Experimental Studies of Edge Turbulence, Convective Transport

Transcription

Experimental Studies of Edge Turbulence,
Convective Transport and SOL Flow in the
Spherical Tokamak QUEST
Doctoral Thesis
July, 2013
By
Santanu Banerjee
(Professor Hideki Zushi, Supervisor)
Advanced Energy Engineering Science
Interdisciplinary Graduate School of Engineering Sciences
Kyushu University
Acknowledgements
Slowly setting into the final lap of my doctoral studies, it is a ‘dream come true’ moment for me.
I would like to express deep gratitude to my supervisor, Professor Hideki Zushi on this occasion.
He has been a constant source of motivation and guidance ushering my apparently incoherent
thoughts towards a well knit study with definitive objectives. I enjoyed his thorough
understanding of plasma physics and especially tokamak plasma. His constant encouragements
motivated me to take on the problems by their horns. These three years of his affectionate
patronage will remain as an everlasting memory in my life. ありがとうございました先生。
I sincerely acknowledge Professor Nobuhiro Nishino and Professor Tomohiro Morisaki for the
collaborative research and their deep interest in my work. I sincerely thank Professors Hiroshi
Idei, Kazuaki Hanada and Kazuo Nakamura for their constructive criticism of my work from
time to time. I also thank Professors Akihide Fujisawa, Makoto Hasegawa and Yoshihiko
Nagashima for many useful discussions in due course of my study. I also thank Professor
Keisuke Matsuoka for his able support during my experiments and glitch free operation of the
QUEST device.
I sincerely thank Professor P.K. Kaw, Dr. P. Vasu, Dr. J. Ghosh and the members of the
academic committee of the Institute for Plasma Research (IPR) for their motivations and
providing me this opportunity to pursue my doctoral studies at Kyushu University, Japan.
I would like to thank Mrs. A. Higashijima, Mr. S. Kawasaki and Mr. H. Nakashima for their
technical support. I also wish to acknowledge the QUEST office ladies for their kind support and
help. Special thanks to Ms. R. Isayama, Ms. K. Nakamura, Ms. J. Miyachi, Ms. K. Kono, and Ms
Y. Tominaga. I really enjoyed the events either hosted or initiated by the office ladies.
I am really fortunate to share a comfortable research space with my colleagues in the Zushi-Idei
laboratory. I would like to thank specially Dr. S. Tashima for her constant support and immense
help during my stay in Japan. I would like to thank Mr. T. Ryokai, Mr. K. Nagata, Mr. T. Inoue,
ii
Mr. Y. Mahira, Mr. Y. Inoue and Mr. T. Itado. I also thank the foreign students, Dr. E.
Kalinnikova, Dr. S.K. Sharma, Dr. A. Rusinov and Mr. K. Mishra for the intriguing discussions
on plasma physics as well as society and customs of different countries.
At this point, I feel the urge to acknowledge a host of friends and close relatives in India who
have wished me well and helped me all along my stay over here. My father Mr. Sarashi Kumar
Banerjee and my mother Mrs. Tripti Banerjee have provided me the platform from where I can
launch myself towards the field of active research and pursue my studies towards this long
cherished goal. Special thanks to my in laws, Mr. Prasanta Kumar Chatterjee and Mrs. Manashi
Chatterjee for their constant support and blessings. I would like to thank my friends from IPR
technical training program batch of 2002 and the Spectroscopy Diagnostics Division. I would
also like to thank my family members, especially my uncle and aunt and my elder brother for
their patronage. I am also thankful to a lot many of my other friends from Durgapur and
Ahmedabad and relatives whose contributions are really worth mentioning in my life.
Last but not the least I must acknowledge my beloved wife Dr. Kasturi Banerjee for her great
patience, warm encouragements and support. Without her heartiest desires and motivations I
would have not achieved this success. I owe a lot of this achievement to her.
Santanu Banerjee
Kyushu University, Japan
2013
iii
Abstract
Issues related to edge turbulence and transport in tokamaks are quite indispensible, as they
dictate the dynamical plasma behavior both in the plasma core and the edge. Edge turbulence
may have a dramatic impact on the fusion reactor operation by causing rapid release of energy
and particles which may produce significant local damages on the first wall. On the other hand,
when controlled effectively, edge turbulence could also play a beneficial role in removing
exhaust particles that, if accumulated, would lead to fuel dilution, quenching the fusion
reactivity. Another important phenomenon is the plasma flow along the magnetic field lines in
the scrape off layer (SOL). It is believed to play a vital role in the regulation of instabilities,
turbulent transport and L-H transition. Plasma flow can attain velocities approaching a
significant fraction of the local sound speed. A number of mechanisms are known to generate
parallel flows in the SOL: ionization imbalances, Pfirsch–Schlüter flows, poloidal transport
asymmetries (e.g. ballooning-like transport), and toroidal rotation. However, experimental
evidence of RF-induced poloidal flow is less readily available.
A two-fold objective is set for this thesis. First, the characteristics of the edge and SOL
turbulence and convective transport are studied in both slab annular plasma featuring open
field lines and Ohmic plasma with well defined last closed flux surface. Statistical features of
the edge fluctuations and physical mechanisms controlling the generation and propagation of
blobs are considered imperative for the core confinement efficiency and heat and particle
transport to the material wall. Fluctuations and blob trajectories can be traced comprehensively
in 2D with tangential fast imaging across a wide region in the SOL. Hence it can provide
significant improvements over the single point probe measurements. The second aspect is the
characterization of the SOL flow. This is aimed at gaining knowledge of the flow pattern in the
SOL and its impact on the turbulent transport. Tangential fast imaging diagnostic along with
the conventional Langmuir and Mach probes in the SOL can provide a wealth of information
regarding the poloidal flow components. This thesis is therefore organized as follows:
In Chapter 2, brief descriptions of the spherical tokamak QUEST and diagnostics are outlined.
iv
Chapter 3 deals in the edge turbulence and convective intermittent transport in slab plasma.
Two types of slab plasma with different ECR heating are studied.
In the first part, statistical aspects of the convective transport with respect to the variation in
magnetic field pitch are studied. Amplitude and waiting time of the blobs attains a
maximum for highest Bz/Bt. 2D statistical analysis of the images enables us to identify blob
formation location precisely. Accelerated radial propagation was observed for large blobs.
In the second part, effect of mirror ratio on turbulence is studied with the change in poloidal
field curvature. Fluctuation characteristics are quite different for the poloidal field coil pairs
PF17, 26 and 35 with high, moderate and low magnetic shears respectively. Coherent peak
appears for deep PF well (PF35) beyond Bz ~ 13 mT.
In chapter 4, plasma turbulence characteristics in the edge and SOL of Ohmic plasma are
summarized. Intermittency, dominated by blobs, is observed in the SOL. A simple parabolic
relation exists between skewness and kurtosis, and the probability density function (PDF)
significantly deviates from Gaussian beyond the density gradient region. A model has been
proposed to characterize the PDFs in the density gradient and far SOL regions.
In chapter 5, observation of ECW induced SOL flow is reported. Definite flow structures with
long range radial and poloidal correlation and a distinct mode at 781 Hz are observed. Cross
correlation of intensity shows poloidal spin-up and radial out-flow. Also, a novel technique
based on particle image velocimetry is developed to further analyze the flow velocity of the
coherent mode. Increase in H and ion saturation current suggests strong cross-field transport.
This may be driving the SOL parallel flow under the unique scenario of ECW induced inboard
poloidal null configuration in QUEST.
In conclusion, this study has provided deeper insights in the generation mechanisms and
propagation dynamics of the coherent convective structures (blobs). The effect of field pitch and
curvature may provide better controls on the intermittent transport at the edge. Further,
characterization of the SOL flow induced by ECW, which is one of the most common auxiliary
heating and current drive systems in fusion devices, may provide better regulation of instabilities
and help in achieving improved confinement.
v
List of abbreviations
ACA – auto conditional average
CAD – Computer aided design
CCA – cross conditional average
CMOS – Complementary metal oxide semiconductor
ECRH – Electron cyclotron resonance heating
ELM – Edge localized mode
FOV – Field of view
FPS – Frames per second
FWHM – Full width at half maxima
HFS – High field side
IPN – Inboard poloidal null
ITER – International Thermonuclear Experimental Reactor
LCFS – Last closed flux surface
LFS – Low field side
LOS – Line of sight
MHD – Magneto-hydrodynamic
PDF – Probability density function
PF – Poloidal field
QE – Quantum efficiency
SN – Single null
SOL – Scrape off layer
TF – Toroidal field
TITR – Tangential image tomographic reconstruction
UHR – Upper hybrid resonance
vi
Contents
Acknowledgements
Abstract
ii
iv
List of abbreviations
1
Introduction
Foreword
1.2
Edge turbulence and transport
1.3
Scrape off layer (SOL) flow
1.4
Motivation: study of convective intermittent transport and SOL flow
1.5
Objective
1.6
Organization of this thesis
2
3
5
6
8
8
10
Device description
12
2.1
Q – shu University Expt. with Steady State Spherical Tokamak (QUEST)
2.2
Wide angle visible imaging system
2.3
Tangential fast visible imaging system
2.4
Reciprocating probe
References
3
1
1.1
References
2
vi
14
14
17
18
Edge turbulence in the slab plasma
A.
13
19
Statistical features of coherent structures at increasing magnetic field pitch
3.1 Introduction
20
3.2 Experimental conditions
22
3.3 Variation of the source plasma with field pitch
3.4 Statistical properties of the fluctuations
3.4.1
Blob generation location
3.4.2
Quadratic relation between s and k
25
27
29
30
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3.5 Generation and propagation of coherent structures (blobs)
3.5.1
Blob filaments originating from coherent poloidal mode
3.5.2
Conditional averages
3.5.3
Time between two bursts
3.5.4
Blob propagation
3.6 Discussions
31
33
36
37
38
3.7 Conclusions I
B.
31
40
Variations in edge turbulence induced by poloidal magnetic field curvatures for 8.2
GHz slab plasma
3.8 Introduction II
42
3.9 Experimental condition
3.10 Statistical analysis
3.11 Correlation analysis
45
46
3.11.1 Correlation coefficient
46
3.11.2 Power spectral density
47
3.12 Conclusions II
References
4
42
49
50
Edge turbulence in inboard limited plasma
4.1 Introduction
54
4.2 Experimental setup and fast camera imaging
4.3 Characteristics of the Ohmic plasma SOL
4.4 Statistics of the intensity fluctuations
5
4.5 Discussions
65
4.6 Conclusion
67
References
69
56
60
61
ECW induced scrape off layer (SOL) flow
5.1 Introduction
53
71
72
5.2 Experimental details
73
viii
5.3 Spectral characteristics of intensity fluctuations
75
5.4 Estimation of poloidal component of parallel velocity
77
5.5 Particle image velocimetry through orthogonal dynamic programming (ODP)
5.6 Strong outward particle flux serves as source
5.7 Conclusions
References
6
7
79
82
84
85
Conclusions and future scope
6.1 Conclusions
89
6.2 Future scope
91
88
List of publications and presentations
93
ix
List of publications/presentations
Peer reviewed journals:
1. Santanu Banerjee, Hideki Zushi, Nobuhiro Nishino, Yoshihiko Nagashima, Kazuaki
Hanada, Saya Tashima, Tsubasa Inoue, Kazuo Nakamura, Hiroshi Idei, Makoto Hasegawa,
Akihide Fujisawa and Keisuke Matsuoka, “Turbulence velocimetry of tangential fast
imaging data on QUEST”, accepted in Plasma Fusion Res. 2013
2. Santanu Banerjee, H. Zushi, N. Nishino, K. Hanada, S.K. Sharma, H. Honma, S. Tashima,
T. Inoue, K. Nakamura, H. Idei, M. Hasegawa and A. Fujisawa, “Statistical features of
coherent structures at increasing magnetic field pitch investigated using fast imaging in
QUEST”, Nucl. Fusion, 52, 123016, 2012
3. Santanu Banerjee, H. Zushi, N. Nishino, Y. Nagashima, K. Hanada, M. Ishiguro, T.
Ryoukai, S. Tashima, T. Inoue, K. Nakamura, H. Idei, M. Hasegawa, A. Fujisawa, and K.
Matsuoka, “Fast visible imaging and edge turbulence analysis in QUEST”, Rev. Sci. Instum.,
83(10), 10E524, 2012
4. Santanu Banerjee, H. Zushi, N. Nishino, K. Hanada, S. K. Sharma, T. Inoue, H. Q. Liu, M.
Ishiguro, T. Ryoukai, S. Tashima, K. Nakamura, H. Idei, M. Hasegawa, A. Fujisawa and K.
