discharge must be sufficiently collisionless.
Also, it is noticed that the EHO bursts are in ECE channels upshifted from the resonance location
of the edge harmonic oscillation[2]. In contrast, for the ELM bursts in H-mode, the most intense
burst channels of the ECE and ECEI are usually observed in the channel downshifted in
frequency 1-3 GHz from the resonance frequency of the location of the precursor oscillation. In
addition, the bandwidth of bursts in both H-mode and QH-mode is believed to be less than 500
MHz, which is similar to the H-mode cases; while the intensity of the QH-mode bursts is smaller
than the bursts in H-mode cases. Consequently, whereas for ELM bursts Δf is often 3~6 GHz,
the continuous EHO burst Δf are always less than 2 GHz and more often Δf≤ 1GHz.
Another major finding is that the EHO bursts are synchronized with one particular EHO with
dominant EHOs present [2,3]. MHD behavior is not necessary, but occurs in most cases of the
bursts, like disruption precursor, ELM precursor, and EHOs. The EHOs can be observed at the
magnetic probes, so on some shots, the ECE bursting is found to be in phase with the probe
signal at a specific toroidal angle. Furthermore, the bursts observed on the ECEI system are
found to be rotating in the same direction and with the same apparent poloidal velocity as the n =
1 EHO on the same flux surface.
3.3.2 QH-mode Burst Conditions
Two conditions are required for the QH-mode bursts. One is that the plasma be relatively
collisionless; however, it has not been found yet that there exists an absolute collision frequency
threshold. Although, as found in reference [2], there does exist some threshold collision
frequency in similar shape. In addition, a threshold collision frequency in some particular shots
also exists for bursts to happen. The other condition is that electrons are transported from the
core and then get trapped near the edge. With the appearance of edge MHD behavior, the
electrons are more likely to be trapped, so the bursts are more likely to happen.
For the collisionless condition, one example of shot 121390 is shown in Fig. 3.20. In the figure,
the top is the bursting channels of the ECE system, while the bottom is the calculated value of
ne/Te1.5; here, ne is the line-average value along the radial direction, and Te is the measured
temperature from the ECE channel near the magnetic axis. This value is proportional to the
electron collision frequency, which is
,
where is the Coulomb logarithm with the usual value of 5-15. Comparing the times when
the bursts occur and when they do not as shown in this figure, it is apparent that it indicates a
threshold 1.9✕1012 cm3keV-1.5 of value of the ne/Te1.5 below which bursting occurs. In addition,
the electron collision frequency is 1.14 ms-1 if we assume =10.
Figure 3.20 The QH-mode burst dependence on the collision frequency νe. Top is the time history
of the ECE channel 9, bottom is the calculated value of the ne/Te1.5. Two vertical red lines mark
the starting and stop time of the bursts; one horizontal line marks the threshold values.
Another example is shot 149101 as shown in Fig.3.21; the top is the time history of the ECE
channels 10 in blue and 11 in purple; the middle is the calculated value of ne/Te1.5, where ne is the
line-average value along the radial direction, and Te is the measured temperature from the ECE
channel near the magnetic axis; and the bottom is the calculated ECH deposition power. The
ECH is turned on from 2.2 to 4.6 s, which matches with the burst duration. When ECH turns on,
the temperature increases, and the collision frequency decreases, and then the bursts show up.
Figure 3.21 The QH-mode burst dependence on the collision frequency νe. Top is the time history
of the ECE channels 10 in blue and 11 in purple, middle is the calculated value of ne/Te1.5, and
bottom is the calculated ECH deposition power. Two vertical blue lines mark the starting and
stop time of the bursts.
For the second condition, shot 153291 is a good example shown in Fig. 3.22. In this figure, from
top to bottom are four ECE channels from low frequency to high frequency, one ECEI channel,
and two Dα channels. Two vertical blue lines mark the starting and stop time of the bursts.
During the time interval 2100 to 2300 ms, the Dα signal exhibits large fluctuations and there are
bursts in some channels of the ECE and ECEI systems. Here, the Dα signal has 200 Hz
fluctuations, with amplitude of 50%. In addition, Fig. 3.23 is the zoom in of these signals; the top
is ECE3 at 85.5 GHz, the middle is LFS1308, which is one of the ECEI channels near the
midplane at 85.8 GHz, and the bottom is FS07, one filtered scope channel measuring Dα
intensity. Here, it is apparent that the bursts time is very near to the peak of the Dα. Therefore, it
suggests that trapped electrons are needed in the edge; large fluctuations mean that there are
some period of formation and relaxation of the trapped particles.
Figure 3.22 The QH-mode bursts dependence on trapped electrons in the edge. A) to d) are
four ECE channels from low frequency to high frequency, in which ECE1 is slightly inside the
LCFS. E) is one ECEI channels in 85.8 GHz, which is very close to the ECE3 of 85.5 GHz.
F)and g) are two filtered scope channels which measures the Dα radiation intensity. Two
vertical blue lines mark the starting and stop time of the bursts.
Figure 3.23
The correlation of bursts and the Dα signal. Top is ECE3 at 85.5 GHz; middle is
the ECEI channel at 85.8 GHz at midplane; bottom is one filtered scope data measuring the Dα
intensity.
3.3.3 QH-mode Burst Emission Mechanism
One peculiarity of the EHO burst emission mechanism is non-symmetric magnetic fluctuations.
Shot 146473 as shown in Fig.3.24 is a reversed plasma current (Ip) shot, and the poloidal
magnetic field (Bp) is negative. If the magnetic fluctuations are negative, then Bp is increasing.
ECEI is located at the 270° port, which is very close to the magnetic fluctuation coil (277°).
During the bursting time interval of 2.3 to 4 s, for magnetic fluctuations data, its minimum is less
than -40 Gauss, and its maximum is about 20 Gauss, so the speed of increase of the magnetic
field is faster than the decrease. In addition, during this time the absolute toroidal magnetic field
drops from 0.25 T to 0.22 T.
Figure 3.24
QH-mode burst emission mechanism. Top is LFS1304 at 83.2 GHz, and midplane
ECEI channels slightly outside the LCFS; middle is the poloidal magnetic fluctuation data
located at the 277° midplane which is very close to the ECEI location at the 270° port; bottom is
the accumulated magnetic field data at the same position.
Now we zoom in the ECEI data and the magnetic fluctuation data as shown in Fig 3.25 and Fig.
3.25. In the time 2.75 s in Fig. 3.25, there is dominant n=1 EHO with a frequency of 10.75 kHz;
while in time 3.4 s in Fig 3.26, there is broadband EHO without a dominant one. In the top figure
of 3.25 and 3.26, it is clear that the bursts have strong correlation with the increasing bursts in
magnetic data. When there are bursts in the ECEI data, there are increased bursts in the magnetic
fluctuations; the reverse is not true.
Figure 3.25
QH-mode burst emission mechanism with n=1 10.75 kHz EHO present. The top
one has a wide time range from 2752 to 2758 ms; the bottom one is the zoom-in of the spikes at
2756.3 ms. The purple line is the ECEI data, the green line is the magnetic fluctuation data. In
the top figure, a horizontal red line marks the zero point. In the bottom figure, two vertical blues
lines mark the time of the millimeter wave burst and the magnetic fluctuation burst.
Figure 3.26
QH-mode burst emission mechanism with broadband EHO present. The top one
has a wide time range from 3415 to 3440 ms; the bottom one is the zoom-in of the spikes at
2429.1 ms. The purple line is the ECEI data, and the green line is the magnetic fluctuation data.
In the top figure, a horizontal red line marks the zero point. In the bottom figure, two vertical
blues lines mark the time of the millimeter wave burst and the magnetic fluctuation burst.
If we compare the bursts time in ECEI data and magnetic fluctuations, it is found that the
magnetic fluctuation bursting time is delayed by 9 μs with respect to the ECEI burst time. Then,
considering the phase difference between 277° and 270° of the n=1 mode at 10.75 kHz, the
magnetic data should be delayed by 7/360/(10.75kHz)=2 μs. Also, from the calculated time delay
from ECEI and magnetic fluctuation data, the magnetic fluctuation data has a 13 μs delay with
respect to the ECEI system. Consequently, these bursts are synchronized within an error of 1 μs.
Finally, considering the data-sampling rate of the magnetic data (200 kHz), the error will add to
6 μs, which is 1/17 of the circle.
3.3.4 EHO Structures
The microwave imaging reflectometry (MIR) system commissioned in June 2013 on the DIII-D
tokamak [19] provides another important imaging tool to characterize the EHOs; however, there
was only one day allotted for QH-mode experiments after its commission. Unfortunately, during
this time, no millimeter-wave bursts were observed on either the ECE or ECEI systems.
Therefore, its data is only used to characterize the EHO structures as of now.
Firstly, the EHOs are a low-m number mode. Shown in Fig. 3.27 is a contour plot of the
magnetic fluctuation data of the n=1 EHO mode in time 1.18 s at 9.5 kHz. From this figure, m=2, here ‘-‘ means it propagate in contour-clockwise in lab frame. This fit is obtained from the
midplane magnetic data.
Figure 3.27 Contour plot of magnetic field fluctuations over poloidal angle and time of n=1
EHO. A black line marks the phase evolution over time. From time 1.1897 to 1.1899 s, the phase
changed -2*2π when the mode rotated 2π in poloidal angle, so it is an m=-2 mode.
Shown in Fig. 3.28 is a contour plot of the magnetic fluctuation data of the n=2 EHO mode in
time 1.88 s at 17.8 kHz. From this figure, m=-2; here, ‘-‘ means it propagates in contourclockwise direction in the lab frame. This fit is obtained from the midplane magnetic data.
Figure 3.28 Contour plot of Magnetic field fluctuations over poloidal angle and time of n=2
EHO. A black line marks the phase evolution over time. From time 1.8818 to 1.1822 s, the phase
changed -4*2π when the mode rotated 2π in poloidal angle, so it is m=-4 mode.
The ECEI and MIR magnetic systems are set for determining the structures of the n=2 EHO.
Figure 3.29 shows the diagnostic setups from the EFIT data at time 1800 ms in shot 155165. The
left part is the map of the poloidal magnetic coil sets at the toroidal angle 322 degrees; all the
coils are measuring the poloidal magnetic fluctuations. Inside the tokamak, the dashed line is the
contour of the psi from 0.1 to 0.9 with increments of 0.1. The right part is the zoom-in of the
ECEI and MIR setups on the edge; the blue rectangle is the ECEI imaging location while the red
rectangle denotes the MIR imaging locations. The LO frequency is set to 83 GHz, so the channel
LFS1305 (fifth channel from right) at the midplane has a frequency of 89.1 GHz which is very
close to the LCFS at 89.3 GHz.