Matsuoka, “Statistical Analysis of the Convective Intermittent Transport at the Edge Region
of QUEST”, IEEJ Transactions on Fundamentals and Materials, 132(7), 545-554, 2012
5. Santanu Banerjee, H. Zushi, N. Nishino, K. Hanada, H. Q. Liu, M. Ishiguro, T. Ryoukai, S.
Tashima, K. Nakamura, H. Idei, M. Hasegawa, and A. Fujisawa, and the QUEST group,
“Statistical interpretation of the density fluctuations from the high-speed visible images of
edge turbulence on QUEST”, IEEE Transactions on Plasma Science, 39(11), 3006, 2011
Conference presentations:
1. Santanu Banerjee, H. Zushi, N. Nishino, Y. Mahira, K. Nagaoka, K. Mishra, K. Hanada, S.
Tashima, Y. Nagashima, K. Nakamura, H. Idei, M. Hasegawa, A. Fujisawa and K. Matsuoka,
“Scrape off layer flow characteristics investigated using fast visible imaging in QUEST”, 12th
Asia Pacific Physics Conference (APPC12), July 14 – 19, 2013, Makuhari Messe, Chiba,
Japan
2. Kishore Mishra, H. Idei, H. Zushi, S. Tashima, S. Banerjee, M. Hasegawa, K. Hanada, K.
Nakamura, A. Fujisawa, K. Matsuoka, Y. Nagashima, S. Kawasaki, A. Higashijima, H.
Nakashima and QUEST Group, “Characteristics of high poloidal beta ( p) plasma formed by
electron cyclotron waves in spherical tokamak QUEST”, 12th Asia Pacific Physics
Conference (APPC12), July 14 – 19, 2013, Makuhari Messe, Chiba, Japan
93
3. Santanu Banerjee, H. Zushi, N. Nishino, Y. Mahira, K. Mishra, K. Hanada, S. Tashima, A.
Ejiri, T. Yamaguchi, Y. Nagashima, K. Nakamura, H. Idei, M. Hasegawa, A. Fujisawa and K.
Matsuoka, “Experimental investigation of electron cyclotron wave induced plasma flow in
the scrape off layer of QUEST”, 3rd Asian-Pacific Transport Working Group (APTWG2013)
Meeting , May 21 – 24, 2013, Jeju Island, Korea
4. Santanu Banerjee, H. Zushi, N. Nishino, Y. Nagashima, K. Hanada, S. Tashima, T. Inoue,
K. Nakamura, H. Idei, M. Hasegawa, A. Fujisawa and K. Matsuoka, “Edge turbulence
characteristics of the Ohmic-ECRH driven plasma current phase investigated with fast
visible imaging in QUEST”, 22nd International Toki Conference (ITC22), November 19 – 22,
2012, Ceratopia Toki, Toki-city, Gifu, Japan
5. H. Zushi, S. Tashima, M. Ishiguro, M. Hasegawa, S. Banerjee, N. Nishino, M. Isobe, K.
Hanada, H. Idei, K. Nakamura, A. Fujisawa, Y. Nagashima, K. Matsuoka, S.K. Sharma, H.
Liu, K. Toi, T. Maekawa, A. Ejiri, T. Yamaguchi, J. Hiratsuka, Y. Takase, M. Kikuchi, A.
Fukuyama, Y. Ueda, O. Mitarai, S. Okamura, “Non-inductive current start- up and plasma
equilibrium with an inboard poloidal field null by means of electron cyclotron waves in
QUEST”, 24th IAEA Fusion Energy Conference, October 8 – 13, 2012, San Diego, USA
6. Santanu Banerjee, H. Zushi, N. Nishino, K. Hanada, M. Ishiguro, S. Tashima, T. Inoue, K.
Nakamura, H. Idei, M. Hasegawa, A. Fujisawa, K. Matsuoka and Y. Nagashima, “Edge
turbulence study with fast visible imaging in QUEST”, 2nd East Asian Workshop on
Laboratory, Space, Astrophysical Plasmas, June 26 – 29, 2012, Jeju Island, Korea
7. Santanu Banerjee, H. Zushi, N. Nishino, Y. Nagashima, K. Hanada, M. Ishiguro, T.
Ryoukai, S. Tashima, T. Inoue, K. Nakamura, H. Idei, M. Hasegawa, A. Fujisawa, K.
Matsuoka and the QUEST group, “Variations in edge turbulence induced by poloidal
magnetic field curvatures for 8.2 GHz slab plasma in QUEST”, 19th Topical Conference;
High-Temperature Plasma Diagnostics (HTPD19), May 6 – 10, 2012, Monterey, CA, USA
8. Santanu Banerjee, H. Zushi, N. Nishino, K. Hanada, S.K. Sharma, T. Inoue, H.Q. Liu, M.
Ishiguro, T. Ryoukai, S. Tashima, K. Nakamura, H. Idei, M. Hasegawa, A. Fujisawa and the
QUEST group, “Statistical analysis of the convective intermittent transport at the edge
region of QUEST”, 16th International Workshop on Spherical Torus (ISTW2011);
September 27 – 30, 2011, National Institute for Fusion Science, Japan
9. N. Nishino, H. Zushi, S. Banerjee, K. Hanada, S.K. Sharma, H.Q. Liu, M. Ishiguro, S.
Tashima, K. Nakamura, H. Idei, M. Hasegawa, A. Higashijima, A. Fujisawa and the QUEST
group, “Two-dimensional HeII Doppler shift image measurement in QUEST”, 16th
International Workshop on Spherical Torus (ISTW2011); September 27 – 30, 2011, National
Institute for Fusion Science, Japan
10. Santanu Banerjee, H. Zushi, N. Nishino, K. Hanada, H. Honma, H.Q. Liu, M. Ishiguro, T.
Ryoukai, S. Tashima, K. Nakamura, H. Idei, M. Hasegawa, A. Fujisawa and the QUEST
group, “Origin and evolution of coherent convective structures investigated using fast
94
imaging in QUEST”, 1st Asia Pacific Transport Working Group (APTWG2011) International
Conference; June 14 – 17, 2011, National Institute for Fusion Science, Japan
Besides, there are a number of presentations in the Physical Society of Japan (JPS) spring and
fall meetings and the Japan Society of Plasma Science and Nuclear Fusion Research (JSPF)
meetings.
- -
95
CHAPTER ONE
Introduction
1.1 Foreword
1.2 Edge turbulence and transport
1.3 Scrape off layer (SOL) flow
1.4 Motivation: study of convective intermittent transport and SOL flow
1.5 Objective:
1.6 Organization of this thesis
References
Introduction
1.1 Foreword
Nuclear fusion powers the Sun and stars as hydrogen atoms fuse together to form helium, and
matter is converted into energy. The fuel gas hydrogen, heated to very high temperatures changes
from gas to plasma in which the negatively charged electrons are separated from the positively
charged atomic nuclei (ions). Normally, fusion is not possible because the strongly repulsive
Coulomb forces between the positively charged nuclei preventing them from getting close
enough together for fusion to occur. However, if the conditions are such that the nuclei can
overcome the electrostatic forces to the extent that they can come within a very close range of
each other, then the attractive nuclear force (which binds protons and neutrons together in atomic
nuclei) between the nuclei will overwhelm the repulsive (electrostatic) force, allowing the nuclei
to fuse together. Such conditions can occur when the temperature increases, causing the ions to
gain energy and eventually reach speeds high enough to bring the ions close enough together.
The nuclei can then fuse, releasing an enormous amount of energy.
The most favorable fusion reaction is between the nuclei of the two heavy isotopes of hydrogen –
deuterium (D) and tritium (T). Each D-T fusion event releases 17.6 MeV (2.8 x 10-12 J, compared
with 200 MeV for an U-235 fission). Deuterium occurs naturally in seawater (30 g m-3), which
makes it very abundant relative to other energy resources. Tritium does not occur naturally and is
radioactive, with a half-life of around 12 years. It can be made in a conventional nuclear reactor,
or in the present context, bred in a fusion system from lithium. Lithium is found in large
quantities (30 ppm) in the Earth's crust and in weaker concentrations in the sea. Thus, despite the
challenging task of plasma confinement at high temperature, the option of nuclear fusion stands
out as the most viable energy source to serve the ever increasing energy demand while
addressing effectively the carbon free energy issue for clean environment.
In the Sun, increase in ion energy to a level where fusion can occur, without the plasma being
disrupted is possible due to the perfect plasma confinement with massive gravitational forces. On
the contrary, such conditions are rather challenging to achieve on the Earth. Fusion fuel –
different isotopes of hydrogen – must be heated to extreme temperatures of the order of 100
million degrees Celsius, and must be kept dense enough, and confined for long enough, to allow
the nuclei to fuse. The aim of the controlled fusion research program is to achieve 'ignition',
2
Introduction
which occurs when enough fusion reactions take place for the process to become self-sustaining,
with fresh fuel then being added to continue it. The answer to this problem is magnetic
confinement fusion. In magnetic confinement, hundreds of cubic meters of plasma at a density of
less than a milligram per cubic meter are confined by a magnetic field at a few atmospheres
pressure and heated to fusion temperature by Ohmic heating, auxiliary heating like with
microwaves and finally fusion alpha particle self-sustained heating. The most promising device
to confine plasma is a TOKAMAK (a Russian acronym of
" i.e. toroidal'naya kamera s magnitnymi katushkami) where plasma is
confined by a combination of toroidal and poloidal field coils such that the plasma particles
traverses a distance million times the device dimension before getting lost on the vessel wall
[Wesson]. As a first step towards a fusion reactor, an International Thermonuclear Experimental
Reactor (ITER) is under construction at Cadarache in southern France under the auspices of
seven partners like China, European Union, India, Japan, Korea, Russian Federation and the
USA. ITER has been designed to deliver 500 MW of fusion power, ten times the input power
and sustained for up to 1000 s. The plasma volume is 8.4 times the largest operating tokamaks
like Europe’s JET and Japan’s JT-60U.
Confinement of the plasma at fusion temperatures is nevertheless not trivial as the plasma is
highly susceptible to various type instabilities leading to eventual disruption. There is a growing
consensus that the turbulent process at the edge affects the overall particle and energy
confinement of the core plasma. The edge plasma is particularly important as it bridges the hot
core and the material wall. Consistent efforts are on worldwide to identify the causes of density,
potential and temperature fluctuations in the edge plasma and to estimate the particle and energy
transports induced by fluctuations.
1.2 Edge turbulence and transport
Issues related to turbulence and transport in tokamaks are quite indispensible, as they dictate the
dynamical plasma behavior both in the plasma core and the edge. Edge turbulence may have a
dramatic impact on the reactor operation by causing rapid release of energy and particles of the
plasma which may produce significant local damages on the first wall [1]. Edge turbulence on
the other hand, when controlled effectively, could also play a beneficial role in removing exhaust
3
Introduction
particles that, if accumulated, would lead to fuel dilution, quenching the fusion reactivity [2].
Edge turbulence is typically characterized by very high relative fluctuation levels, leading to
strong nonlinear effects and to the formation of macroscopic field-aligned structure, often
referred to as ‘blobs’ (or blob-like structures, filaments).
The edge plasma contains both closed (inside the separatrix) and open (outside the separatrix)
magnetic field lines, which terminates on the material surfaces. Both heat and particle fluxes are
transported through the separatrix into the SOL by anomalous processes. In low-confinement
mode (L-mode) cross-field anomalous transport is relatively large while in high-confinement
mode (H-mode) it is significantly weaker. However, in H-mode, the edge plasma is subject to
violent events associated with destabilization of magneto-hydrodynamic (MHD) modes, so
called edge-localized modes (ELMs), which are not observed in the L-mode plasma.
Wall
+
B
VE
Plasma Blob
-
F
E
Figure 1.1: Schematic of a plasma blob showing
mechanism responsible for the radial transport.
B and curvature driven charge polarization
Early experimental studies of edge plasmas in tokamaks had already revealed rather largeamplitude turbulence in the edge region (e.g. plasma density fluctuations of the order of the
averaged plasma density, n/n ~ 1) and an intermittent character of the turbulence. Moreover, the
very first applications of fast cameras for diagnostics of edge plasma phenomena identified the
existence of coherent structures [3]. Later, such structures were also found with two-dimensional
(2D) probe arrays [4] and with imaging diagnostics, such as the gas-puff imaging (GPI) systems
[5] on NSTX and Alcator C-Mod. A near comprehensive physical picture of the radial
4
Introduction
convection of coherent plasma structures called blob-filaments or simply ‘blobs’ has been
portrayed by a rapidly growing volume of theoretical, computational and experimental work. It
also became clear that the dynamics of plasma filaments generated by ELMs is very similar to
blob dynamics [6], which suggests some similarities in the physics of ELM filaments and blobs.
Theory and simulations predict that blobs and ELM [7,8] filaments are born as a result of the
nonlinear saturation of underlying edge turbulence or coherent magneto-hydrodynamic (MHD)
instabilities, respectively.
Experimental observations show that these coherent objects are
spatially localized in the two-dimensional (2D) plane perpendicular to B, resembling “blobs” of
enhanced density against a lower-density background. They are spatially extended along the
direction of the magnetic field, appearing as field-aligned “filaments” in a three-dimensional
(3D) view of the SOL. Theoretically, it has been predicted that blobs in tokamaks move towards
first walls in the low field side due to E×B drift caused by the charge separation in blobs driven
by the gradient and curvature of the magnetic field [9-12]. A propagation model of blobs was
proposed in [10], based on an assumption that a filament with large plasma density at the outer
side of the torus is peeled off the bulk plasma, as sketched in Fig. 1.1 [10,13]. Then, plasma
polarization (i.e. charge separation) caused by effective drifts at low field side of a torus
(curvature and grad-B drifts in tokamaks), results in a radial E×B convection of blobs toward
walls. The magnitude of the electric field and, therefore, the convection speed are determined
from a balance of polarization and parallel currents. In Refs. [10], the blob was assumed to be in
the far SOL and the parallel current to be limited by sheath “resistivity”. In this case, it was
shown that indeed the blobs can propagate as a coherent structure with a speed of the order of a
few hundred meters per second, which was roughly in agreement with then-available
experimental data.
1.3 Scrape off layer (SOL) flow
Plasma flow along the magnetic field lines in the scrape-off layer (SOL) is believed to play a
vital role in the regulation of instabilities, turbulent transport and L-H transition since it can alter
the E B shear profile [1,14-16]. The regulation mechanism [14] is quite simple. When a fluid
eddy is placed in a stable laminar background flow whose speed varies transverse to the flow
direction, the eddy is stretched and distorted as different fluid parcels in the eddy are advected
5
Introduction
(carried along) at different speeds. If the eddy is isolated, it can be stretched to many times its
original scale length. When the eddy is constituent of a turbulent flow, however, it loses
coherence when stretched to the eddy coherence length along the direction of the background
flow. The eddy coherence length is the distance over which the eddy flow remains correlated and
can be thought of as roughly the distance between two adjacent eddies of comparable scale, a
distance on the order of the eddy diameter in fully developed turbulence.
Plasma flow along magnetic field lines has been measured in the scrape-off-layer (SOL) of many
tokamaks [17–28], with velocities approaching a significant fraction of the local sound speed. A
number of mechanisms are known to generate parallel flows in the SOL: ionization imbalances,
Pfirsch–Schl¨uter flows, poloidal transport asymmetries (e.g. ballooning-like transport), and
toroidal rotation. However, experimental evidence on RF-induced poloidal flow is less readily
available. Analytical models and numerical simulations have been proposed to reconstruct the
observed flows and their impact on impurity distributions. The success rate of such models is
still very low owing to the complexity of the flow pattern.
1.4 Motivation: study of convective intermittent transport and SOL flow
According to one of the first model of radial propagation velocities [29], blobs basically
propagated to the low field side riding on E×B drift, where E and B show electric field to
poloidal direction and toroidal magnetic field, respectively. The electric field can be originally
formed by self-induced charge separation due to grad-B and curvature drifts and keeps a certain
value via current paths through sheathes at attached region of metallic walls. However, the idea
of the formation of induced electric field is still ambiguous and the possibilities that other
mechanisms may play the crucial role such as ion polarization current [30] and ion-neutral
friction force [31]. Moreover, the radial propagation models of the structures are quite debatable
and experimental verifications are far from adequate, resulting a number of unresolved physics
issues and an ‘yet to be’ recognized mechanism is one of the key areas of magnetic fusion
research.
In high performance fusion devices, these investigations are hindered by their complex interplay
with atomic effects and by the intrinsic difficulty in diagnosing fusion grade plasmas with
6
Introduction
adequate temporal and spatial resolution, even in the plasma boundary. As a consequence, a
conclusive comparison with theoretical models is hampered by limited accessibility for
diagnostics in large magnetic confinement devices. These difficulties motivate the development
of basic plasma physics experiments dedicated to fluctuations, turbulence and transport studies,
which offer better diagnostic access and more flexibility in the use of control parameters.
Provided suitable observables for comparisons are defined, observations from these relatively
cold and low density plasmas can be used as reference cases for fusion grade plasmas.
Some aspects of the physics of waves related to turbulence and cross-field transport can be
addressed in linear devices [32], but toroidal geometry is important in order to have the
ingredients that drive turbulence in fusion experiments; namely, magnetic field line curvature in
combination with plasma gradients. A line of research has been motivated by these limitations,
namely the study of basic physics aspects of the edge turbulence in plasma environments that are
qualitatively similar to, yet much simpler than those of the edge of burning plasmas. Some
detailed measurements using simulated experiments, greatly contribute to the clarification of the
physical mechanism of blobs. Recently, similar experiments are reported were performed on
TORPEX. Blobs in the SOL region of tokamaks are simulated in plasmas created using electron
cyclotron resonance heating (ECRH) at 2.45 GHz [33]. However blobs’ characteristics are not
yet well understood because of complexity involved and the difficulty of measurements. These
motivate the further development of diagnostics of blob and dedicated physics study in toroidal
slab annular plasmas owing to the unique feature of wide SOL-like region. Blob generation and
their propagation can be studied in comprehensive details in such geometry.
Regulation of instabilities and characterization of impurity transport and particle balance is
clearly a necessary task for the efficient steady state operation of magnetic fusion reactors, such
as ITER [1]. Plasma flow in the SOL plays the quintessential role in both these aspects. The
flow is expected to expel helium ashes and to retain impurities in the divertor region. Plasma
flow parallel to the magnetic field lines may consist of a combination of Pfirsch–Schlüter ion
currents, u//PS, toroidal plasma rotation, u//rot, and a parallel component driven by cross-field
transport, u//trans, arising to satisfy particle balance [16]. Information on the poloidal component
of the flows is essential to reconstruct the total flow pattern in the SOL. For the impurity
7
Introduction
retention, it is required that the friction force by the SOL flow towards the divertor plate exceeds
the thermal force in the vicinity of the divertor throat. It has been experimentally observed,
however, that the flow direction is sometimes opposite; from the outer plate side to the SOL
middle side in the outer SOL region (low field- side) of tokamaks [16,34]. This backward flow is
seen when the single null point is located in the ion ∇B drift direction, while it vanishes for the
reversed null point location. The physics mechanisms of this backward flow have not yet been
fully known [35]. Tangential fast imaging diagnostic along with the conventional Langmuir and
Mach probes in the SOL can provide a wealth of information regarding the poloidal flow
components. Velocimetry techniques adapted from fluid mechanics for the fast visible images
can provide further insight on the flowing structures or specific modes. Thus the dominant
mechanisms behind SOL flow, especially the RF induced flow, can be analyzed in greater detail.
1.5 Objective
A two-fold objective is set for the thesis. First, the characteristics of the edge and SOL
turbulence and transport are studied in both slab annular plasma featuring open field lines and
Ohmic plasma with well defined last closed flux surface (LCFS). Statistical features of the edge
fluctuations and generic mechanisms controlling the generation and propagation of coherent
convective structures are considered imperative for the core confinement efficiency and heat and
particle transport to the material wall. These issues are quite compelling and envisaged crucial
for the future fusion devices like ITER and beyond.
The second aspect addressed in this thesis is the characterization of the SOL flow and the
associated mechanisms. This is aimed at gaining knowledge of the flow pattern in the SOL and
its impact on the turbulent transport. Further, flow generation mechanisms and the physical
parameters that can control the flow are important as they can provide the necessary knob to
regulate the particle exhaust and turbulence driven transport at the edge.
1.6 Organization of this thesis
This thesis is organized as follows:
8
Introduction
In Chapter 2, brief description of the spherical tokamak QUEST is outlined along with the
diagnostic tools that have been used during the experimental studies of turbulence and transport.
Detailed description of the experimental conditions and plasma parameters are given in the
respective chapters wherever deemed necessary.
Chapter 3 deals in the edge turbulence and convective intermittent transport in slab plasma. Two
types of slab plasma with different ECR heating (2.45 GHz and 8.2 GHz) are studied. On the
first part, statistical aspects of the convective transport with respect to the variation in magnetic
field pitch are dwelled upon, while in the second part the effect of mirror ratio on turbulence is
studied with the change in poloidal field curvature.
In chapter 4, plasma turbulence characteristics in the edge and scrape off layer of Ohmic plasma
are summarized. Statistics of the intensity fluctuations are discussed and a model has been
proposed to characterize the probability density function (PDFs) in the density gradient and far
scrape off layer regions.
In chapter 5, observation of ECW induced scrape off layer flow is reported. Cross-correlation
analysis is performed to evaluate the flow velocity. Also, a novel technique based on particle
image velocimetry using orthogonal dynamic programming is developed to further analyze the
flow velocity of the coherent mode flowing in the SOL. Probable flow mechanisms are
summarized.
Finally, in chapter 6, the summary and future plans are discussed.
9
Introduction
References
[1]
Loarte A et al 2007 Nucl. Fusion 47 S203.
[2]
Wesson J 2004 Tokamaks (International Series of Monographs on Physics Vol. 118)
(Oxford: Oxford University Press).
[3]
Goodall, D H J 1982 J. Nucl. Mater. 111–112 11.
[4]
Zweben S J 1985 Phys. Fluids 28 974.
[5]
Terry J L et al 2003 Phys. Plasmas 10 1739.
[6]
Rudakov D L et al 2002 Plasma Phys. Control. Fusion 44 717
[7]
Zohm H 1996 Plasma Phys. Controlled Fusion 38 105
[8]
D’Ippolito D A, Myra J R and Zweben S J 2011 Phys. Plasmas 18 060501
[9]
D’Ippolito D A et al 2002 Phys. Plasmas 9 222.
[10] Krasheninnikov S I et al 2001 Phys. Lett. A 283 368.
[11] Aydemir A Y 2005 Phys. Plasmas 12 062503.
[12] Garcia O E et al 2004 Phys. Rev. Lett. 92 165003.
[13] Myra J R, et al 2005 Phys. Plasmas 12 092511.
[14] Biglari H, Diamond P H and Terry P W 1990 Phys. Fluids B 2 1
[15] Terry P W 2000 Rev. Mod. Phys. 72 109
[16] LaBombard B et al 2004 Nucl. Fusion 44 1047
[17] Wan A S, LaBombard B, Lipschultz B and Yang T F 1987 J. Nucl. Mater. 145–147 191
[18] Vershkov V A, Grashin S A and Chankin A V 1987 J. Nucl.Mater. 145 611
[19] Vershkov V A 1989 J. Nucl. Mater. 162 195
[20] Pitts R A, Vayakis G, Matthews G F and Vershkov V A 1990 J. Nucl. Mater. 176 893
[21] Boucher C, MacLatchy C S, Le Clair G, Lachambre J L and St-Onge M 1990 J. Nucl.
Mater. 176 1050
[22] MacLatchy C S et al 1992 J. Nucl. Mater. 196–198 248
[23] LaBombard B et al 1997 J. Nucl. Mater. 241–243 149
[24] Asakura N et al 1999 Nucl. Fusion 39 1983
[25] Erents S K, Chankin A V, Matthews G F and Stangeby P C 2000 Plasma Phys. Control.
Fusion 42 905
[26] Asakura N et al 2003 J. Nucl. Mater. 313–316 820
10
Introduction
[27] LaBombard B, Gangadhara S, Lipschultz B and Pitcher C S 2003 J. Nucl. Mater. 313–316
995
[28] Pitts R 2004 private communication on flow measurements in TCV
[29] Krasheninnikov S I et al 2008 J. Plasma Physics 74 679.
[30] Garcia O E et al 2005 Phys. Plasmas 12 90701.
[31] Noam Katz et al 2008 Phys. Rev. Lett. 101 15003.
[32] Carter T A 2006 Phys. Plasmas 13 010701.