Figure 3.29 Diagnostic setups for the EHO structure characterization. The left part is the
poloidal magnetic coil set in the toroidal angle of 322 degrees; all the coils are measuring the
poloidal magnetic fluctuation. Inside is the contour of the psi from time 1800 ms in shot 155165.
The right part is the zoom-in of the ECEI and MIR setups on the edge; the dashed black line is
rho=0.7, 0.8, 0.9 from left to right and solid cyan line is the contour of the Q value. The blue
rectangle is the ECEI imaging location, while the red rectangle is the MIR imaging location.
Thanks to David Eldon for the IDL program of magnetic map.
A simultaneous imaging of the ECEI, MIR and magnetic coils is achieved for the n=2 EHO in
time 1815 ms. Figure 3.30 a) is the simultaneous imaging of ECEI LFS, MIR, and the poloidal
magnetic coils set. Here, the absolute magnetic field is obtained and the time calibrated well
firstly; then, since it is an n=2 EHOs, the phase are delayed by 2*(322-270)=104 degrees. From
this figure, the phase of the ECEI LFS data is in phase with the MIR data in the midplane;
consequently, the temperature and density changes are in phase. However, the magnetic data in
the midplane is not in-phase with the ECEI LFS data, which means that the EHO might have
some complicated structures. Figures 3.30 b), c), and d) are the time evolution of the ECEI LFS,
MIR, and Magnetic coils data; each frame is separated by π/8. The n=2, m=-4 EHO is a very
high wavelength mode (kpol<6 m-1, λpol>1 m), the poloidal rotation is not very obvious in the
ECEI LFS and MIR data, since they only cover about 0.15 π of the toroidal angle. However, the
rotation is very clear in the magnetic data, and it rotates in the counter-clockwise direction.
Figure 3.30
EHO structure on three systems. a) is the simultaneous imaging for ECEI LFS,
MIR and Magnetic coils, of which the left part is ECEI LFS, the middle part is the MIR data, and
the right part is the magnetic data. b), c), d) are the phase evolution of the EHO structure in
ECEI LFS data, MIR data, and Poloidal Magnetic Field Data respectively, each frame is
separated by π/8 phase.
3.3.5 Burst and Burst Stops with n=2 Dominant EHO
Although the intensity of bursts in QH mode is lower than the ELMy case, these bursts in QHmode last longer, and in some cases even saturate the signal over 2 s. Shown in Fig.3.31 is an
example that these bursts almost saturate the signal from 2.7 to 5.0 s. From part a), at time 2.5 s,
some intermittent bursts show up; and when the collision frequency drops, around 3 seconds, the
bursts become continuous; then around 4.9 s, the intensity become lower, and the bursts become
intermittent again; and at 5.1 s, the bursts disappear (this might due to the loss of trapped
electrons). From part b), around time 2.2 s, there appears a dominant n=2 EHO mode, and the
magnetic fluctuations get stronger; this EHO mode lasts until 4.9 s, which agrees with the time
that the continuous bursts disappear.
Figure 3.31
Bursts evolution. A) Millimeter wave bursts observed on ECE 9; b) MIRNOV coil
data measuring poloidal magnetic field fluctuations; c) ne/ Te1.5, which is proportional to
collision frequency.
Then let us zoom in to the case that has intermittent bursts (top figure of Fig. 3.32) and
continuous bursts (bottom figure of Fig. 3.32). From the intermittent bursts, we know that the
bursting is in phase with the peak of the magnetic fluctuation data at the 277 degree coil; and for
the continuous bursts cases, the bursting cessation is in phase with the valley of the magnetic
fluctuation data at the 277 degree coil. However, the reverse is not true: not at all times when
there is a peak of the magnetic fluctuation data is there a millimeter-wave burst in the ECE
channel; and not at all the times when there is a valley of the magnetic fluctuation data is there a
millimeter-wave burst stop. It is therefore concluded that the burst and the burst stop are 180° out
of phase with respect to the dominant n=2 EHO.
Figure 3.32 Bursts phase comparison. Top: Intermittent bursts case around time 2.51 s;
Bottom: Continuous burst case around time 3.25 s. In the top, the blue lines are the bursting
time; while in the bottom, the blue lines indicate the burst stops times.
As a summary, in Fig. 3.33, the locations where bursts and burst stops are more likely to occur
are marked in the flux surface and the magnetic field data and magnetic fluctuation data. This
figure will serve future simulation and theory development.
Figure 3.33 Bursts phase and burst stop phase. Bursts are marked as pink cross; burst stop are
green dot. Top is their locations in flux surface. Bottom is the magnetic data in blue and the
magnetic fluctuation data in brown.
3.4 Model for Millimeter Wave Bursts
To explain the millimeter wave bursts, a model should be comprised of three main parts as
shown in Fig. 3.34, One is the wave resonance that explains how the wave is trapped; the second
one is the wave-particle interaction which explains how the wave gets amplified, and the final
one is the emission mechanism which explains how the millimeter wave bursts are emitted.
In the wave resonance, it is required to explain the nature of the interaction wave, whether it is an
electromagnetic wave or electrostatic wave, including the propagation direction, and finally the
wave dispersion relation. In the wave-particle interaction, the direct question is how to transfer
the energy from the electrons to the wave. Here, there are two main questions, one is what
particles and what portion of the particles are interacting with the wave, and the other is how to
form bunching and synchronism. In the emission mechanism, the questions to be answered are
how does the energy of the wave get confined and emitted, and what is the relationship with the
MHD behavior.
Figure 3.32 Model for the bursts mechanism.
As a trial model, this dissertation will present the Cyclotron AutoResonance Maser (CARM) and
Gyro-BWO models [20] as shown in Fig 3.33 to explain these bursts. Some grounds for this
hypothesis will be addressed for each part. Firstly, in the wave resonance, a regular right -handed
electromagnetic wave traveling parallel to the magnetic field is assumed. The wave dispersion
relationship is given by ω2=k2c2+ωωp2/(ω-Ωe). Then secondly, some coherent beams formed by
trapped electrons at the regular thermal temperature are interacting with the wave, and in the
cyclotron direction it forms bunching and synchronism with the millimeter wave. In order to
form the synchronism, ω=kv+2*Ωe. Here, the reason to use the second harmonic wave is that the
observed millimeter wave bursts are close to the second harmonic frequency of the electron
cyclotron frequency. This gives two interaction points; the lower frequency is the Gyro-BWO
model that explains the bursts in H-mode, and the higher frequency is the CARM model that
explains the bursts in QH-mode. And finally, the millimeter wave occurs at the location when
particles are pumping in for H-mode cases (since it is similar to the BWO) and when particles
are pumping out in QH-mode cases (since it is similar to a CARM).
Figure 3.35
CARM Model for the bursts mechanism.
Firstly, in the wave resonance, a right-handed electromagnetic wave traveling parallel to the
magnetic field is assumed. The basis for this assumption are two key observations, one is that the
intermittent bursts rotate with the same poloidal speed as the EHOs on the same flux surface[3]
and that the continuous bursts only happen on one radial channel in the ECE system, a model is
more likely to be in the poloidal direction. Otherwise, if it occurs in radial directions, some more
explanations need to be made for the singularity of the bursts. The other key observation is the
downshifted burst frequency in H-mode [1] and the upshifted burst frequency in QH-mode [2],
which can be explained by the two interaction resonance points of the wave and the particles.
Firstly, the Gyro-BWO point can explain the downshifted burst frequency in ELMy cases in Hmode. And before the ELM time, the flux surface will be pushed outward, so the bursts are more
likely to go outward which matches with the observation in Reference [1]. Furthermore, it also
explains the upshifted burst frequency well in QH-mode. As an example in Reference [2], at the
EHO location in shot 121391 at time 2.35 s, the electron cyclotron frequency is 43.75 GHz, and
the plasma frequency is about 20 GHz, and electron temperature is 2 keV. Then, by this model,
bursting at 82.6 GHz is predicted from the Gyro-BWO point and 93.0 GHz from the CARM
point. It is noted that the CARM point is very close to the observed 92.5 (±0.75) GHz from ECE
measurement. And indeed, it is upshifted from the 2nd harmonic frequency of the electron
cyclotron frequency.
Secondly, in the wave-particle interaction, coherent electron beams formed by trapped electrons
at the regular thermal temperature are interacting with the wave, and in the cyclotron direction
bunching and synchronism is formed with the millimeter wave. In the H-mode bursts, no
runaway electrons have been observed in hard x-ray diagnostics during the ELM times, which
indicates it is an interaction with electrons with regular thermal velocity. Both the bursts in Hmode and QH-mode are narrowband, and the strongest burst is only on one channel of the ECE
or ECEI systems, which agrees with this high-Q model. Low collision frequency is necessary,
and in QH-mode it may act as a switch for the bursts to turn on and off; otherwise it will distort
the bunching needed in this model. The trapped electrons are also necessary, in the QH-mode,
the bursts clusters are synchronized with the peak of the Dα Fluctuations.
Thirdly, for the emission mechanism, the millimeter wave occurs at the location when particles
are pumping in for H-mode cases (since the Gyro-BWO is a backward travelling wave) and
when particles are pumping out in QH-mode cases (since the CARM is a forward travelling
wave). The radial speed of the bursts is more likely to go outward during ELMs in H-mode
cases; for example the speed is -33MHz/μs at 1.38 seconds at shot 103698 identified on
Reference [1], and it matches that the flux surface is pushed outward. In QH-mode cases, the
Bursts happen when particles are pumping out as identified by section 3.3. MHD behavior is not
necessary, but occurs in most of the cases of bursts (ELMy precursor, disruption precursor, and
EHOs). They act like a trigger and are synchronized with the bursts.
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Chapter 4
Data Correction for FIReTIP System
4.1 FireTIP System Introduction
4.1.1 System Overview of FIReTIP
The layout of the Far Infrared Tangential Interferometry/ Polarimetry system [1] is shown
in Figure 4.1 and consists of the lasers, optics system, optic tower, Bay-K window, and flanges.
Three CH3OH lasers [2] pumped by a CO2 laser generate a signal frequency at ~2.5 THz
(wavelength = 119 μm) to probe the NSTX plasma. The following optical system combines and
splits the lasers to form two reference beams and 7 probing beams through the mirrors and lens
on a horizontal table[3]. The 7 probing beams are then elevated to the top of the tower and arrive
at the window on the Bay-K flange. Seven different beam colors represent the 7 beam channels.