[33] Fasoli A et al 2009 “Wave particle interactions in plasmas: Alfven waves, turbulence and
blobs”19th International Toki Conference.
[34] Asakura N and ITPA SOL and Divertor Topical Group 2007 J. Nucl. Mater. 363–365 41
[35] Takizuka T, Shimizu K, Hayashi N, Hosokawa M and Yagi M 2009 Nucl. Fusion 49
075038
11
CHAPTER TWO
Device description
2.1 Q – shu University Experiment with Steady State Spherical Tokamak (QUEST)
2.2 Wide angle visible imaging system
2.3 Tangential fast visible imaging system:
2.4 Reciprocating probe
References
Device description
2.1 Q – shu University Experiment with Steady State Spherical Tokamak (QUEST)
QUEST is a medium sized spherical tokamak [30] with major and minor radii of 0.68 and 0.4 m,
respectively. The diameters of the center stack and the outer wall are 0.2 and 1.4 m respectively
with flat divertor plates at b (= ±1 m) from the mid-plane. Eight toroidal field coils (TF coil) can
produce typical toroidal magnetic field, Bt = 0.29 T at R = 0.6 m. The poloidal magnetic field
coils (PF coils) and QUEST size is schematically shown in figure 2.1. The poloidal magnetic
field, Bz, is produced by
PF coils of PF1/PF7, PF2/PF6, PF3 – 1/ PF5 – 1 and PF3 – 2/ PF5 – 2.
The center solenoid coils are PF4 – 1, PF4 – 2 and PF4 – 3, which are providing the flux for the
plasma via Ohmic heating and capability to supply the magnetic flux of 200 mVs-1. The chamber
aspect ratio Ac (= Rc/ac ~ 1.4) is derived as the ratio given by (Rout - Rin) / (Rin + Rout), where the
chamber major radius Rc = (Rin + Rout) / 2 ~ 0.78 m, and the chamber minor radius ac = (Rout - Rin) /
2 ~ 0.55 m. The chamber elongation factor
c
is given by Z0/ac ~ 1.8.
Figure 2.1: QUEST device showing various PF coils and the flat divertor plates.
13
Device description
Two RF systems with frequencies 2.45 GHz (< 50 kW) and 8.2 GHz (< 200 kW) are used for
heating and current drive. For 2.45 GHz, waves are launched from the low field side in the O –
mode, and for 8.2 GHz both O – mode and X – mode can be injected. They are injected on the
mid plane. For 2.45 GHz and 8.2 GHz, typical fundamental resonance position, Rres1, are 0.37 m
(2.45 GHz) and 0.33 m (8.2 GHz), respectively.
2.2 Wide angle visible imaging system:
The Memrecam fx K5 fast camera (NAC Image Technology) is used for this experiment from a
radial port with a field of view (FOV) of 60 . NAC’s Memrecam fx K5 provides 2D light
sensitivity with ultra high speed and mega pixel resolution. The K5 records brilliant color images
or crisp monochrome images with resolutions up to 1280 X 1024 pixels at 1000 FPS (frames per
second). Using an advanced CMOS sensor, the K5 captures images at frame rates up to 168,000
FPS with ISO10000 monochrome (~576 Lux @ 1000 FPS F4) in light sensitivity. The electronic
shutter opens to 3 micro seconds, and the signals are digitized to 10 bits. The camera is used at
20 kHz and each frame is made up of 288 × 240 pixels. The camera with the wide angle lens is
shown in figure 2.2.
Figure 2.2: Memrecam fx K5 fast camera with wide angle lens
2.3 Tangential visible imaging system:
A Photron Fastcam SA5 complementary metal oxide semiconductor (CMOS) camera with frame
rate of 7000 frames/s (fps) at full resolution (1024 × 1024) is used for tangential imaging on the
mid-plane of QUEST. Spatial resolution on the tangency plane is 3.7 mm. The camera is
14
Device description
operated from the tokamak control room via Gigabit Ethernet, and image acquisition is initiated
by an external trigger synchronised with the tokamak operational sequence. Image is transferred
away from the view port by a 4.5 m long imaging fiber bundle manufactured by Schott. At the
back end the camera is connected with the fiber bundle through an image intensifier (IMI). Each
frame is made up of 242 × 242 pixels/526 × 240 pixels, and framing rate is 20 kHz/50 kHz. The
SA5 camera with the IMI and filter wheel is shown in figure 2.3.
The camera can achieve a maximum speed of 775 kfps with an image size of 128
experiment we used 704
24. In this
520 pixels with maximum achievable speed of 20 kfps. However, the
actual image is much smaller and higher speeds can be selected with smaller image size. In this
case, the photon flux is the limiting factor for achieving higher speed. Quantum efficiency (QE)
is 35% at 500 nm. The camera is affected by Bt and the stray field of Bz. Hence, a safe distance of
4 m is maintained from the TF coil with the fiber bundle and associated optics.
The Hamamatsu make C10880-03C IMI is equipped with a single stage multi channel plate and
a 16 mm diameter phosphor screen. The relative intensity of the phosphor screen decays to 1%
within 1 s. Luminous gain available is 105 (lm/m2)/lx. The multialkali phtocathode gives a wide
spectral response with ~15% QE over the visible range. Gain, gate width and delay time is
controlled and set from a PC through the RS-232C interface. The front end is attached to a 50
mm C-mount lens (YMV5095, Yakumo) and the back end is connected with the camera through
a 1:1 relay lens. The IMI is affected by axial magnetic field and hence it is mounted radially w.r.t.
the TF coils.
The IG-154 fiber bundle is made up of 10 micron elements with an active area of 4 mm
4 mm.
The numerical aperture is 0.63 with a resolution of ~50 LP/mm at a QE of 28% at 500 nm. A 6.5
mm objective lens at the front end and a 16~160 mm zoom lens (VZCH16160 Seikou Opltical
Ltd.) at the back end are used. Up to ~200 keV hard X-rays are produced in QUEST by the RF
generated fast electrons and this environment can significantly reduce the transmission of the
fiber after certain time. Hence, the fiber is shielded from the hard X-rays with 1 cm thick lead
tube.
15
Device description
Figure 2.3: Tangential fast visible imaging with Photron SA5 camera with auxiliary components
like image intensifier, filter wheel, zoom lens and relay lens.
Comparison with images using a H filter indicates that the observed visible image is mainly due
to the H emission. In order to analyze temporal and spatial evolution of images it is assumed
that the neutrals n0 are distributed uniformly in the chamber and images are due to the local
evolution of plasma or propagating plasmoid whose electrons can excite the neutrals
immediately [1,2]. The intensity I( ul) of a spectral line of wavelength
ul
due to a transition from
the upper level u to the lower level l is given (in photons m-2 s-1 sr-1) by:
I
ul
1
4
x2
nu Aul dx
x1
1
4
x2
PEC exct ne , Te ne n g dx
(1)
x1
Here Aul is the spontaneous transition probability from upper to lower level and nu is the
population number density of the upper level u (= 3) of the emitting ion [3]. In the collisional
radiative approximation, ignoring recombination, the emissivity can be attributed to the
excitation of ground state atoms (ng) by electrons and the consequent photon emission. PECexct is
the ‘effective’ photon emission coefficient for the excitation of ground state atoms by the
electrons and is a function of ne and Te. The integration denotes the tangential line of sight for
each pixel that traverses through the plasma from x1 to x2. It has been shown that, at similar ne
and Te in TORPEX, the mean value of the light emission signal recorded with a tangential fast
16
Device description
camera depends linearly on ne at varying neutral hydrogen density and ECRH power [4]. Hence,
in our case too, it is reasonable to interpret the intensity fluctuations as density fluctuations,
although, more precisely it resembles plasma pressure fluctuations. Contextual references to
these considerations are again deliberated in chapters 3 and 4.
2.4 Reciprocating probe
A reciprocating ceramic probe head (diameter 20 mm) consisting of seven tungsten probe tips of
diameter 1 mm and length 2 mm each, is inserted radially below mid-plane. The probe head can
be rotated about its axis to align the central probes toroidally or poloidally. Schematic of the
probe head is shown in figure 2.4. In order to avoid damage due to hot electrons in the ECW
phase, probes can be inserted only up to 20 cm from the vessel wall. Hence, only the far-SOL
(FSOL) can be scanned in a shot by shot basis in reproducible discharges to measure floating
FSOL
potential ( f) and ion saturation current ( I sat
) at 50 kHz.
Figure 2.4: Left: Schematic of the probe head with 7 tips; Right: Assembled probe head
17
Device description
References
[1] Jha R, Kaw P K, Mattoo S K, Rao C V S, Saxena Y C and ADITYA Team 1992 Phys.
Rev. Lett. 69 1375
[2] Ono M et al 2003 Plasma Phys. Control. Fusion 45 A335
[3] Prakash R, Jain J, Kumar V, Manchanda R, Agarwal B, Chowdhari M B, Banerjee S
and Vasu P 2010 J. Phys. B: At. Mol. Opt. Phys. 43 144012
[4] Iraji D, Diallo A, Fasoli A, Furno I and Shibaev S 2008 Rev. Sci. Instrum. 79 10F508
18
CHAPTER THREE
Edge turbulence in
the slab plasma
A. Statistical features of coherent structures at increasing magnetic
field pitch for 2.45 GHz slab plasma
3.1
Introduction I
3.2
Experimental conditions
3.3
Variation of the source plasma with field pitch
3.4
Statistical properties of the fluctuations
3.5
Generation and propagation of coherent structures (blobs)
3.6
Discussions
3.7
Conclusions I
B. Variations in edge turbulence induced by poloidal magnetic field
curvatures for 8.2 GHz slab plasma
3.8
Introduction II
3.9
Experimental conditions
3.10 Statistical analysis
3.12 Conclusions II
Edge turbulence in slab plasma
A. Statistical features of coherent structures at increasing magnetic field pitch for 2.45
GHz slab plasma
3.1 Introduction I
Edge turbulence in plasma confinement devices continues to remain as one of the most important
research topics as it plays vital role in the performance of the plasma core and core to edge
transports of heat and particle fluxes. This is deemed crucial for future fusion devices like ITER
[1] and beyond as the confinement of plasma is determined largely by turbulent plasma processes
[2] at the edge. Anomalous convection in the edge plasma transport has been reported
experimentally for a wide range of plasma devices [3-9]. Experimental evidences show that
mesoscale plasma structures, that extend along the magnetic field lines, often called as ‘blobs’
are convected from the region of last closed flux surface (LCFS) well beyond the scrape-off
layer (SOL) [2]. Blobs being omnipresent at the edge region of both tokamaks and stellarators [9]
and with the confirmation of their role in enormous particle and energy fluxes in the far SOL,
these convective intermittent structures gained serious importance in the edge plasma community.
These coherent structures are localized in the two-dimensional (2D) plane and appear as ‘blobs’
of higher density in contrast with the lower density ambience. They are spatially extended along
the magnetic field lines and appear as filaments in three-dimensional (3D) view of the SOL.
Origin of the blobs has been attributed to the nonlinear saturation of the underlying edge
turbulence or coherent magneto-hydrodynamic (MHD) instabilities [2,10]. Qualitative theory of
blob dynamics suggests that due to some turbulent processes in the vicinity of the LCFS, a
filament with large plasma density at the low field side (LFS) of the torus is peeled off from the
bulk plasma [2]. The models assume plasma polarization caused by the curvature and B drifts at
the LFS of tokamaks leading to the E
B convection of the blob towards the main chamber wall.
However, the models propose different damping mechanisms and the predictions on the radial
propagation velocity of blob filaments diverge accordingly. The first model cites sheath
dissipation at the target as the damping mechanism [2,11,12]. The second model includes
damping through a diamagnetic current in the filament [13,14]. Finally a third modified model is
proposed to include both the above models as limiting cases. Here the electron diamagnetic
current
acts as the drive for the blob motion and the current loop is closed by the ion
20
polarization current, sheath currents, and the ion current caused by a neutral friction force [15].
In the limit where sheath losses and the ion-neutral collisions are negligible, the blob velocity
(vb) is proportional to (2a)1/2, a being the blob size. If sheath losses become dominant, vb scales
as 1/a2 and when ion-neutral friction dominates, vb is inversely proportional to the ion-neutral
collision frequency (
in)
independent of a. Both the sheath dissipation model and the modified
model predict velocity damping for larger filaments and are confirmed through experiments [1518]. Nevertheless, the main constraint that prevents rigorous validation of these models through
extended traces of blob motion is that the SOL and edge are typically thin in the conventional
tokamak discharges. Hence, the velocity damping concept for larger filaments may not be
ubiquitous and thereby seems inconclusive.
The other imperative aspect of blob dynamics is the source plasma itself that drives the edge and
SOL turbulence and subsequently the blob generation. Statistical features of turbulence can
provide essential information about both the source plasma and the propagation dynamics of the
intermittent blobs. Probability density functions (PDFs) of density fluctuations at the edge from
various machines suggested a large deviation from the Gaussian statistics with strongly skewed
curves, reflecting intermittence. Comparison of edge turbulence data taken from machines with
different configurations [19-23] was done [24]. Dealing with the complete PDF often proves to
be cumbersome and higher order moments like skewness (s) and kurtosis (k) may provide the
necessary details. However, only very few detailed reports are available till date on the statistical
properties of the blob-generation and propagation regions.
This paper deals in our efforts to achieve better understanding of the source plasma, criteria for
blob generation and also the propagation dynamics in toroidal devices. In the spherical tokamak
QUEST blob generation and propagation is studied by two dimensional fast imaging technique
in slab plasma with a simple magnetic configuration characterized by open field lines [25]. Slab
annular plasma is formed by electron cyclotron resonance heating (ECRH) near the resonance
region and instabilities are excited depending on the ratio of the vertical (Bz) and toroidal fields
(Bt) [26,27]. The Bz/Bt (field pitch) is varied in an attempt to regulate the source plasma
~
fluctuations and the blob characteristics. Relative fluctuation level ( I/ I ) near the ECR layer was
found earlier to be ~ 5% at Bz = 0 and increased ~ 25% with increasing Bz [25]. Although the line
21
tying stabilization effect was expected with increasing Bz and decreasing connection length
between the upper and lower flat divertor plates, the fluctuations and their nonlinear evolution
was large and significant at higher Bz. Slab plasma in QUEST also presents a unique feature of
the propagation of blobs across a long distance in the R-Z plane (2D). Such blob motions can be
traced comprehensively with tangential fast imaging. The region beyond the steep density
gradient of the slab towards the LFS resembles the SOL of normal tokamak discharges.
Relatively weak fluctuation at the ECR region and intermittent strong fluctuations dominated by
blobs in the outer SOL are observed. Hence, in this work, we attempt to address the following
two aspects of blob dynamics with the core idea of varying Bz/Bt. Fluctuations of the source
plasma are characterized. Statistical features of the initial perturbations and trigger mechanisms
of blobs are analyzed by steepening the density gradient. Finally, the size, frequency and
acceleration of the blobs [28,29] along the excursion are investigated.
Outline of part A is as follows: the experimental setup is discussed next. Change in the source
plasma with increasing Bz/Bt is characterized in section 3.3. Section 3.4 provides an account of
the statistical analysis of the image data. Blob amplitude, waiting time and velocity are
determined as a function of Bz/Bt with the conditional averaging technique in section 3.5. Results
are discussed in section 3.6 and finally, some conclusions are drawn in section 3.7.
Open magnetic field configuration is realized with both Bt and Bz field components without
plasma current (< 1 kA). Slab-annular plasmas, intersecting the divertor plates, are initiated with
hydrogen and ECRH at 2.45 GHz. Plasmas extend vertically near the resonance layer Rres (~ 0.37
m) corresponding to the resonant field of Bres = 87.5 mT, and diffuse outward depending on RF
power and Bz/Bt. Bz is varied in the range of -1.5 ~ 6.7 mT. When Bz/Bt is varied, the pitch
distance
Lc
z
2 R Bz Bt , pitch angle
tan
1
B z Bt
and
the
connection
length
2b Bt Bz of field lines between the flat divertor plates are changed. Typical electron
density and temperature at the edge are ne ~ 5
1016 m
speed cs is ~10-34 km/s and effective ion gyro-radius
s
3
and Te ~ 1–12 eV. The ion acoustic
is ~ 3-9 mm. Plasma beta is quite low at
~ 10-4. Three radial locations are defined; the plasma source region (0.35 < Rs < 0.6 m),
22
bounded by a relatively sharp boundary, the intermediate (0.4 < Rim < 0.8 m) and the source-free
(0.7 < Rsf < 0.9 m) regions respectively (figure 3.1). Rim is characterized by a steep intensity
gradient near the plasma boundary and Rsf by very weak intensity or essentially vacuum,
depending on Bz/Bt. Fairly good agreement of the helix angle with
(
z
) of initial helix-sinusoidal perturbations with
z and
vertical wavelength
was observed earlier [25]. Both drift and
interchange modes being intrinsic to this plasma [25], experiments are conducted to investigate
the helical perturbations near the outer plasma edge, where B p > 0.
1
PF2
Rsf
0
Rim
Rs
0.5
-0.5
PF6
-1
0.5
1
1.5
(a)
Figure 3.1: (a) cross sectional view of the QUEST vessel showing the arbitrary positions of the
three regions Rs, Rim and Rsf. Flux contours are shown for the PF26 coil. Dotted rectangle shows
the extent of the images; Solid horizontal lines represents the divertor plates (b) top view of
QUEST showing the field of view (FOV = 60 ) of the fast camera.
The Memrecam K5 fast camera is used for this experiment from a radial port with a field of view
(FOV) of 60 (figure 3.1b). Each frame is made up of 288 × 240 pixels, and framing rate is 20
kHz. The intensity fluctuations can be interpreted reasonably as plasma density fluctuations as
discussed in chapter 2.
23
Figure 3.2 shows a typical time series of images showing evolution of the initial perturbations
into helical filaments. These filaments move across field lines and eventually die off at the LFS.
Radial and vertical extents of the elliptical cross-section filament at Rsf are 0.15
0.30
0.03 m and
0.05 m respectively. Further details of the filaments are discussed in section V. A bright
spot can be seen on the right hand edge of each image (at R = 0.87 m and z = 0 m). This is a
point source illuminated through a view port in the FOV of the camera for spatial calibration of
images along with CAD drawings. These pixels have been excluded in consequent analyses.
Figure 3.2: Time series of an individual blob event is shown in false color. Images run from left
to right and top to bottom and the consecutive images are 50 s apart. Center stack is shown as
broken vertical lines. The blob filament is shown with the eye-guide in the second frame.
The wide angle view resembles tangential line of sight (LOS) for each half of the image. This
leads to LOS integration of local emissivities which may hinder the fluctuation assessments. A
quantitative evaluation of this effect is carried out under the framework of the TITR code [33].
Simulated emissivity profiles, for different Bz/Bt are subjected to the LOS integration geometry
matrix and the resultant brightness profile is obtained. Figure3.3 shows the profiles for Bz/Bt =
1.7%. It can be seen that due to the slab geometry, this detrimental effect is limited to the region
up to ~Rs. For R
Rim this effect is appreciably smaller and for Rsf and beyond it is negligible.
This has been taken into account and fluctuation characteristics are ascertained only for the
region Rim and beyond. This situation improves further with the increase in Bz/Bt as the plasma
column shrinks more towards the center stack and the vacuum region increases. However, for
24
Bz/Bt = 0, the effect is severe all through the radial direction and fluctuation characteristics are
inconclusive.
Emissivity and brightness (AU)
500
Simulated emissivity
Integrated brightness
R
400
s
R
im
R
300
sf
200
100
0
0.2
0.4
0.6
0.8
1
R (m)
1.2
1.4
1.6
Figure 3.3: Simulated emissivity and line integrated brightness profile along the radial direction
for Bz/Bt=1.7% at z = 0.05 m.
3.3 Variation of the source plasma with field pitch
In this section we present the framework of the plasma production mechanism and its variations
with increasing Bz/Bt. Intensity fluctuations from each pixel are considered as raw time series
1
n
signals. PDF p(x) of the time series is characterized by the mean (
(
2
1
n
n
I tj
2
), where µi is i-th central moment (
1
n
i
j 1
and standard deviation (
2
n
I tj
n
I t j ) and variance
j 1
i
). R-z contours for
j 1
) are shown in figure 3.4 for the right half of the image. Slab
plasmas in QUEST show a small up-down asymmetry, but the radial profiles remain consistent
along z. From the first column it can be seen that the plasma shrink towards the fundamental
ECR layer (0.37 m) with increasing Bz since Bt was maintained at the same value. For Bz = 0 case,
both the fundamental and second harmonic ECR layers are clearly decipherable in spite of the
LOS integration for the tangential FOV. For most of the pixels
be seen that
shows a non-zero value. It can
drops off to ~0 at R > 0.58 m for Bz/Bt = 7.7%, while a finite
showing the existence of intermittent bursts in that region.
exists in that region
increases from a maximum value of
25
150 (AU) for Bz/Bt = 0 to 200 (AU) with the increase in Bz/Bt to 1.7%. One of the candidates
explaining such a behavior may be the reduced E
B losses at higher Bz and better confinement
notwithstanding the activation of loss channels due to the shortening of Lc [26]. Beyond that Bz
the convective intermittent transport dominates and reduces the mean intensity again to 140
(AU) for Bz/Bt = 7.7% (row 3 of figure 3.4). The intensity never maximizes at the ECR
fundamental layer (R = 0.37 m) but peaks radially outward from it. This may be due to the upper
hybrid resonance (UHR) with the frequency
frequency and
at R
max
4.52
ce
2
pe
uh
1016 m-3 (2.17
max
z (m)
Row 1
z (m)
Row 2
z (m)
Row 3
is the electron plasma
Standard deviation ( )
200 -0.1
-0.2
-0.2
100
-0.3
0.4
profile peaks
1016 m-3).
Mean
0.6
0.8
80
60
40
-0.3
-0.4
0.2
200 -0.1
0
-0.2
20
0.4
0.6
0.8
100
0.4
0.6
0.8
60
-0.4
0.2
200 -0.1
-0.2
40
-0.3
0
20
0.4
0.6
0.8
100
0.4
0.6
R (m)
0.8
0
60
40
-0.3
-0.4
0.2
0
80
-0.2
-0.3
0
80
-0.2
-0.3
-0.4
0.2
pe
as the UHR layer, ne is calculated at UHR to be
-0.1
-0.4
0.2
-0.1
; where
is the electron cyclotron frequency. For Bz/Bt = 1.7% (7.7%),
0.59 m (0.44 m). Assuming R
-0.4
0.2
-0.1
2 1/ 2
ce
20
0.4
0.6
R (m)
0.8
0
Figure 3.4: Mean ( ) and standard deviation ( ) of the intensity time series. . Row 1: Bz/Bt = 0;
Row 2: Bz/Bt = 1.7%; Row 3: Bz/Bt = 7.7%. Solid, dashed and dash-dot lines denote Rs, Rim and
Rsf respectively.
As the plasma shrinks with increasing Bz/Bt, increase in the negative gradient of intensity at Rim is
observed. Further, figure 3.5 shows that / at Rim increases as a logarithmic function with Bz/Bt.
This ratio can be interpreted as the ratio of the stochastic to the deterministic terms in the
26
nonlinear Langevin equation as discussed in section 6. Hence, figure 3.5 may be interpreted as an
increase in the stochastic forces due to the steepening of the density gradient.
0.8
0.7
/ at Rim
0.6
0.5
0.4
0.3
0.2
-3
10
-2
10
Bz / Bt
-1
10
Figure 3.5: / at Rim shows logarithmic increase with Bz/Bt.
3.4 Statistical properties of the fluctuations
Signals for 100 ms are considered as the time series for the statistical analysis. The time window
is shifted across the total recording duration of 660 ms and varied in length to check the
statistical stationarity and the 100 ms window seems reasonable for achieving that. Good
reproducible discharges are obtained for each Bz/Bt and reasonable consistency is achieved in the
statistical analysis of this data set. PDFs of fluctuations from the two regions (Rim and Rsf) are
compared for one intermediate (=1.7%) and one high Bz/Bt (=7.7%) to investigate the deviation
from the Gaussian statistics with increase in Bz. The Bz/Bt = 0 case is rather difficult as the field
lines are closed and the LOS integration is severe all along the radial extent. Figure3.6 shows the
time evolution of intensities normalized by standard deviation , x = (I-µ)/
at Rim and Rsf
respectively, and the corresponding p(x) at Rim at two instances of Bz/Bt. p(x) start to deviate from
Gaussian and become skewed at Rim with increasing Bz. At Rs, p(x) remains close to Gaussian
even for higher Bz/Bt, but, the actual fluctuation characteristics cannot be ascertained here due to
LOS integration effect. In case of higher Bz/Bt, signal at Rsf is characterized by large and
intermittent positive bursts. p(x) in this region are strongly asymmetric and positively skewed.