Figure 4.1: Layout of FIReTIP system and its equatorial section (left top)
The top left of Figure 4.1 shows the top view of the NSTX plasma. Seven chords are
transported through the horizontal mid-plane of the plasma to form a fan beam configuration
(which can invert the line-integrated data to local values and covers the cross section of the
plasma) for 2 D density and magnetic profile and fluctuation measurements. The corresponding
normal distances (in cm) are listed on the left. Channels # 1 and 2 are used for overall density
measurements. Channels #5 and 7 with the addition of Channel #6 available in 2008 are for edge
fluctuation monitoring. Channels #3, 4 and 5 can monitor core plasma fluctuations with major
line integral path probing through the plasma center. The retro-reflectors at the edge of the
plasma perimeter reflect the beams back along the same path to the source (with a minimum of
scattering) to make double-pass measurements.
4.1.2 Laser Wavelength Selection
In the process of choosing the wavelength λ of the laser, the wave propagation, resolution,
and noise level of the system are major concerns that come to attention. Firstly, λ has to be
chosen to be small to ensure that the wave propagates relatively straightly through the plasma
with minimum refraction so that the laser beam will keep reaching the retro-reflector. However,
the shorter the wavelength is, the smaller the signal will be, and thus the larger the contribution
from vibration noise. Consequently, there is a trade-off issue between reliability and resolution.
The transverse density gradient deflects the probe beam. If we define the direction along its
path by the x axis and its transverse d
irection as the y axis, then we can obtain the deflection angle [4]
.
The index of refraction of the plasma is given by
where ,
is the plasma critical density which is determined by the probe laser
wavelength; for the 2.5 THz laser, the critical density is 1.4×1023 m-3. This equation indicated
that the plasma has high and stable index of refraction with high laser frequency and vice versa.
For the interferometer case, the critical density usually is significantly larger than plasma density,
i.e. ncrit>>ne, so we can rewrite the angle to
.
Consequently, the deflection angle is proportional to λ2. For channel 3 of the FIReTIP system,
assuming a parabolic density profile with 1020 m-3 peak density at R=32 cm and zero density at
R=169 cm, the deflection angle for a single path will be θ= 0.013° at 2.5 THz. The deflection
angle will increase to 1.3° if we decrease the frequency by an order to 250 GHz. Both of them
are very small, and the retro reflector will adjust the angle back, and it will cancel back when it
passes backward.
Another effect is the deviation from the reflector. Now consider the case that the laser beam
has the largest deflection angle at the beginning; this is a simulated worst case where it is
assumed there exists a density filament at the plasma edge. Figure 4.2 gives a schematic
illustration concerning this case; the laser comes from the air side into the plasma and is
deflected due to a different refraction index, and assume that the laser passes through a straight
line. Mark the insertion angle as α, and the refraction angle as β; the deflection angle will be β- α.
After passing through a distance L, from a triangular function, the deviation distance will be
D=2L×sin{(β-α)/2}≈L×sin(β-α), since the angle β- α is very small. To determine the maximum
deflection angle, β=π/2, so sin(α)=μ0=(1-ne/ncrit)0.5, so D=L×cos(α)=L× ( ne/ncrit)0.5; this means
that the deviation distance is proportional to the probe laser wavelength. In the FIReTIP system,
the longest distance is in Channel 1 where L=3.1 m; taking the filament density as 1019 m-3, then
the deviation distance D will be 2.6 cm at 2.5 THz, and 26 cm at 250 GHz. Compared with the
10 cm reflector, 2.5 THz clearly is more reliable to provide consistent data.
Figure 4.2: Schematic figure for deflection distance
For a polarimetry run, one important issue is that when a circular wave propagates
perpendicular to the magnetic field, it will become an elliptically polarized wave. The reason is
that the ordinary and extra ordinary waves traverse at different speeds, which is the CottonMouton effect. However, since we are measuring the angle difference between the right hand
and left hand circular waves, it is essential to ensure they do not convert into each other. Here,
the phase difference between them is called the Cotton-Mouton angle, and it is a good indicator
of the percentage that they convert into each other. Suppose the perpendicular magnetic field
B=0.5 T, and that the density is 1020 m-3; using the maximum double pass length (Channel 1) 6.2
m, the Cotton-Mouton angle Φ = 4.84 × 10-11λ3∫n B2 dx will be 0.013 rad=0.75° at f=2.5 THz,
and will be 750° at f=250 GHz. When the Cotton-Mouton angle is 180°, it means that it will
change from a right hand circular wave into a left hand circular and vice versa. Consequently,
then it will become impossible to obtain the right Faraday angle.
On the other hand, the interferometry phase difference is proportional to the wavelength, and
the Faraday rotation angle is proportional to the square of the wavelength. Therefore, shorter
wavelength will lead to smaller phase shift, which decreases the resolution of the signal.
Furthermore, vibration noise 2πδ(L)/λ is proportional to λ, where δ(L) is the variation of the
optical length. Most of it comes from the reflector vibration, so for most of the channels, an
isolated tower is used to hold the reflector in order to decrease the noise. One minimum
requirement is that the vibration noise be less than π in a minimum time interval if there is no
correction method; in other words, the variation of the optical length is less than half the
wavelength. However, vibration noise can be well corrected by the use of a two-color system [5,
6], and it is less serious in polarimetry than in interferometry.
Currently, the wavelength of the FIR laser is chosen to be 119 μm from both propagation and
resolution considerations. With this wavelength, approximately 30 interferometer fringes (about
ten thousand degrees) and 60° of Faraday rotation angle [7] are expected for typical NSTX
plasmas. Therefore, for interferometry with the full video bandwidth of 4 MHz [8], the noise
level is near 5 degrees, which results in an SNR of 2000; for polarimetry with 10 kHz bandwidth,
the noise level is 0.5 degrees, which gives an SNR of 120.
4.1.3 Implementation of FIReTIP
Figure 4.3 shows the measurement schematics of the FIReTIP system. The system employs
the heterodyne detection technique which affords two major advantages over direct detection:
good amplification and filtering; eliminating the phase increase/decrease ambiguity by adding an
intermediate frequency. Two conventional cavity tuned FIR lasers, with frequency separated by
~2 MHz, generate linearly polarized beams that are orthogonal to each other, and are then
combined with a polarizer. The combined beams then pass through a quarter-wave plate to
transform the linearly polarized waves to right and left-hand circularly polarized waves. The
third laser, which is Stark-tuned by ~5 MHz, provides a local oscillator beam to convert the
frequency down to the MHz region through the Schottky diode corner cube mixers. The mixer is
designed to accept an RF input frequency at 2.5 THz and has excellent signal to noise ratio
characteristics. The probing signals double-pass the plasma and experience phase shifts which
are denoted as A* and B*; while the remaining beams going to the detector directly are reference
signals denoted by A and B. The observed beat frequencies on the spectrum analyzer are shown
in the figure. Both reference and probing signals are then sent to the IF electronics for phase
detection. The phase difference between signal B (A) and B* (A*) gives the interferometry
information and the phase difference between A* and B* is used for polarimetry measurements.
f1= f0 – 1.0 MHz
FIR Laser
f0
FIR Laser
Stark Laser
f2= f0 + 1.0 MHz
f1
λ/4
Plate
NSTX
Plasma
fR fL
f2 Polarizer
fLO
fLO= f0 – 5.0 MHz
f0
f0
Beat freq. from these 3 lasers:
f1 – f2 = 2.0 MHz
fLO – f1 = 4.0 MHz
fLO – f2 = 6.0 MHz
Reference
Mixer
Signal Mixer
A B
A* B*
Electronics
Polarimetry: phase difference of (A* - B*)
Interferometry: phase difference of (B - B*)
Figure 4.3: Implementation of the FIReTIP system
4.1.4 FIReTIP IF Electronics
The new IF electronics system was designed by Dr Wen-Ching Tsai; she has many details
in her Ph.D. thesis [9]. This system was installed on NSTX in 2009 and provides low noise
plasma signals by employing automatic gain control and phase locking for both interferometry
and polarimetry paths. There are two optional ways of measurement: the wideband
Interferometer Only Operation and the Narrowband Interferometer/ Polarimeter Operation. In
the interferometer only configuration, only two lasers (fLO and f1) are running. Both the reference
signal (6 MHz) and the plasma signal first pass through an up-converting mixer (21.75 MHz) and
band-pass filter (flat insertion loss over its 10 MHz bandwidth), and then they pass through a
down-converting mixer (96 MHz), low-pass filter (78 MHz) and the phase lock loop; finally,
they are sent to the phase comparator. These two filters in the system are to ensure single
sideband mixing. For the Narrowband Interferometer/ Polarimeter operation, the two plasma
signals are separated by a sharp edge (more than 40 dB loss at f0±1.2 MHz) and flat top (with
bandwidth of 1 MHz) 11 MHz filter and all the DC phase signal is finally converted to 70 MHz
for the phase comparator. The new phase comparator employs two phase comparison techniques:
the digital fringe counter circuit gives two output voltages that are respectively proportional to
the input phase difference and π plus the input phase difference with a 3 dB video bandwidth of
1.0 MHz; the IQ Demodulator mixer Circuit, which generates two output signals corresponding
to R×sin θ and R×cosθ, needs some calculation to obtain the phase.
Figure 4.4: Schematic figure for FIReTIP IF electronics
4.1.5 System Phase Noise
The electronics were tested in the interferometry-only mode using (a) FIR laser inputs
without plasma, and (b) FIR laser inputs with plasma. Their random phase noise contents are
best illustrated using power spectral density plots, where the spectrum noise level is normalized
by the resolution bandwidth.
Figure 4.5. Phase evolution of interferometry measurements
Phase noise spectra acquired with FIR laser signals are presented in Figure 4.5 together
with data collected by the previous FIReTIP electronics under similar conditions (test shots taken
without plasma). An improvement in the phase noise spectral resolution by at least 10 dB with
respect to the previous electronics and a 4 MHz upgrade are achieved. Also observed in Figure
4.5 is the rise of low frequency components in the presence of plasma (shown in circles and
rectangles).
4.2 Phase Measurement Electronics and Data Correction Methods
4.2.1 Phase Measurement Electronics
Two phase comparison methods are used for the phase delay measurement between the
plasma and reference signal. One method utilizes a digital fringe (F)-counter (C) circuit, which
employs the zero crossing phase comparator to obtain the phase delay; the other approach is the
analog in-phase (I)-quadrature (Q) demodulator method, which provides the phase by taking the
arctangent of the in-phase and quadrature-phase multiplication. These two circuits were
discussed in detail in Dr. Tsai’s thesis [8]; here, only some brief summaries are given below.
The digital FC circuit’s block diagram was shown in Figure 4.6, which consists of divideby-8 prescalers (PE3513), zero crossing phase comparators, lowpass filters, and gain amplifiers.
First of all, the input signal is about 70 MHz; the divide-by-8 section will bring it from a 70 MHz
analog signal to about an 8.7 MHz digital signal. Subsequently, the plasma signal is divided into
two parts, one of them will reverse its signal by hex inverter 74F04 to give a half circle phase
delay. Then, each of them gets the phase compared with the reference signal; in the bottom part
of Figure 4.6, their voltage output versus the phase difference is plotted. Then it passes through a
high order lowpass filter to attenuate the 8.7 MHz pulse signal while retaining the DC-1 MHz
signal. In the final stage, an amplifier and level shifter are placed to adjust the DC voltage to lie
between +/- 2.5 V in order to meet the input range of the following digitizer, which is currently a
14-bit digitizer with 2 MHz maximum sampling rate.
Figure 4.6 Top: Schematic of the digital fringe counter circuit;
Bottom: output signal versus the phase difference.
The dual D-type flip-flop chip SN74HC74 from Texas Instruments acts as the key
component in the zero-crossing comparator. Its function table is given in Table 4.1; the
is
set to high and D input is set to low. Firstly, the reference signal is converted into a negative
pulse signal by connecting inverted
(i.e. Q) into the
input and the reference into CLK.
The ↑ in the CLK will bring Q to low, but immediately it will bring
to low, which will result
in Q into high. Then, the output of first chip Q1 will connect to the
, and the plasma signal
will connect to the CLK. Then, the negative trigger will set the output into high; only ↑ in the
CLK will bring the output to low, and the low state will last until the arrival of another trigger.
Consequently, the phase difference will be proportional to the time duration of the high status in
each circle, which is proportional to the DC voltage. Through this method, we obtain a linear
relationship between the phase difference and the DC voltage.
INPUT
OUTPUT
L
H
X
X
H
L
H
L
X
X
L
H
L
L
X
X
H†
H†
H
H
↑
H
H
L
H
H
↑
L
L
H
H
H
L
X
Q0
Table 4.1 Function table of the SN74HC74
Here, one very important parameter is the negative pulse length of the trigger signal. If it
is too short, it will not trigger the second chip to the high state; if it is too long, then it will keep
the output at the low state all the time, since the ↑ in the CLK is blocked during this time. In the
actual case, it is about the total delay time of the flip-flop and inverter, which is tp=15+3.7=18.7
ns, which is higher than the required pulse duration of 17 ns. Compared with a typical input 8.7
MHz signal, with a circle of 115 ns, it will approximately be 1/6 of the circle. This part will
contribute significantly to the nonlinearity of the phase difference and the DC voltage.
The second method is more straightforward, which employs in-phase (I)-quadrature (Q)
demodulators MiniCircuits MIQY-70D. The 5 MHz IF bandwidth of the mixer is sufficient to
maintain the 4 MHz bandwidth of the signal. It also has very small amplitude and phase
unbalance, which will directly contribute to accurate data interpretation, and it has excellent 3rd
and 5th harmonic suppression. Its block diagram is shown in Figure 4.7 left. The LO signal is
divided into two parts which are 90° out of phase, and the RF is divided with the same phase,
and then they are modulated together. The in-phase part gives Vi=R×cosθ and quadrature part
gives Vq=R×sinθ, which is shown in Figure 4.7 right, where R is the product of the two input
amplitudes and θ is the phase difference between these two signals. Then, the output phase can
be calculated through the arc tangential function of Vq/Vi. These voltages are sent to a 14-bit
digitizer with 12 MHz sampling rate in the end.
Figure 4.7 Left: block diagram of I&Q demodulator; Right: output voltage versus the phase
difference
4.2.2 Fringe Jump Error
Fringe Jump error widely exists in plasma interferometry measurements, such as JET,
Tore Supra, and LHD [10, 11, 12] . The main reason is loss of signal during some plasma events,
limited sampling rate, and the vibration noise. Furthermore, in the case of the Edge Localized
Mode (ELM) [10] , pellet injection [12], and fast density changing events, the laser beam will
receive some deflection, which can manifest itself as some loss of power, and even temporal loss
of signal. In the case of a crash or collapse, the density change might be too fast for the system to
catch due to the limited sampling rate; and for real-time density feedback, it is more critical
because of the lower sampling rate applied.
In the FIReTIP system, attention was devoted to ameliorate these difficulties because of
the relatively short laser wavelength, the extremely wide video bandwidth, and high sampling
rate. From the basic interferometer formula, ne,avg=3.6×1014θ/(λL), one fringe is 2π, at the longest
channel the double pass length L=6.2 m, so one fringe is equivalent to 3×1018 m-3 line averaged
density. This value will increase slightly in the case of the other FIReTIP channels since the path
length will decrease. For case of the 10 MHz sampling rate, if the plasma changes one fringe at
the lowest sampling interval, it means 3✕1022 m-3 per millisecond, which is 3000 times faster
than the typical plasma rate of increase in NSTX. Unfortunately, in the FY 2010 operation
campaign, the FIReTIP system suffered from a low laser power problem, which usually leads to
some discontinuity of the signal, which will cause fringe jumps. The other problem is the
vibration noise. Since the noise is inversely proportional to the wavelength, even small vibrations
will result in significant signal problems; for example, a 118 μm shift of the reflector in the
optical direction will cause two fringe jumps in the data. Therefore, these fringe jumps still
widely exist in the data.
Examination of the data shows that most of the sudden changes in density do have a
similar amount of variation in each case. Most of the fringe jumps have a 2π phase shift, and
even some larger changes turn out to be a cascade of 2π [13]. The occurrence time is a few
microseconds. Statistical analysis of the data shows that almost every fringe jump happens in one
direction, independent of the laser polarization. This means that these errors occur in the
electronics instead of at the plasma. FC1 and FC2 usually increase by 0.625 V in several
microseconds; the phase of IQ always undergoes a 2π phase increase. This means that the plasma
phase is missing 2π in a short time. This information, coupled with knowledge of the low laser
power issue, raises the question of the cause of the electronics problem. The most probable
reason is that the PLL cannot track and lock-in the input signal when the input signal level is too
low. Currently, the VCO MiniCircuits ROS-70-119 acts as the last stage signal source.
Considering the extreme case, if the input signal goes to zero, then it will reset the tuning voltage
to zero, and then the VCO will generate a 55 MHz output. Consequently, compared to the
reference 70 MHz, it will miss 2π phase in 0.06 μs in this extreme circumstance.
For the fringe counter method, since the phase is divided by 8, this 2π phase will appear to
be a Vm-m/8 voltage jump in the final data. The video bandwidth is 1 MHz, and then the rise time
(from 10% to 90%) will approximately be 0.34/bandwidth=0.34 μs [14] for a Gaussian response
system. Therefore, for 1 MHz sampling rate, the rise time is 1/3 of a step. In the actual case, two
steps (2 μs) are used to consider about the fringe jumps in case some data points are taken
between the rise time. For the IQ method, in the case of signal discontinuity, the phase will
increase rapidly. However, if it comes back to be in track and locked-in sufficiently rapidly, then
it will quickly return to normal, because the 2π phase shift will not affect the output voltage. For
example, if there is a π/2 phase difference between the signal and noise, there will be a π/2 jump
when it changes from the real signal to noise, but that will be canceled out when it returns to the
signal. Only the longer duration noise intervals will contribute to the total phase, since the noise
itself might undergo a 2π phase shift in the discontinuity time. Fringe jumps in shorter time will
not show up in the output voltage, so longer times are used to identify and correct the fringe
jumps. Currently, a period of 10 μs (120 steps in 12 MHz sampling rate) is used to identify these
errors.
The fringe jump does depend on the signal levels; therefore, it is different from shot to
shot. On some shots, there are less than 5 fringe jumps, but others had more than 2000 jumps.
Therefore, careful consideration needs to be taken to correct these errors. In the following section,
data correction for both Fringe Counter and IQ methods are discussed.
4.2.3 Data Process for Fringe Counter Method
Dr June-Woo Juhn [13] had developed one algorithm to correct the fringe jump problem.
It works well for most shots, but for cases with frequent fringe jumps, it encounters some
problems. In shot 134791 shown in Figure 4.8, the top two figures show the output voltages of
FC1 and FC2; the bottom shows the density obtained from this method. There are more than
2000 fringe jumps in it, and clearly there are many (about 170) that are not corrected, which
leads to an impossible density with negative value.
Figure 4.8 The original FC output data and corrected density data by Dr Juhn’s algorithm
A new algorithm for the fringe counter method developed in this dissertation research is
discussed below. Three stages are performed to obtain the final density as shown in Figure 4.9.
The first step is to examine the signal to decide whether it is a reasonable signal; if it is not, the
simple solution is to stop and prevent misuse of the data. The second stage is to choose the
correct signal, since two signals are available with π phase difference. The final stage is to adjust
the increment properly, which leads to the total phase and density.
Figure 4.9 Flow chart of the FC method
Firstly, several criteria are employed to determine the quality of the signal. If they are too
soft, considerable erroneous data may be retained and may lead to misuse. If they are too rigid,
considerable usable data might be discarded. Here, two rules are applied. The first one involves
checking the phase difference between the two outputs FC1 and FC2. The phase difference
between the two outputs should be close to π, so the absolute voltage difference should be 2.5 V.
However, there is a slight phase delay between these two outputs, and the difference will become
increasingly different from π when a fringe jump happens and the bottom and ceiling changes. If
we consider the 0.07 V typical noise level, a criterion of 1.5 V is applied. Only a mean absolute
voltage difference greater than 1.5 V will be considered as representative of good data. This is
also a good indicator for the connection of the digitizer. If the digitizer is unplugged for any one
of them, the phase difference will be close to half of the maximum voltage which is less than 1.5
V; if both are un-plugged, the difference will be close to zero. The other is to check the
frequency of the fringe jumps. If the fringe jumps happen too frequently, then they will probably
destroy the integrity of the signal. The criterion applied here is less than 100 fringe jumps in
continuous 10,000 steps (10 ms). Since we know there tend to be more fringe jumps in crucial
plasma situations, this check will last for the whole processing. It is worthwhile to mention that if
it does not pass this criterion at some point, it will destroy the profile measurement, but
fluctuation measurements might be possible after that time.