However, at Rsf, there are no intrinsic fluctuations and only the survival and propagation of high
27
density blobs can be observed far away from the source plasma. Due to the limitation of dynamic
range of the camera pixels and absence of background plasma, intensity at Rsf remains
predominantly at zero with occasional positive bursts of the blobs. Hence, p(x) at Rsf is not
shown here.
(I- )/
4
0
R = 0.65 m and z = -0.25m
10
Rim
Experimental
Gaussian
0
-2
10
-1
R = 0.89 m and z = -0.25m
Rsf
PDF
Bz/Bt = 1.7%
2
5
0
0.82
4
10
-2
10
0.84
0.86
0.88
-2
0.9
R = 0.4 m and z = -0.25m
-1
0
1
2
0
10
Rim
4
5
-1
R = 0.69 m and z = -0.25m
Rsf
PDF
Bz/Bt = 7.8%
-2
4
Experimental
Gaussian
2
0
3
10
-2
2
10
0
0.82
0.84
0.86
0.88
Time (s)
0.9
-2
-1
0
1
2
(I- )/
3
4
5
Figure 3.6: Time evolutions of the intensity (I) fluctuations normalized by the standard deviation,
I/ = (I- )/ at Rim and Rsf respectively. Normalized PDFs and the corresponding Gaussians at
Rim for Bz/Bt = 1.7%; and Bz/Bt = 7.8% are shown in the right panels.
The higher order moments of p(x) like skewness s = µ3/ µ23/2 and kurtosis k = µ4/ µ22-3
characterize the shape of the PDF. These shape factors can be explored to understand the
statistics of the fluctuations leading to the physical stochastic principles34. Statistical features for
the right half of the images (figure 3.2) are shown in figure 3.7. s values remained low up to Rim
and thereafter it shows a steep positive gradient for Bz/Bt = 1.7% and 7.7%. k values remain very
low or close to 0 till Rim and then increases rapidly at the immediate vicinity of Rim on the LFS.
Such increase in s and k is not apparent in the Bz/Bt = 0 case. Both s and k remained mostly
28
uniform along z- direction. Certain regions of negative skewness are observed for smaller Bz/Bt.
This may be due to the decrease in density (and hence intensity) below the mean value on the
high field side of Rim as a consequence of blob ejection. Low s island is also visible at Bz/Bt =
7.7%, but the value remains positive in this case. This statistical analysis leads to two important
observations: (i) a reasonable understanding of the region of blob generation and (ii) the nature
of the fluctuations from the mutual relationship of s and k. These are detailed in the following
subsections.
Row 1
z (m)
-0.1
Skewness (s)
Kurtosis
2
-0.2
1
Row 2
z (m)
3
-0.2
2
-0.3
0 -0.3
-0.4
0.2
-1 -0.4
0.2
0.4
0.6
0.8
-0.1
2
-0.2
1
2
-0.2
1
0.4
0.6
0.8
2
-1 -0.4
0.2
0.8
0
-0.2
-0.4
0.2
0.6
1
3
0 -0.3
R (m)
0.8
-0.1
-0.3
0.4
0.6
2
-1 -0.4
0.2
0.8
0.4
-0.2
-0.4
0.2
0.6
0
3
0 -0.3
0.4
1
-0.1
-0.3
-0.1
Row 3
z (m)
-0.1
1
0
0.4
0.6
R (m)
0.8
Figure 3.7: skewness (s), kurtosis (k) of the intensity PDF are shown in 2D for three different
Bz/Bt. Row 1: Bz/Bt = 0; Row 2: Bz/Bt = 1.7%; Row 3: Bz/Bt = 7.7%. Solid, dashed and dash-dot
lines denote Rs, Rim and Rsf respectively.
3.4.1
Blob generation location
To bring out the statistical features more clearly, a radial slice of the moments and the inverse
gradient scale length of intensity ( L p1
of z = -0.25
R
ln
) are plotted in figure 3.8 at a vertical distance
0.1 m from the mid-plane. The blob generation region is shown with the shaded
bar. The mean intensity has a steep negative gradient in this region. This region is also
characterized with k ~0 and maximum Lp-1. Hence, this analysis reveals that the Rim region with
29
maximum Lp-1, sharply varying s and minimum k may be the most probable location for blob
generation. Further, rapid growth can also be observed in the radial profiles of / in figure 3.8.
None of these signatures are apparent in the Bz/Bt = 0 case and the radial profiles remains almost
flat along the radius.
(b): Bz/Bt = 7.7%
max
1
/
0.5
0
3
2
1
0
1
0.5
s
s
s
//
max
max
(a): Bz/Bt = 1.7%
k
2
2
1
1
0
0.2
0.1
0
-0.1
0.5
0
0.2
0.1
0
-0.1
0.75
0.4
R
/
0
2
/
0
2
/
k
4
-
--
RR
//
/
k
4
0
3
2
1
0
0.55
0.6
0.65
(m)
RR (m)
0.7
0.45
0.5
0.55
R (m)
R
(m)
0.6
0.65
Figure 3.8: Radial profiles (at z = -0.25 0.1 m) of the normalized mean intensity, s, k, / and
the inverse scale length respectively. Blob-generation regions are shown with the shaded bar.
3.4.2
Quadratic relation between s and k
s and k are plotted for three Bz/Bt (0, 1.7% and 7.7% respectively) in figure 3.9. Data show a
well defined distribution around a quadratic curve as observed by Labit et al [19]. Such a
distribution is now being considered as fairly general as it has been observed in varying
experimental conditions and devices. But, there were very few attempts to include such a wide
range of magnetic field configuration and regions across the plasma cross-section in the scatter.
The green cross, cyan squares and red circles represent the s vs. k relation at Rs
(Rim - Rs)/2 and Rsf
(Rim - Rs)/2, Rim
0.1 m respectively. k is shifted by +5, +10 and +15 for these three plots.
The black dots represent data from the entire poloidal cross section. For Bz/Bt =0, data points
from all three regions overlap each other. They start to segregate with increasing Bz/Bt. The
30
scattered points are fitted to a parabolic relation ( k
As 2
C ), and the coefficients A and C are
determined. It can be seen from figure 3.9 that the value of A increases from 1.14 to 1.2 with
increasing Bz/Bt but never reaches the earlier reported [19] value (A=3/2). C was found to be ~0
in all cases. Further, s and k from 30 shots with a wide range of Bz/Bt (at the fundamental
resonance) and covering the entire poloidal cross section are evaluated. This also includes shots
with negative Bz/Bt (up to -1.7%). Values of coefficients A and C are obtained from the parabolic
fits and the mean values are 1.17
0.07 and ~0 respectively.
3.5 Generation and propagation of coherent structures (blobs)
3.5.1
Blob filaments originating from coherent poloidal mode
Evolution of the helical perturbations with the increase in Bz can be observed from the image
frames of the three Bz/Bt, shown in figure 3.10. The time averaged (100 ms) frame is subtracted
from the actual frames to separate out the coherent structures from the background slab plasma.
For Bz/Bt = 0, the entire poloidal cross-section is filled with thin rings stacked vertically with
subdued intensities. They represent the closed field lines in the absence of Bz. As Bz is increased
(Bz/Bt = 1.7%), strong sinusoidal waves are generated at Rim and this eventually leads to
prominent helical convective structures as seen at Bz/Bt = 7.7%. In the right most panel of figure
3.10, three helical structures can be seen, the top one has evolved completely, the middle one is
still evolving and the last one is just born.
31
40
35
Bz/Bt = 0
Kurtosis
k
Kurtosis k
30
25
2 + 0.02
kk=1.14s
= 1.137s2+0.02
20
15
10
5
0
-5
-1
40
35
Kurtosis k
30
25
0
1
2
3
4
5
3
4
5
2
3
Skewness s
4
5
Bz/Bt = 1.7%
2
+ ~0
1.19s2+1.77e-008
kk==1.19s
20
15
10
5
0
-5
-1
40
35
0
1
2
Bz/Bt = 7.7%
Kurtosis
k
Kurtosis k
30
25
k
+ ~0
1.20s22+9.88e-011
k ==1.2s
20
15
10
5
0
-5
-1
0
1
Skewness s
Figure 3.9: k as a function of s from the entire poloidal cross section (black dots) is fitted (solid
line) to the parabolic relation ( k As 2 C ) for increasing Bz/Bt (0, 1.7% and 7.7%
respectively). The green cross, cyan squares and red circles represent the s vs. k relation at Rs
(Rim - Rs)/2, Rim (Rim - Rs)/2 and Rsf 0.1 m respectively.
32
Vertical
z distance
(m) (m)
Bz/Bt = 0
Bz/Bt = 1.7%
Bz/Bt = 7.7%
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
0
0
-0.2
-0.2
-0.2
-0.4
-0.4
-0.4
-0.6
-0.6
-0.6
-0.8
0.2
0.4 0.6 0.8
Radial distance (m)
R (m)
-0.8
0.2
0.4 0.6 0.8
Radial distance (m)
R (m)
-0.8
0.2
0.4
0.6
0.8
R (m)
Figure 3.10: Frames from three different Bz/Bt values, subtracted with the temporal mean of the
intensities. The fine and evenly distributed plasma filaments condense to strong sinusoidal waves
at Rim and then finally the prominent helical convection sets in with the increase in Bz/Bt.
3.5.2
Conditional averages
In this section, we intend to focus more on the intermittent bursts, separating them from the
background plasma. Intermittent convective bursts like blobs are submerged in the background
turbulence. Conditional averages are used to highlight distinctive features of a signal. This
technique can be used to separate the coherent structures from the background turbulence and
study their properties independently. In our case, intensity level (amplitude) of the intermittent
bursts serves as the selection criterion for applying this technique. Intensities above 2.5 times the
standard deviation (threshold) are selected as the intermittent blobs from a larger time window of
600 ms. In case of bursty signals, the bursts are reasonably greater than the background
fluctuation and hence, the choice of the threshold is not crucial and anything above the standard
deviation can be selected [35].
For studying the time traces of these high intensity events, we track 7 data points on each side of
a given maximum. This generates a matrix of 15 × Nmax, where Nmax is the number of maxima.
This selection ensures that none of the bursts are favoured artificially by selecting a lot of
fluctuations, as the maxima are generally apart from each other by 15 or more data points. The
33
conditional average is obtained by averaging over Nmax. Once the maxima are selected, the autoconditional average (ACA) indicates the case where the maxima selection and the averaging are
performed on the intensity fluctuation signal of the same pixel. On the other hand, crossconditional averaging (CCA) describes the case where the selection is made on the intensity
fluctuation signal of one pixel and the averaging is done on that of another pixel.
ACA are calculated for the fluctuation signals of all three regions. For Rs and Rim, ACA are
calculated for the vertical span of z = 0.2 m to z = -0.3 m at a resolution of 6.7 mm and mean of
the ACAs along z are plotted for these two regions. For Rsf, however, ACA is calculated only at
z=-0.25 m, due to the curvature of the view port limiting the FOV on the right hand side of the
images.
(a)
(b)
130 <ACA> of I
z
Rs
180 <ACA> of I
z
Rs
120
(i)
110
150 <ACA> of I
z
Rim
Intensity (AU)
ACA of I
(ii)
100
(iii)
200
150
100
50
Rsf
100
50
140
120
80
CCA of IRs with IRim
200
(iv)
CCA of IRsf with IRim
70
-400
-300
-200
140
200
150
100
50
150
160
-100
0
( s)
100
200
(i)
<ACA> z of IRim
Peak height
(ii)
ACA of I
Rsf
(iii)
CCA of IRs with IRim
(iv)
150
70
60 CCA of IRsf with IRim
50
40
(v)
30
300
400 -400 -300 -200 -100
(v)
0
( s)
100
200
300
400
Figure 3.11: (a) Bz/Bt = 0 and (b) 7.8%. (i)-(iii): ACAs for the time series signals at Rs, Rim and
Rsf respectively. (iv)-(v): CCAs between IRs and IRim and between IRsf and IRim respectively.
ACAs of all the three regions show peaks for Bz/Bt = 7.8% case (figure 3.11). Peak height was
maximum in case of Bz/Bt = 7.8% showing that the blob events are more prominent with respect
to the background plasma in that case. In case of Bz/Bt = 0, however, no distinct peaks were
observed showing that the coherent structure formation was not facilitated at lower Bz/Bt.