Secondly, since there are two outputs FC1 and FC2, it is important to choose the right
one for the phase increment calculation. During the phase shift from π- to π+, there will be a
ceiling to bottom change from +2.5 V to -2.5 V, and vice versa. This change is not transient; it
takes time to undergo this change. As we discussed, it will take at least 0.34 μs, and the data in
between will become meaningless. Therefore, it is important to avoid the bottom-ceiling change
when calculating the increment. Since FC1 and FC2 have π phase difference, switching in turn is
used to avoid the chosen signal reaching the bottom and ceiling. One voltage range needs to be
set first, then choose the one in this range to be the signal, then with the time change if the signal
goes beyond this range, chose another to be the signal, and so on and so forth. Here, the range is
set to be [-1.875 V, 1.875 V]. To choose the right voltage, several things are taken into
consideration. Firstly, we want it to be linear from the voltage to phase, as discussed in the
electronics section; about 1/6 of the circle might be nonlinear in the worst case. Therefore, it is
better to keep away from this phase, which means the criterion will be less than 2.5✕(1-1/6)=2.08
V. Secondly, one case definitely needs to be avoided, which is the simultaneous occurrence of
two events in the selected signal: the bottom-ceiling change and the fringe jump. When the range
is very wide, if one fringe jump brings the signal to the bottom-ceiling change, the ending
voltage might be in the rise time of the bottom-ceiling change, and then this change is treated as
a real density change. To eliminate this case, the voltage will be less than 2.5-0.625=1.875 V,
where 0.625 V is the equivalent fringe jump voltage. Most of these cases are eliminated except
for the cascade of the fringe jump in a short time interval. Thirdly, the criterion cannot be too
small; that will lead to frequent bottom and ceiling changes, which will adversely affect the
accuracy since the absolute difference exhibits small fluctuations. In addition, it clearly cannot
be less than half of the maximum; otherwise, no good signal can be found in some times.
Thirdly, in the increment adjustment, it is very important to identify and correct the fringe
jump errors. It was found that most fringe jumps happen in two steps, so both steps 1 and 2 are
checked to identify the fringe jump. Here, the criterion for identifying the fringe jump is set to be
above 0.55 V. One fringe equivalent voltage is 0.625 V, and there is 0.07 V typical noise above
the signal, so a more rigid voltage of 0.55 V is taken as a better indicator. How to correct
thesefringe jump errors is also challenging, since there is usually some data in between these
jumps. Since the total of the phase increment is 2π or a cascade for these fringe jumps, only an
integer multiple of 2π will be added or subtracted to keep the phase change smaller than this
criterion in these given steps.
After the total phase is obtained, it is easy to check the polarity of the LO and Plasma
signal (the plasma signal can be 6 MHz higher or lower than the reference signal). Then, the
basic interferometry formula is employed to obtain the line-averaged density. In order to
evaluate the accuracy of the data, we compare this with the Thomson Scattering (TS) data [15].
In order to compare, the line average density from the TS data is calculated by assuming a linear
density profile between each of the Thomson points. Figure 4.10 shows the corrected density
obtained by this process; the red dots are the calculated line-averaged density from TS, while the
black lines are the Fringe Counter data calculated using this new process. This check will help
identify data problems from either TS or FIReTIP. Already, it has successfully pointed out
several shots where the TS shutter was only half opened in the experiment.
Figure 4.10 Compared TS data (red dot) and FC method data (black line).
4.2.4 Data Process for the IQ Method
A similar three stage algorithm is performed to obtain the final density from the IQ method as
shown in Figure 4.11. Firstly, the signal is examined to make reasonable processing. The second
stage is filtering the signal. The final stage is to calculate the phase increment and correct the
fringe jump errors, which lead to the total phase and density.
Figure 4.11 Flow chart of the IQ method
In the first stage, several rules are applied to determine the status of the signal. The first
rule is to examine the sum of the square of the two outputs. As we know, the two outputs are
Vi=R×cosθ and Vq=R×sinθ, so the sum of the squares of the two outputs are Vi2+Vq2=R2. In the
actual situation R=2.5 V, so the criterion that the mean square sum of the two outputs exceeds 5
V is used to determine whether it is good signal. This rule also helps checking whether the two
outputs are connected to the digitizer. The second rule is to check the frequency tracking. When
there is not sufficient laser power, the carrier frequency of the plasma signal will not be the same
as that of the reference signal, so there is no way to calculate the correct phase. Here, to make
sure the frequency tracking is good, the carrier frequency difference between the plasma and
reference signals needs to be less than 50 kHz, i.e. the peak frequency in the output spectrum
must be less than 50 kHz. The last rule is that there should not be frequent fringe jumps. Since
this has less fringe jumps than the fringe counter method, a more rigid rule is applied here: less
than 20 fringe jumps in 12,000 steps (1 ms).
In the second stage, it is very important to understand the necessity and possibility of
using the lowpass filter here. It is critical to filter out the high frequency noise which is generated
when the signal is not in track and locked-in. When the laser is attenuated or deflected by the
plasma, the signal is very weak; consequently, the VCO will generate signals away from the
right frequency, so it will result in high frequency noise. In addition, LO leakage from the first
mixer will also cause 6 MHz noise in the output. After low pass filtering, the video bandwidth
becomes smaller and the phase noise will become smaller as well, which will be critical for the
lower sampling rate, such as 5 kHz for real time control. On the other hand, since there is no step
voltage change for the continuous phase change, the filtering is possible. All the phase
information is retained in the signal after only mixing and division.
Then, the phase increment is calculated. In each step, we assume that the phase change is
close to zero (especially in the high sampling rate cases), so we will define the range of phase
change to be [-π, π]. After calculating the phases θ1 and θ2, the phase increment will be the
minimum of three phases: θ2-θ1, θ2-θ1-2π, and θ2-θ1+2π. Note that the fringe jump error needs to
be corrected later. Considering the noise, the 9/10×2π is phase criterion is applied to determine
the fringe jump error. Since shorter time scale fringe jumps will not show up at the output
voltage, a longer time than that used in the Fringe Method is applied here to check them. All the
steps in 120 steps (i.e., 10 μs) will be checked to ensure that the phase increment is below this
phase criterion. An integer multiple of 2π will be added or subtracted to correct this error to meet
the criterion.
The final stage is determining the density from the total phase from the basic
interferometry formula. Subsequently, this density will be compared with TS data if possible.
Finally, if the data match well, it will be uploaded to the data cluster. Figure 4.12 is one example
of the compared line-average density for channel 3 on shot 139321; the red dots are the TS data
and the black lines are FIReTIP data.
Figure 4.12 Compared TS data (red dot) and channel 3 IQ method data (black line) in shot
139321
4.3 Real Time Feedback Control
4.3.1 Real Time Density Feedback Control Possibilities
As a standard density diagnostic tool in tokamaks throughout the world, interferometry
usually serves as a key tool to measure, monitor in real time, or even feedback control the
density of the plasma. It is an important tool in support of physics studies and scenario
optimization; for example, it is able to help maintaining the right collisionality. Although NSTX
has a well-established real-time control system, density feedback control has historically been
difficult, since in the case of boronized walls, deuterium density pumping is difficult with wall
pumping alone[16]. However, with the addition of the lower divertor cryo-pump in NSTX
Upgrade, it is possible to achieve real-time density feedback control. The FIReTIP system in
NSTX is able to obtain both the density profile and up to 4 MHz fluctuations in the achieved data
from high sampling data. However, under low sampling real-time digitization, there is a question
of whether it can provide reliable electron density data.
Firstly, can it respond sufficiently fast to catch the phase change in each step? For a
typical shot, the line-averaged density rate of increase is about 1020 m-3 in 1 s, and the decrease
rate is 1020 m-3 in 0.05 s. For a time interval of 0.2 ms (5 kHz sampling rate), the increased
density is about 2×1016 m-3 while the decreased density is about 4×1017 m-3. Both of them are
smaller than the half-fringe equivalent line-averaged density; the minimum one is 1.5×1018 m-3 in
channel 1. However, some transient events like ELMs, pellet injection, and disruptions will
cause more dramatic changes in this time, which will be higher than the density. Furthermore,
because of the fringe jump errors due to low laser power and electronics, at least 2 steps are
required to adjust the errors; this will drop the maximum detectable density-change rate by a
factor of two. However, if these fringe jump errors can be corrected by some upgrade of the
electronics and signal strength, then the maximum detectable density-change rate can be
increased to 4 fringes per step for the fringe counter method, which will be 1.2×1019 m-3 in 0.2
ms, which will be enough for the real density change in this time interval.
Secondly, there is a question as to whether it can provide density data with low noise
level. The NSTX vacuum vessel vibrates with an amplitude of about 1 mm during the shots; this
will therefore result in 3×1019 m-3 in density errors. Therefore, the channels with the reflector
inside the chamber definitely cannot provide reliable data. As a consequence, only the channels
with the reflector on the isolated tower are proposed to provide density feedback. Although the
isolated tower was used, several shots had extremely weird vibration after the plasma had
collapsed, which gave about 400 μm to the total optical length and about 1019 m-3 to the lineaveraged density. However, for the corrected data, below is a summary for the FC method
employed on Channel 3 over the year 2010 shots. There are 1788 shots that meet the requirement.
1775 shots out of these shots have averaged-line density close to the TS data before the collapse;
the maximum difference is less than 6×1018 m-3 which is two fringe equivalent density. The other
13 of them have a maximum difference greater than 2×1019 m-3. Among them, three of they are
identified as the TS shutter problems; one had a laser polarization problem; 9 of them had a
problem to correct the FIReTIP fringe jump errors because the Fringe Jump and signal switching
happened at the same time. Therefore, this means the regular vibration noise is definitely very
small; the vibration to the total optical path is less than two fringes, i.e., 2*118.8=237.6 μm. Note
that the fringe error correction is not perfect, and this error also contains other errors in the two
systems and converting errors between these two methods, the vibration noise should be lower
than two fringes.
Last but not least, there is a question as to whether it can stop feedback control if the
density is not usable. For both methods, it is capable of identifying several connection problems,
for example whether the digitizer is not connected to the output, or if either the laser or digitizer
is not turned on. However, as mentioned above, there remain nine of the 1788 shots that have
significant problems with fringe error correction. That means that for the desired real time
operation a more rigid criterion needs to be applied. For example, insistence on the absence of
two fringe jumps in 10 ms is sufficiently rigid; in that case it ensures that the total number of
fringe jumps is less than 100 per NSTX shot. Since the abovementioned 9 shots each have more
than 300 fringe jumps, so it will give a stop to these 9 shots. Consequently, so it will give stops
to all the unusable cases in the 2010 campaign. However, the use of a more rigid criterion means
that more shots will not be suitable for real-time density feedback. To make density feedback a
common tool for each NSTX shot, some upgrades need to be done to reduce the fringe jump
errors.
In summary, the FIReTIP system is capable of regular density feedback except for some
extreme cases. To overcome the limitations imposed by these extreme cases, more work needs to
be finished: fringe jump errors need to be eliminated by improving signal (laser) power and
upgrading the electronics so that the signal can response to the real density change; during the
plasma discharge, the shot, extreme vibration must be avoided so that the noise level of the
system is sufficiently low; otherwise a two color interferometer might be necessary to correct the
noise. More rigid criteria must be adopted to give reliable stops when unusual cases happen;
system upgrade needs to be performed to give better signal strength.
4.3.2 Real time Density Feedback Control Realization
Since FIReTIP on NSTX Upgrade is a three channel system, and all three of the channels
are located at a different tangential radius, it can provide simple profile information, and
different channels or their combination can be chosen shot-by-shot for different physical studies
purposes. For example, the combination of Channel 1 and Channel 3 will provide density
information on the High Field Side of the plasma.
Currently, fringe jump errors are the dominant error sources; therefore, the IQ method
with fewer fringe jumps is good candidate for density control. Another reason is that the IQ
method is perfect for conducting filtering; it even corrects some of its fringe jumps; in the fringe
counter method, the errors will not be filtered out, and might cause the smoothed ceiling-bottom
change (since the rise time is 0.34/BW), which is not satisfactory for data processing. Also, from
the electronics noise level, the IQ method is also lower than the FC method; the root mean square
phase noise up to the bandwidth at 10 kHz is 0.39° for the IQ method and 0.50° for the FC
method. In Figure 4.13, the black line is the real-time channel 3 data in shot 141318 calculated
by the IQ method, while the red dots are the TS data. Here, a 5 kHz digital filter is applied, after
which data are taken at 5 kHz sampling rate, following which the basic phase increment method
is employed to obtain the phase and the density. From the figure, the matching is seen to be quite
good even at the collapse, and it goes close to zero after the shot.
Figure 4.13 Comparison of TS data (red dots) and real-time IQ method data (black line) of
channel 3 on shot 141318
However, if the fringe jump errors are suppressed well in the NSTX Upgrade, it is the FC
method that offers advantages because it can track eight times faster density changes than the IQ
methods. As discussed above, this capability will be important for extreme transient plasma
events, like ELMs and pellet injection. Furthermore, the disadvantages for the Fringe Counter
method will be less serious. If there are no fringe jumps, the signal switching will be easier and
errors due to the switching signal will be smaller. Furthermore, the phase noise actually does not
matter to the overall density, since both of them are two orders of magnitude smaller than onefringe jump errors. However, one low pass filter needs to be added before the digitizer, otherwise
it will pick up the over frequency range noise, which will be about ±6° for the FC method.
4.4 Future Work
4.4.1 Signal Power Upgrade
These fringe jump errors will become major problems in real-time controls, and are very
likely to disrupt the real-time signal. To reduce them, the fundamental solution is to improve the
signal level. Moreover, the signal to noise ratio will be improved as well, so the phase noise will
decrease concurrently, which is very important for the polarimetry run.
One way is simply to increase the laser power. The first step is to simply rebuild the laser;
any misalignment or damage to the mirrors inside the laser cavity will result in significant
reduction in laser output power. Since this system operated very well in the initial runs, reexamination and rebuilding of the laser will definitely help the operation. Another way is to
increase laser pump power; currently, all three FIR lasers are pumped by the same CO2 laser
(running polarimetry required the third laser). Therefore, a possible upgrade is to let each FIR
laser have its own CO2 pump laser. Finally, one can decrease the number of run channels. In
2010, only 3 channels or even a single channel of interferometry were running, which
nevertheless yielded important data. For example, the Thompson Scattering is calibrated with
these data in a designated shot. In the Upgrade, it is very important to maintain at least three
channels, one passing through the high field side, a second going through the magnetic axis, and
the third one to measure the edge fluctuations.
Another approach is to reduce the power losses. An important step would be to replace
the old corner cube mixer with a newer and lower conversion loss mixer. The older corner cube
mixer that is currently utilized was made by MIT Lincoln Laboratory [17] and suffers from
severe signal attenuation with a conversion loss of about 60 dB. With the continued development
of THz and sub-millimeter wave technology, there exist better mixers with lower noise
temperature and lower conversion loss. For example, the WR-0.4FM fundamental waveguide
mixer from Virginia Diodes has about 200 mV/mW response at 2.5 THz, which gives an
insertion loss of about 20 dB. It therefore provides about 40 dB improvement in signal strength.
Another relatively straightforward step is to enclose the system and therefore decrease the air
humidity. Signal losses are 5 dB more in summer (45% humidity) than in winter (35% humidity).
A simple enclosure was constructed in 2011, and by pumping dry compressed 10% humidity dry
air into the system and maintaining positive pressure inside, the air humidity had decreased to 25%
in summer. It was shown that there was at least a 10 dB power increase and that the signal
frequency tracking is much more stable. In order to decrease the air humidity further, it requires
enclosing the system better and adding dry-air purge. A similar system in the Alcator C-Mod
Polarimeter [18] reduces the humidity level to 2% by purging dry air in the enclosures, and will
conserve more than 70% of the laser power from water vapor absorption.
4.4.2 Electronics Upgrade
As the last stage of the FIReTIP system, it acts like the brain in people, so it is essential
to get everything clear and quiet. Below are several aspects about the upgrade suggestions.
1. AGC Circuit
It sits in the 1st place, so it contributed directly to the signal to noise ratio. One important
characteristic is that when the input power is varying, how much does the output power vary.
Here, we know that the output power should be a real signal, excluding the LO leakage through
the mixer. However, in the design, the feedback probe is placed after the mixer and before the
bandpass filter, which definitely decreases the ratio between the real plasma signal to the LO
leakage noise. It should be noted that this explains why there exists a 6 MHz peak signal in the
I&Q method and a 6 MHz/8=0.875 MHz signal in the FC method.
A good solution might be to employ double stage AGC circuits. Firstly, this provides
wide input power range. Examining the data from the 2010 year, it definitely is worth
implementing this improvement. Secondly, it will result in a flat response of the output power.
Clearly this will contribute better to the Phase Lock Loop in the following stage. Finally, but not
least important, it can increase the power to the PLLs. Since the power level is more stable, the
circuits can be adjusted to provide higher power and in the working range, which will help the
PLLs have wider lock-in and tracking bandwidth.
2. Phase Locked Loops
Since most of the problems arise from the low power case, a reasonable idea is to adjust
the non-tracking cases. As discussed earlier, when the input power is low or goes to zero in
extreme cases, the circuits of these PLLs will go to low frequency because it is not the right
tracking. One possibility is adjusting the output to be the same frequency, or at least as close as
possible to the reference frequency when there is no input power in the plasma signal. That
requires a major modification to the circuit, since a DC voltage needs to be combined with the
feedback voltages. However, it is definitely possible, and this modification will help decrease the
fringe jump errors.
3. FC Method
One important chip that can be inserted into the advanced version is the dual-Q flip-flop.
There is no necessity to use a dual one (except for cheap cost), but one should use fast response
ones. For example, the flip-flop SN74AUC1G74 from Texas Instruments can have a minimum
pulse duration of 1 ns, which is to be compared to the 17 ns for the current one. Furthermore, we
can use this one for converting the reference into a negative trigger, too. For Vcc=1.8 V, the
minimum delay time is 1.1 ns; this means that Q instead of inverted
into the
can be directly feedback
. Therefore, this will cut the typical negative length of the trigger from 18.7 ns to
1.5 ns, which will significantly improve the signal to noise ratio and the linearity of phase and
DC voltage.
Data reveal that most of the fringe jumps in the Fringe Counter method are in one direction: FC1
and FC2 usually increase by 0.625 V in several seconds. This means that the plasma phase is
missing 2π in a short time. Beside the PLL tracking reason, another possible reason is that the
divide-by-8 divider does not detect one waveform. The chip is comprised of three serial
connections of positive-edged D-type flip-flops. In the data sheet, the voltage input needs to be a
minimum of 0.5 Vp-p, and the input edge rate is required to be faster than 80 mV/ns from DC-10
MHz. In order to make sure these requirements are met, one amplifier before this divider can be
added. The amplifier will not affect the frequency of the rising edge even in saturation, but it will
increase the voltage change rate from negative to positive, and it will help ensure that the
maximum voltage is higher than 0.5 Vp-p.
Another possible future upgrade is to cut the divide-by-8 divider to eliminate the fringe
jump error; then a 2π phase jump will not affect the output voltage. It is not recommended, but is
rather one last step. One reason of having it is that the old flip-flop only works up to 29 MHz,
while we have a 70 MHz signal. The new flip-flops will have a maximum 250 MHz clock input,
so that will work. With 2.2 ns maximum delay time, for the undivided 70 MHz signal, it will be
1/6.6 over the whole circle, which is better than the typical case of the current circuit.
Last but not least, the delay time of these two FC outputs is slightly different. For
example, in the inverter chip 74F04 that gives plasma signal of 180° phase delay, it added more
delay time to the other. It is not a major problem for regular data, but will become an important
error source for one situation: the simultaneous happening of a fringe jump and signal switching.
A fringe jump will bring 1/8 of the voltage range change, so it is highly possible that it will lead
to the signal switching. There are some data points between the fringe jump in most cases; if
signal switching happens in between, these errors will be a fraction of 2π and very hard to correct.
However, a more balanced signal will help reduce these errors since the fringe jump happens at
the same time. Therefore, a 180° power divider might be more suitable for the delay concern.
4. Electronics Linearity Characterization
The electronics linearity is critically important since it is directly related to the final data
interpretation. For polarimetry, the maximum signal is less than 120°; the nonlinearity will
significantly increase phase error.
For interferometry, it is more critical for the fringe counter method. The nonlinearity error will
reset for the IQ method after a 2π phase change, but it will not reset for the fringe counter since
only the linear regime is used in data processing. The linear regime will determine which output
voltage will be used to obtain the phase increment on each step. The slope of the response
(voltage to phase) will determine how to convert the voltage to the phase. Currently, the slope is
calculated from the maximum voltage, which is based on the assumption that it has full linear
response over the whole band. The slope is higher in the linear regime than the whole band, and
in the data processing only the linear regime is used; this will result in a fixed ratio of errors in
the phase and density. In order to decrease this error, the linearity needs to be measured. One
possible substitution method to obtain the slope is to compare TS and IQ method data, since the
IQ method only acquires the ratio of two outputs, which is dimensionless.