Distance between Rim and Rsf for Bz/Bt = 7.8% is 0.3 m. Maxima of CCARsRim are at
= 0 s as
34
the distance between these two zones are very small. But, maxima of CCARsfRim trails to the
positive time interval
= 200 s. Hence, the blobs move from Rim towards Rsf with an average
radial velocity ~1500 m/s. Knowing the velocity, the radial scale length of the blobs can be
evaluated from
at 1/e of the peak of CCARsfRim for Bz/Bt = 7.8%. It turns out to be 60 cm,
which is typically much larger in such slab plasmas with wide Rsf (resembling SOL) as compared
to large aspect ratio tokamaks with rather thin SOL. The ACA peaks in our case are symmetric
about
= 0 unlike previous reports where a sharp increase and a gradual fall of the intensity
was observed along the blob lifetime on the probes. This may be due to the low temporal
resolution (20 kHz) of the images in our case as compared to the conventional Langmuir probe
measurements.
ACA at Rim reveals that the peak height increases with Bz/Bt (figure 3.12). At lower Bz/Bt, the
fluctuations are mainly dominated by the background turbulence and p(x) remained Gaussian in
all the three regions. At higher Bz/Bt, p(x) deviates from Gaussian due to the advent of blobs. A
striking resemblance between figure 3.5 and figure 3.12 suggested that the blob amplitude have
strong correlation with the stochastic forces (refer to section VI) at Rim as the instabilities are
exited more and more with the increasing Bz/Bt.
Peak height of ACA at Rim
120
100
80
60
40
20
0 -3
10
-2
10
Bz / Bt
-1
10
Figure 3.12: Peak height of the ACA at Rim shows logarithmic increase with Bz/Bt.
35
500
Bz / Bt = 1.7%
PDF at Rim
400
Fitted
= 3.37E-4 s
300
200
100
a
0
0
2
-4
8
T (s)
x 10
4
6
-3
x 10
Fitted
(s)
6
4
2
b
0 -3
10
-2
10
Bz / Bt
-1
10
Figure 3.13: a: Histogram of time between two bursts and the exponential fit at Rim for Bz/Bt =
1.7%. b: the exponential fitting parameter (s) as a function of Bz/Bt.
3.5.3
Time between two bursts
The waiting time between two bursts and its PDF p(x) is calculated by selecting the maxima as
described earlier. Figure3.13a shows p(x) of the waiting time at Rim for Bz/Bt =1.7. p(x) shows an
exponential distribution, as evident from the solid black exponential fit ( y
e
t
). Thus the
blob generation may be interpreted as a Poisson process, occurring continuously and
independently at a constant average frequency. Figure3.13b shows the fitting parameter
for
p(x) at Rim as a function of Bz/Bt. Again, there is a remarkable correspondence among / (figure
3.5) at Rim, blob prominence above background plasma at Rim (figure 3.12), and the waiting time
36
for blobs (figure 3.13b) with the increase in Bz/Bt. At lower Bz/Bt frequent but smaller intensity
blobs are apparent while the intensity is increased at the cost of the frequency with the increase
in Bz/Bt.
Radial velocity (m/s)
2000
1800
z
t
1600
1400
1200
1000
800
Radial velocity at Rsf (m/s)
B / B = 7.7%
a
0.5
0.55
0.6
R (m)
0.65
0.7
2400
2200
2000
1800
1600
1400
1200 -3
10
b
-2
10
Bz / Bt
-1
10
Figure 3.14: a: Radial velocity profile for Bz/Bt = 7.7%. Accelerated propagation along the
radius was observed. b: vRsf of candidate shots as a function of Bz/Bt.
3.5.4
Blob propagation
To quantify the radial velocity profile of the blobs conditional averaging is performed at discrete
radial locations beyond Rim. Spatial resolution for the camera pixels on the tangency plane is 6.7
mm. Hence, knowing the full width at half maxima (FWHM) of the ACA peaks and the blob size
at the same radial locations, the velocity profile can be estimated. Blob size along the radius is
37
estimated from the camera images while tracking individual blobs along their helical trajectories.
FWHM of the intensity peak for the blobs in each frame of a blob sequence gives the blob
diameter along both R and z directions and their average serves as the effective blob diameter
(deff). Blob size can be tracked only for R > 0.49 m in this case and up to that the size is taken as
constant. deff evolves from 19 cm to 30 cm along the radius, reaching the maximum diameter at
~Rsf. Figure 3.14a shows the velocity profile for Bz/Bt = 7.7%. Shaded region indicates the
standard deviation in velocity along the z direction. Hence, accelerated propagation is observed
till ~Rsf and such a trend is prevalent in all Bz/Bt. Radial velocity at Rsf (vRsf) reaches to 1700
200 m/s. vRsf is shown as a function of Bz/Bt in figure 3.14b. However, no significant variation is
observed in vRsf with increasing Bz/Bt.
3.6 Discussions
With the increase in Bz/Bt, the intensity fluctuation amplitude grows and PDF of the fluctuations
at Rim and beyond deviates from the Gaussian and becomes positively skewed. At this point we
attempt to understand the physical basis of the increased level of fluctuations and blob ejection
with the increase in Bz/Bt. Assuming that the intensity fluctuations in our case resembles the
plasma density fluctuations as stated in section 2, a simple nonlinear Langevin equation [36-38]
for a random variable x, representing the plasma density, is:
d~
x
~
~
x b~
x1
x t
dt
where,
(2)
is the linear growth rate and b is the nonlinear damping amplitude. (t) represents a -
correlated Gaussian process with amplitude Q,
t
t'
Q t t ' . (1+ ) is the exponent of
nonlinear damping. Tilde denotes the fluctuation. However, it can be noted that identifying the
terms in equation (2) with exact physical processes is clearly non-trivial from the present dataset.
Hence, the model represents nonlinear systems in general and is not specific to this problem. The
corresponding Fokker-Planck equation is:
P
t
x
~
x b~
x1
1 ~
Qx P
2
Q 2 ~2
x P
2 x2
(3)
First two terms on the right hand side of the stochastic differential equation (2) denotes the
deterministic part of this process, while the last term represents the stochastic part. Observed /
38
of the intensity fluctuations (section 3 and 4.1) resembles the ratio of the stochastic to the
deterministic contribution of equation (2). Hence, the rapid growth of
/
at Rim with the
increase in Bz/Bt signifies a sudden increase in the stochastic forces. This increased stochasticity
can broaden the PDF, while maintaining the Gaussian distribution. However, the PDF is
observed to deviate from Gaussian from Rim onwards with the increasing Bz/Bt. This may happen
only when the multiplicative nature of the noise term in equation (2) is considered. The plausible
explanation may be that with the increase in Bz/Bt, as the plasma shrinks towards the ECR layer,
the density gradient steepens. This effect may have increased the stochastic forces and also
couples the density fluctuations with the noise term.
The coefficient A in section 4.2 is always observed to be < 3/2. Steady-state solution of equation
(3) P0
t
P0 ~
x
0 yields the expression,
N~
x
1 2
Q
exp
2b ~
x
Q
where, N is the suitable normalization constant, N
(4)
2
Q
1
Q . For
= 1,
expression (4) assumes the gamma distribution and A can be precisely 3/2. However, if
> 1, A
2b Q
2
can attain values < 3/2. Hence, a situation with greater than second order nonlinear damping may
be envisaged in our case. From the PDF of waiting time, the blob generation is inferred as a
Poisson process. This conforms to the recent stochastic modeling of intermittent SOL
fluctuations [39] that predicts a parabolic relation between skewness and kurtosis for such
processes as observed in this work.
Blob propagation velocities can reach about 1/10 of the ion acoustic speed in QUEST making the
process of radial convective transport competitive with the parallel transport. Accelerated radial
propagation for these large sized blobs is observed. This is in sharp contrast with the sheath
dissipation model. However, in DIII-D [16], blobs propagate radially with E
B drift velocities
while decelerating from ~2.6 km/s near the LCFS to ~0.33 km/s near the vacuum vessel. Such
behavior was also reported by Alcator C-Mod [17] and HL-2A tokamaks [18]. Blob propagation
region in these experiments are significantly narrow as compared to that of QUEST slab plasma
and thereby limits the accelerating mechanisms to manifest. It has been predicted by simulation
39
[40] that for a non uniform plasma density along the direction of blob propagation, the leading
and trailing faces of the blob see a density difference and hence the blob experiences a resultant
force towards the lower density region. Likewise, while travelling from Rim towards Rsf the blobs
may encounter a force against the density gradient which may cause the accelerated propagation.
Acceleration may also occur due to -
B force along the radius. Simultaneous measurements of
blob velocities with fast camera and probes in QUEST are reported earlier. Blob velocities are
measured [28,29] both directly with the ion saturation current from two spatially separated probe
pins and through the E
B estimation from the measured blob electric field <Eb>. With <Eb>
remaining almost constant along the radial direction, the E
B drift velocity might have
increased with the 1/R decay of Bt. These measurements also predict radial acceleration and
agree well with the velocity estimation in this work.
3.7 Conclusions I
Light intensity fluctuations from the slab annular plasma are studied in the QUEST device with
fast imaging technique at a temporal and spatial resolution of 50 µs and 6.7 mm respectively.
These plasmas provide the unique opportunity to study blob formation and propagation with the
tangential fast imaging diagnostic technique, owing to the wide SOL-like region beyond the
steep density gradient towards the LFS. Bz/Bt (at the ECR layer) is varied from -1.7% to 7.8% to
investigate fluctuations of the source plasma that presumably drives the edge and SOL
fluctuations and consequently the triggering mechanism of the coherent convective structures i.e.
the so called ‘blobs’. Further, the dynamics of the blobs in terms of radial velocity, waiting time
and size are also analyzed. Three radial locations (Rs, Rim and Rsf respectively) are defined to
study these mechanisms. Progressive enhancement of fluctuations and consequent blob
generation and propagation are observed with the increase in Bz at a constant Bt. Amplitude and
waiting time of the coherent plasma structures attain a maximum for highest Bz/Bt (=7.8%) in our
experiment. 2D statistical analysis of the images enables us to identify the blob formation region
precisely at Rim with a steep intensity gradient. Signatures of conducive environment for blob
generation like the sudden enhancement in s, minimum k, steep positive gradient of / and the
highest Lp-1 are evident at Rim. s and k follow the parabolic constraint for all Bz/Bt while
segregation of s was observed for Rs, Rim and Rsf respectively with increase in Bz/Bt. A distinct
coherent sinusoidal mode appears at Rim for Bz/Bt beyond 1% and subsequently the blobs are
40
ejected. High radial blobs velocities (~1700 ± 200 m/s) are observed. This is in agreement with
radial velocities of blobs seen in PISCES and MAST [41, 42]. Accelerated radial propagation
was observed for large sized blobs (~30 cm diameter), emphasizing the need to revisit the blob
propagation scalings proposed so far [43].
41
B. Variations in edge turbulence induced by poloidal magnetic field curvatures for 8.2
GHz slab plasma
3.8 Introduction II
The appearance of improved confinement regimes in tokamaks in regions of weak or negative
magnetic shear [44–53] has enthused considerable interest in the stability properties of such
equilibria. The magnetic shear in case of confined plasma in tokamaks with well defined flux
surfaces is defined as Sc = (r/q)(dq/dr), where q is the safety factor and r is a flux surface radius.
Improved confinement properties are expected to be related to greater stability of the plasma
modes considered to cause anomalous transport. This study aims at investigating the variation in
fluctuation characteristics in slab plasma with different poloidal field curvatures and strength.
Slab plasma, as discussed earlier, provides the unique opportunity to study fluctuations at a wide
SOL-like area towards the LFS and should provide better insight about the relation of microstability with magnetic shear. The magnetic shear is slightly redefined in case of the open
magnetic field lines, terminating on the flat divertor plates.
In this experiment magnetic configuration is chosen with both Bt and Bz field components
without plasma current. Hydrogen plasmas are initiated at 2.45 GHz using ECRH, and pulsed
with 8.2 GHz ECRH. Bz is varied in both curvature and strength by different coil combinations
(PF17, 26 and 35; figure 3.15a) and varying coil currents. Three radial locations, viz. Rs (plasma
source), Rim (steep intensity gradient) and Rsf (ambient intensity tail) are defined as earlier to
study the fluctuations.
The Photron Fastcam SA5 CMOS camera with frame rate of 7000 frames/s at full resolution
(1024 × 1024) is used for tangential imaging on the mid-plane of QUEST. Each frame is made
up of 242 × 242 pixels, and framing rate is 20 kHz. Comparison with images using H filter
indicates that observed visible image is mainly attributed to H emission ( n0ne).