4.4.3 Two Color Interferometry System
In order to compensate for the vibration noise and make it more reliable for real-time
density process, a two color system is a common method employed on large tokamaks
worldwide, like DIII-D, JET, Tore Supra, JT60U [5, 6, 10, 11]. However, different approaches
are adopted; one uses two lasers with different order of frequency, like DIII-D; while the other
uses two lasers with comparable frequencies.
In the first approach, one is extremely sensitive to plasma density changes, while the other is
sensitive to vibrations; consequently, the vibration noise can be corrected very well. On DIII-D,
the CO2 laser has a wavelength of 10.6 μm and the He-Ne laser has a wavelength of 0.63 μm, so
the ratio is 16.74. Although the CO2 laser is sensitive to the plasma density, the one fringe
equivalent density is 4.3✕1019 m-3, which is much higher than the FIR case. In a 6 MHz high
sampling rate digitizer or even in 5 kHz real time sampling rate, one fringe is not in the range of
typical density variations in adjacent sampling points. The He-Ne laser is sensitive to the
vibrations, but because of the equal path lengths and other stabilization technology applied, the
vibration noise is very low, which is about 3 mm in 1.75 s. One fringe equivalent vibration is one
wavelength or 0.63 μm; at 5 kHz sampling rate, it can tolerate a vibration speed of 3.15 mm/s,
which is higher than the maximum vibration speed of 2 mm/s. Therefore, that means neither of
them need to worry about the fringe jump in each phase increment. Assuming that the vibration
length is the same for the two lasers, the phase for
.
where K is a constant equal to the classical electron radius:
.
Then, it is easy to derive that
.
In the other approach, two similar frequencies are used. In Tore Supra and JET[10, 11], both
employ a 195 μm deuterium cyanide acid (DCN) laser as the basic source, and use an additional
118.8 μm source to compensate the vibration noise. In the real-time case, their fringe equivalent
density change rate in adjacent sampling points is in the typical density range. However, due to
the long wavelengths of FIR, on the short time intervals (0.2 ms for real time), the phase
variation due to vibrations is very small and can be neglected. Therefore, the phase increment
will be:
.
It can then be derived that
.
Then, by searching the integer pairs of F1, and F2, the minimum error will be found for solving
the above equation. Then, phase and vibration noise will be calculated.
So for our cases, there are two optional additional sources. One is the CO2 laser which is
used as the pump laser; it has a wavelength of 10.6 μm. The other is the high-k scattering laser,
which will be 602 GHz in the NSTX upgrade; it has a wavelength of 496.3 μm. The CO2 laser
has several advantages. It is much simpler to use. Since the wavelength is small, the optical
design is easier; to share the same optics, it might be possible to just drill a hole in one mirror
center and let the beam pass through. In that case, one avoids the 3 dB loss in the beam splitter;
the total phase due to vibrations and density change will not exceed 2π in minimum time
intervals in real-time, so only the fringe jump errors in the FIR laser signal need be of concern; it
can be modulated at low frequency, for example using a 5 kHz grating, and then the circuit will
be easier. However, the 602 GHz FIR case will give higher resolution of density fluctuations, but
will take great effort to achieve good performance.
4.4.4 New Layout For Polarimetry
As a combination on the same optical path in the plasma, interferometry and polarimetry
provide very important information about the density and magnetic fluctuations. The case of
interferometry alone will provide only the density fluctuations , and the
polarimetry case will cover both the density and magnetic fluctuations; its first order fluctuation
is , so it is possible to separate these fluctuations by spectrum and
intensity. It might therefore be possible to obtain the correlation between these two fluctuations
on each specific frequency band.
Good news for the case of polarimetry is that the upgrade of NSTX will almost double
the toroidal magnetic field from 0.55 T to 1 T, which will almost double the Faraday rotation
angle, i.e. the phase signal, which will help to increase the signal to noise ratio. In order to
further decrease the electronics noise, the optical separation method can be done to separate the
right-handed and left-handed circular waves. This method also requires that additional mixers
must be added, although that means additional cost, the mixing harmonic product will be
decreased dramatically.
To understand the approach, we let them pass through a quarter wavelength plate. Let us
assume that the fast axis is the coordinate X-axis. The right-handed circular wave will
be ; after passing through the quarter-wave plate, the electric field will be 90° retarded
along the Y-axis, so the electric field will become , which is a linear polarized wave 45°
degrees below the fast axis. Similarly, it will convert the left-handed circular wave to
a linear polarized wave ), which is 45° above the fast axis. These two waves are
perpendicular to each other. Then, using one polarizer along any one of them, one will pass
through and the other will get reflected.
One very important reason this method can be used is that the Cotton-Mutton effect of
these two waves is very small in the plasma. It is the Cotton-Mutton effect that changes the
circular wave to an elliptically polarized wave. For the maximum case, B=0.55 T, l=6.6 m,
n=1020 m-3, the Cotton-Mouton angle Φ = 4.84 × 10-11λ3∫n B2 dx=0.013 rad=0.75 degree. For
NSTX-U, the maximum value of B will be 1 T, and then this angle will be 3 degrees. If we do
not consider the correlation between the Cotton-Mouton effect and Faraday rotation, it will only
convert (1+sinΦ-cosΦ)/2(1+sinΦ+cosΦ)×100%=1.3% from a right-handed circular wave to a
left-handed circular wave, and 1.3% for the contrary change as well.
Through this approach, a two-laser interferometry and polarimetry system is designed as
in Figure 4.14. Firstly, one ordinary Michelson Interferometer is designed; FIR laser A is
separated into two beams, one goes through the plasma and the other does not. Then, each of
them is mixed with FIR laser B, and we obtain the signals f1= fA * - fB and LO fLO= fA - fB. Then,
by comparing these two, we obtain the desired interferometry data. Secondly, let one divided
FIR laser B go through the plasma as well. Here, the purpose of the polarizer and quarter-wave
plate in the input is to convert them together and convert them into right-handed and left-handed
circular waves, and in the output the opposite. Then, this signal is mixed with FIR laser A,
producing the output f2= fA - fB*. To obtain the polarimetry data, one compares the phase between
the two signal mixer outputs f1 –f2.
By this method, firstly, we reduce the number of lasers from 3 to 2, which clearly
decreases the cost and releases one laser for other uses. Secondly, it improves the video
bandwidth from the original 1 MHz to 4 MHz. If an additional high pass filter is applied for
frequency separation of the right-handed and left-handed waves, it will also maintain at least 3
MHz bandwidth. Last, but not least, it decreases the noise floor. One source is due to the
electronics separation of close frequency, another is the noise of the third laser, and the noise of
the mixing harmonics.
However, this approach does have some disadvantages; one is the cost of a new mixer (it
is about $20,000 for new waveguide mixer). The second is the relatively complicated optical
path if we want to retain the same optical path (that is for depressing the noise level) for each
laser. The third is that relatively high laser power is required, since both of these two lasers are
needed to work as LO, and optical branches for each laser are more.
Figure 4.14 Two laser interferometry and polarimetry system
References
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Diagnostics Instrumentation and High Power Devices”, University of California, Davis, 2011.
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[17] H. R. Fetterman, et al. “Far‐ir heterodyne radiometric measurements with quasioptical
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81, 10D507 (2010)
Chapter 5
Conclusions and Future System Upgrades
5.1 Conclusions
This dissertation mainly presents two microwave imaging diagnostics (ECEI and MIR),
and FIReTIP for the density and magnetic field diagnostic. ECEI provides electron temperature
fluctuation imaging and MIR provides density fluctuation imaging; by combining them on the
DIII-D Tokamak, they are able to reveal new physics insights and advances. Millimeter wave
bursts are an interesting phenomenon observed on both ECE and ECEI systems, which warrants
further characterization, physical modeling, and experimental verifications. Lastly, the FIReTIP
system was introduced and the data are processed with newly developed algorithms for both
regular (post-shot) and real-time density calculations.
The combined ECEI and MIR systems on DIII-D, which provide simultaneous electron
temperature and density imaging at the same plasma volume, are introduced firstly. The ECEI
system is comprised of two major parts, the optical and array system, and the electronics. In the
optical and array system, the signals are rectified and imaged firstly to the antenna arrays, where
some filtering and protesting are applied in the optical path; and the advanced mini-lens lead to a
series advance of the antenna design and signal coupling. The electronic of ECEI has upgraded
to 4th generation, where several automated testing systems are applied for their calibration and
several characteristics are guiding the experiments. Two recent major upgrades are given here,
one is the use of zero bias detectors which has greatly decreased the noise level, and the other is
the expanded radial coverage which doubles the radial view in the plasma. For the MIR system,
both the core and edge covering with the narrow and wide channels spacing are achieved by the
independently controlled dedicated focusing lens and advanced receiver optic systems.
Moreover, the synthetic diagnostic modeling had been accompanied to verify the design, which
shows great agreement with the real plasma response. Some details about the transmitter,
receiver and electronics are presented, which gives the frequency coverage from 56 GHz to 64
GHz, and also gives four simultaneously step tunable frequencies. To calibrate the time base for
ECEI and MIR, some lab tests shows a 6 μs time delay for the ECEI system, which agrees with
the results from the group delay calculated from the circuits. Moreover, the 3/2 NTM are treated
as an input signal to both systems, and then the time delay was obtained from the linear fit of the
phase differences from proper channel and mode frequencies; the results also agree with the lab
results. In addition, the ECEI and MIR systems are also time calibrated to two other important
diagnostics, the ECE radiometer and magnetic fluctuation diagnostic systems.
Intense bursts of mm-wave emission with durations of 5-10 μs have been observed by
both ECE radiometer and ECEI systems during edge localized modes, Quiet H-mode (QH)
modes, and the precursor before disruptions. Both the ECE radiometer system and the ECEI
system employ heterodyne detection methods and have overlapping intermediate frequency (IF)
bands. A new RF spectrometer, spanning this IF frequency range of approximately 2-10 GHz,
has been installed on the DIII-D tokamak. It rules out the RF interference possibilities, which
shows that the bursts are indeed millimeter wave bursts. Moreover, the bursts intensity is
measured, the radiation temperature can go up to 10 MeV. Furthermore, some new imaging
about the bursts is obtained. From these, the locations of the bursts are more likely to be near the
midplane and LCFS; however, the movements are randomized. In the QH-mode low
collisionality plasma, these bursts are synchronized to the edge harmonic oscillation (EHO) and
the rising edge of longer period oscillations in filterscope data. Enhanced electron transport
precedes bursting and we hypothesize that this bursting is due to some of the resulting electron
orbits being in resonance with the 3D structure of the EHO. As a trial model, this dissertation
presents the Cyclotron AutoResonance Maser (CARM) and Gyro-BWO models to explain these
bursts, which need further verification from more designed experimental data and the simulation
results.
The multichannel FIReTIP system provides line-integrated plasma density and magnetic
information from multiple viewing chords on the midplane of the NSTX device. Extremely wide
bandwidth phase comparator electronics for the FIReTIP system were developed and installed on
the NSTX device in 2009, which extends the bandwidth up to 4 MHz when operated in an
interferometry-only configuration. The new electronics provides simultaneous interferometer
phase measurement data using two distinct phase comparator methods; one is the FC approach,
and the other is the IQ approach that achieves the full 4 MHz video bandwidth. New algorithms
have been developed to process the FIReTIP data for both regular post-shot calculations for both
approaches, which shows good agreement with the data using Thompson Scattering where
available. Moreover, the processed real-time data shows great response speed, reliabilities, and in
time stops when data are not correct, which make them suitable for the real time density
feedback control. In real time data, the IQ approaches are more trustworthy due to its better
Fringe Jump handling capability; but the FC approaches will be the future choice for NSTX-U
since the Fringe Jump error will be suppressed with the better signal levels and the density
change will be more dramatic.
5.2 System Upgrades
5.2.1 ECEI System
For the ECEI system, several things will help improve the capability. In Dr. Xiangyu
Kong’s dissertation [1], the pre-amplifier which will reduce the noise temperature of the ECEI
system, the sub-harmonic mixer [2] which will increase the detectable frequency range of
millimeter wave, and the electronics upgrade which promise a better and simpler electronics, are
discussed. Here, two major upgrades will be discussed more thoroughly firstly and followed by
some minor upgrades; one is the absolute temperature calibration and the other is the noise
debugging.
The first one is absolute temperature calibration. Currently, the ECEI system does not have and
absolute temperature measurement; consequently, most of the time, ECEI is used to image the
temperature fluctuations. Usually, it requires some eigenmodes like the MHD behaviors.
However, it is possible to calibrate the whole system. The horizontal calibration by the new RF
Spectrometer discussed in Section 3.1.3 is a very good start, which can calibrate the one
midplane ECEI arrays by interpolating and extrapolating the temperatures.
To have the vertical temperature calibrated, there are three approaches. One is to use the
assumption that temperatures are the same over the same flux surface. By this assumption, firstly
one Equilibrium Fit (EFIT) will be conducted for the time that is of interest. Then, each ECEI
channel can find one point in the midplane that shares the same flux surface with it. And finally
the temperature can be obtained by interpolating and extrapolating by the position. The second
method is moving the plasma vertically (up or down) by one channel. During this time, the
plasma needs to be very stable and we assume that the plasma shape and temperatures stay
constant during this movement. So vertically their temperatures are calibrated relatively. Since
we know the absolute temperature of the array in the midplane, the entire system will receive the
absolute temperature calibration. Here, there are three limitations: one is the plasma stability;
during this movement, the plasma shape and temperature need to hold relatively constant, which
could be challenging; another one is that the optical rays are not purely horizontal, so the vertical
channel spacings are not exactly the same; the last but not least, the plasma shape relative to the
optics has changed, so the original focus location might change as well due to the refraction of
the plasma. The third method is by moving the antenna array vertically by one channel. Since the
size of the array and antenna are designed to be identical, so that the received ECE radiation and
LO power are almost the same by replacing ECE channel. Here, the limitation is that during the
movement, the plasma needs to be relatively stable.
The second one is the noise debugging. Specifically, the HL2A ECEI system has some noise
problems with lower sampling rate at 250 kHz; EAST ECEI system has tens of coherent noises
in the spectra, like 34, 135, 270 kHz; there are also some minor noise problems in the DIII-D
ECEI system. However, some experiments have been conducted for checking the noise sources.
Firstly, the noise in the HL2A ECEI system is identified to be the clock-signal leakage. The
clock signal is 25, 600 kHz; it will convert to 100 kHz when using a 250 kHz sampling rate
digitizer. In DIII-D, all channels of the digitizer are sharing the same ground, which is also the
same ground for the electronics, array box, as well as the BWO. 8 MHz oversampling is applied
initially; then this signal goes through a 2.5 MHz Anti-alias Filter (AFF). Then, it is accumulated
into 1 MHz by a ratio of 8:1. The clock signal will be down-converted to 1.6 MHz; then by
accumulation, it is converted to 400 kHz. This 400 kHz noise is on some of the ECEI channels,
but since the accumulation will has an effect like a sin(x)/x function with the first dip in 1 MHz,
the noise level usually is very small which is comparable to the noise background. However, for
the noise observed in the EAST ECEI system, the noise sources are unknown; three possible
reasons have been pointed out and need future verification. One is the digitizer problem. It is
noticed in the EAST digitizer that there are strong 135 kHz and 270 kHz noises when the
digitizers are open (as shown in Fig. 5.1); these two frequencies match with the regular noise that
is observed in the signals. Another reason might be ground problems. In DIII-D, two similar
digitizers are digitizing the same square wave, one shares the same ground with the signal, which
gives a 3 mV noise in the flat part of the square wave (as shown in Fig. 5.2); the other does not
share the same ground, which gives a 80 mV noise in the flat part of the square wave. The third
one might be some other millimeter wave or RF wave interference. In some rare shots in the
2013 campaign as shown in Fig. 5.3, there appears some noises with a cycle of 0.05 ms in the
DIII-D ECEI system. When there is strong plasma, the noise disappears.
Fig. 5.1
Noise spectrum for the EAST ECEI digitizer. The noise is taken when the digitizer
channel are open. The y-axis is in log scale.
Fig. 5.2
Noise comparison for shared ground (black) and separate ground (blue).
Fig.5.3
Noise with some millimeter or RF interference. a) the overall noise observed in
ECEI, the noise last from 0-1 s and 5.6-8 s. Here 5.6 s is the plasma end. b) Zoom-in of the noise
in ECEI channel.
Beside these two upgrades, there are also some other important upgrades. The first one is
a fully remote control system so that the optics and notch filters can be adjusted from the
Michelson lab or even online without requiring access to the pit area to avoid the long waiting
time for plasma operation. The second one is applying the higher frequency ECEI electronic
modules to the DIII-D system, so that the plasma coverage will be doubled, and more
importantly the ECEI location does not need to be adjusted every day. The third one is another
poloidal ECEI view for access to the divertor region, where most of the heating exchanges are
happening, which make it an ideal location for more physics studies.
5.2.2 MIR System
As an innovative system, MIR system has many potential for further improvement. The
phased array antenna design and application can be founded in Dr. Huan Liao’s dissertation [3].
Here, three other important improvements will be discussed. The first one concerns the
transmitter and receiver system; the second one is the digital LPFs development; and the third
one is the frequency scan control.
The first one is the transmitter and receiver system upgrade. The current one has two
limitations; one is that the noise level of the 880 MHz IQ mixer is relatively higher than the 140
MHz IQ mixer. The other is that there is a gap in the probing band from 56-74 GHz. Figure 5.4
shows one option of the new schematic of the proposed system consisting of illumination sources
and receiver electronics. The numbers of the IF frequencies of 5, 8.3, 11.6, 15 GHz are just a
demonstration of multi-frequency operation; actually, they are all tunable from 2 GHz to 18 GHz
(which will make the correlation very easy). Here, only single side probing is used, so only the
fLO1-fIF are passing. In the receving end, it is mixed with another LO with 140 MHz difference
from the first LO, and then the same IF frequency, so it generates the 140 MHz signals. By
comparing the two LO sources, the 140 MHz reference signal is obtained, and then the phase and
amplitude are finally obtained by the 140 MHz IQ mixer. The problem here mainly concerns the
mixer, which requires 2-18 GHz; this might require up to 4 different mixers for the whole band.
Fig.5.4
A design for MIR transmitter and receiver.
The second one is to find the right digital LPFs for the MIR system. The last stage analog filter
has a cutoff of 1.5 MHz, since currently the digitizing frequency is 1 MHz; therefore, the video
bandwidth is only 500 kHz. Consequently, this means that some proper digital filtering is
needed. The digitizer ACQ132 [4] used in the DIII-D MIR system is manufactured by D-TACQ
Solutions. There is built-in Finite Impulse Response (FIR) filtering that can provide this kind of
filtering. However, time delays are tested by comparison of the regular digitizer and digitizer
with FIR filtering with the same inputs of square waves with frequency varying from 5 kHz to 20
kHz. Figure 5.5 is an example of the digitized signal for the 7.5 kHz input; the time delay is
obtained by comparing the time of the rising edge of the square wave. It shows that there is a
long time delay and that it is not constant over frequencies. At 5 kHz, it is 123 or -77 μs; at 7.5
kHz, it is 89.8 or -43.2 μs; at 10 kHz, it is 72 or -28 μs; at 20 kHz, it is 48 or -2 μs. Therefore,
some new digital filtering needs to be designed and tested.
Fig.5.5
Time delay test for the FIR filtering. A 7.5 kHz square wave is input into both
digitizers. Black line is digitized signal with the FIR filtering; blue line is the digitized signal
without the FIR filtering. The rising edges are compared for two signals, and the time delay for
the FIR filtering is determined to be -43.2 or 89.8 μs.
The last one is the frequency scan for the MIR probing frequency. The IF sources are
provided by four Pronghorn sources which are step-tunable using the Labivew program. This
option could be easily achieved by controlling the frequency of two Pronghorn sources
simultaneously, so that their frequencies remain to be 510 MHz apart. However, to do a full scan
for the IF frequency from 1-9 GHz, the mixers need to be switched at the same time to match the
right frequency band.
References:
[21] Xiangyu Kong, ‘Millimeter-Wave Imaging Technology Advancements for Plasma Diagnostics
Applications’, Ph.D. thesis, 2013 UC Davis
[22] Jiang, Qi, Calvin Domier, and N. C. Luhmann. "A wideband low loss planar microstrip-to-CPS
balun." In Microwave Conference Proceedings (APMC), 2012 Asia-Pacific, pp. 1205-1207. IEEE,
2012.
[23] Huan Liao, Ph.D. thesis, 2013 UC Davis
[24] http://www.d-tacq.com/index.shtml
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