42
Figure 3.15: (a) cross sectional view of the QUEST vessel showing the PF coil pairs 17, 26 and
35-12. Also the arbitrary positions of the three regions Rs, Rim and Rsf are shown with blue
broken lines. Flux contours are shown for the PF26 coil. Dotted rectangle shows the extent of the
images; Solid horizontal lines represents the divertor plates; (b) top view of QUEST showing the
tangential field of view of the fast camera SA5.
-3
20
x 10
PF26
PF17
PF35-12
Bz (Tesla)
15
10
5
0
-5
0
0.2
0.4
0.6
0.8
1
R(m)
1.2
1.4
1.6
1.8
Figure 3.16: R profiles of PF coils at 1 kA coil current.
43
Three pairs of PF coils (viz. 17, 26 and 35) shown in figure 3.15a are used to vary the Bz
topology. Bt is maintained at 293 mT at the resonance layer at R = 0.24 m. Radial profiles of the
PF strengths at 1kA coil current are shown in figure 3.16. PF strength can be quantified in terms
of the pitch distance
z
2 R Bz Bt , connection length of field lines Lc
two divertor plates and pitch angle
the magnetic shear S
tan
1
2 R 2b /
z
between the
Bz Bt . PF curvature can be demonstrated in terms of
R d and the mirror ratio
dR
Bt _ div Bt _ mid . For mirror ratio, the field
lines, starting at the second harmonic layer on the mid plane, are traced to calculate the toroidal
field at the launching (Bt_mid) and terminating point on the divertor (Bt_div). Low energy electrons
follow these field lines. Figure 3.17 shows magnetic shear (17a), and mirror ratio (17b) for the
PF coil parameter space explored here. Three distinct S regimes at the second harmonic for three
PF coils with a variation of factor of 2 are investigated. Mirror ratio
provides deep (PF35),
shallow (PF26) and negative (PF17) PF wells ( < 1) respectively. Note that Bz is a function of R
and hence will have different R profiles for different PF coil pairs. Thus, even for the same Bz at
the fundamental resonance, magnetic shears profiles will be different for the three coil pairs for
the same Bt. Here Lc is varied by one order of magnitude in the experiment by varying the
strength of Bz in the three PF coil pairs. Time series of an individual blob event in case of PF26
operated at Bz = 40.75 mT is shown in figure 3.18.
2.2
PF17
PF26
PF35-12
1
2
1.8
0.9
Mirror ratio
Magnetic shear at second harmonic
1.1
0.8
PF17
PF26
PF35-12
1.6
1.4
1.2
0.7
0.6
0
a
0.01
0.02
0.03
Bz (Tesla)
0.04
b
1
0.05
0.8
0.2
0.4
0.6
R (m)
0.8
1
Figure 3.17: (a): Magnetic shear at second harmonic as a function of Bz is shown for PF17, 26
and 35 respectively. (b): Radial profile of the mirror ratio for the three coil pairs.
44
(I-< >)/
Figure 3.18: (Color online). Time series of an individual blob event is shown. Images run from
left to right and top to bottom and the consecutive images are 50 s apart. A helical filament
emerges from the vicinity of the resonance layer and expands radially until it dies off at the LFS.
4
2
0
-2
4
2
0
-2
10
5
0
R = 0.32 m and z = 0.2m
Rs
R = 0.39 m and z = 0.2m
Rim
R = 0.54 m and z = 0.2m
7.45
7.5
Time (s)
Rsf
7.55
7.6
Figure 3.19: Intensity fluctuations at Rs, Rim anf Rsf respectively for PF26 at 40.75 mT.
Intermittent positive bursts are observed at Rsf intensity signal. These bursts correspond to the
blobs generated at higher Bz with PF26.
3.10
Statistical analysis
Time series for 200 ms are considered for the statistical analysis. Intensity fluctuations from the
three regions (Rs, Rim and Rsf) for a shot with PF26 at 40.75 mT are shown in figure 3.19. Higher
order moments of the probability density function (PDF) like skewness s = µ3/ µ23/2 and kurtosis
k = µ4/ µ22-3 follow parabolic relation as seen earlier. However, mean s shows an increasing
45
trend with Bz while it shows opposite trend for PF17 and PF35 (figure 3.20a). Mean s and k were
maximum for PF26 at the same Bz level as shown for mean s at ~16.4 mT in figure 3.20b. Also
mean s first drops off as function of Lc, but then again increases as shown in figure 3.20c.
~16.4 mT
0.9
PF17
PF26
PF35-12
0.8
1
PF17
PF26
PF35-12
0.9
Mean skewness
0.8
0.7
Mean skewness
0.7
0.6
0.5
0.4
c
0.3
0.2
0.6
0.1
0
0.5
20
40
60
Connelction length (m)
80
100
b
0.4
0.3
0.2
0.1
0.6
0.7
0.8
0.9
1
Magnetic shear at 2nd harmonic
1.1
Figure 3.20: (a)~(c): Mean skewness as a function of Bz, magnetic shear at second harmonic and
the connection length respectively. The dotted line in (b) follows Bz ~ 16.4 mT
3.11.1 Correlation coefficient
Cross-correlation coefficient (cxy) is calculated among a reference pixel and for all the pixels. It
is defined as:
c xy
xy nx y
x
2
nx
2
y
(1)
2
ny
2
46
Where x and y are two time series signals, the bar denotes ensemble average (time) and n is the
number of samples. For PF17, 26 and 35 cxy at Bz ~ 16.4 mT is shown in figure 3.21.
Correlation between Rs and Rim is small for PF17 and maximum for PF26. A distinct coherent
mode appears at Rim and the wavelength ( z) along z grows with
as the PF coils are changed.
Highest was observed for PF35.
3.11.2 Power spectral density (PSD)
PSD shows a coherent peak at ~4 kHz at Rs for PF35 beyond ~13 mT (figure 3.22). Such peak
was not observed for PF17 or PF26 even at much higher Bz.
47
0.5
0.4
0.3
0.2
0.1
0
0.2
0
-0.1
0.3
-0.1
-0.2
0.4
-0.2
-0.3
0.5
0.1
z (m)
z (m)
-0.3
0.9
0.8
0.7
0.6
0
0.5
1
0.5
0.4
a
0.2
0.4
0.6
R (m)
C o rr-co eff
C o rr-co eff
1
0.8
0.3
0.2
1
cRs at z=0.2 m
cRim at z=0.2 m
0.8
0.6
0.4
0.2
0.9
1
0.5
0.4
0
0.6
0.1
0
-0.1
0.2
-0.1
-0.2
0.3
-0.2
-0.3
0.5
0.8
0.4
0.6
0.7
R (m)
0.3
0.5
0.2
0.4
0.1
z (m)
z (m)
0.3
0.4
-0.3
0
0.5
1
cRs at Rs
cRim at Rim
0.2
0.5
0.9
0.8
0.7
0.3
0.2
0.1
b
0.2
0.4
0.6
R (m)
0.8
0
-0.1
1
Figure 3.21: (Color online). cxy for
(a): PF17, (b): PF 26 and (c) PF35
respectively. Background image:
reference pixel at Rs and overlaid
contour: same at Rim.
C o rr-c o eff
C o rr -co e ff
1
cRs at z=0.2 m
cRim at z=0.2 m
0.8
0.6
0.4
0.2
0.5
0.4
0.9
0.3
0.8
0.2
1
0.2
0.7
0.1
z (m)
z (m)
0.9
0.1
0.6
0
0.8
0
0.5
-0.1
0.6
0.7
R (m)
-0.1
0.4
-0.2
0.5
-0.2
0.3
-0.3
0.4
0.3
-0.3
0
0.5
0.3
0.4
c
0.2
C o r r-c o e ff
0.4
0.6
R (m)
1
C o r r-co eff
1
cRs at Rs
cRim at Rim
0.2
0.5
0.8
1
0.2
0.1
cRs at z=0.2 m
cRim at z=0.2 m
0.8
0.6
0.4
0.2
0.2
0.3
0.4
0.5
0.6
0.7
R (m)
0.8
0.9
1
48
-32
1.31912
2.63824
3.95736
5.27648
6.59561
9.89341
13.1912
16.489
s
Magnitude at R (dB/Hz)
-34
-36
-38
-40
-42
-44
-46
-48
-50
0
2
4
6
Frequency (kHz)
8
10
Figure 3.22: PSD for PF35 at various Bz (see figure legend).
3.12 Conclusions II
Fluctuation characteristics are quite different for PF17, 26 and 35 with high, moderate and low
magnetic shear (S) respectively. Vertical wavelength was largest for highest
and decreases
progressively. Highest fluctuations and blobs are recorded for intermediate S (PF26) and shallow
PF well. Coherent mode at ~ 4 kHz appears for deep PF well (PF35) beyond Bz~13 mT. It was
not apparent for either of PF17 and 26.
49
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52
CHAPTER FOUR
Edge turbulence in
inboard limited plasma
4.1 Introduction
4.5 Discussions
4.6 Conclusions
References
4.1 Introduction
The edge plasma in toroidal fusion devices is vital as it interfaces the plasma with the first wall
components and divertors. The radial cross field transport is particularly important as it decides
the strength and strike points of the heat and particle flux to the wall as well as the processes of
recycling, impurity influx and helium ash removal. Transport in tokamaks is generally
‘anomalous’, thus not following the magnitude and parameter scaling of ‘collisional transport’
[1]. Also, the edge plasma is at the immediate vicinity of the confined plasma and thus affects
the quality of confinement as suggested in the achievement of H-mode [2-4]. The cross field
transport is recognized to be dominated by turbulence at the edge [5]. Broadband plasma density
fluctuations play the dominating role in edge turbulence with relatively high fluctuation
amplitude as compared to the average density, with n/n often reaching ~1. Cross field size scale
(autocorrelation) is typically ~0.1-10 cm (i.e. meso-scale) while along the field lines it is of the
order of tens of meters. These are the large 3D filaments, often referred to as ‘blobs’ in 2D. They
are seen as large intermittent bursts of density in the SOL. Edge turbulence is ubiquitous with the
plasma duration, and is usually interpreted as the nonlinear saturated state of drift wave or
interchange instabilities in the edge plasma [6].
Visualization of turbulence study has helped immensely in gaining deeper insights in this field
[7,8]. Recently the importance of the role of blobs on the convective transport and its effects on
the wall loading has been extensively investigated both in experiment and theoretical fields [914]. Nonlinear evolution of drift or interchange instabilities driven by the pressure gradient or
curvature of the magnetic field lines, the role of the E×B flow in shearing off a radially extended
structure and ejection of blobs are active areas of this subject. In the spherical tokamak QUEST
blob generation and propagation is studied earlier in slab annular plasma created by electron
cyclotron waves (ECW) in a simple magnetic configuration characterized by open field lines
[15,16].
It has been reported that in tokomaks, RTPs, stellarators, and linear devices there are
fundamental similarities in the radial transport, which is characterized by intermitted convection
rather than diffusion, extended into the far SOL, and significant recycling [9-12]. Several types
of the probability density functions PDF p(x) are fitted and from the statistical point of view
54
universality of the SOL fluctuations has been proposed. Although the shape of the p(x) varies
inside, near and far from the LCFS, it has been pointed out that the p(x) belongs to a family of
the Pearson type including the Gauss, gamma and beta distributions [19-21]. PDF p(x) of the
1
n
time series is characterized by the mean (
where µi is i-th central moment (
i
1
n
n
n
I t j ) and variance (
j 1
I tj
i
2
1
n
n
2
I tj
),
j 1
), mode or anti-mode at which
j 1
d(log(p(x)))/dx = 0, and multimodality. The higher order moments of p(x), like skewness s = µ3/
µ23/2 and kurtosis k = µ4/ µ22-3represent the shape of p(x). s and k can help determining the
deviation from the Gaussian distribution. These shape factors can be used to understand how the
statistics of fluctuations obey the physical stochastic principles. In ref. [19] it has been found that
there exists a simple quadratic relation between s and k. Based on this relation a plausible p(x) in
the SOL region is proposed to be beta [20,21] or gamma distributions[19]. It has been known
that these p(x) satisfy a probability differential equation (PDE), called the Pearson system with
the form:
d log p x
dx
c0
a x
c1 x c 2 x 2
(1)
The coefficients in the denominator on the right hand side can be derived using the moments [22]
c0
4 k 3s 2
, c1
10k 12 s 2 12
sk 6
10k 12 s 2
12
, c2
2 k 3s 2
10k 12 s 2 12
This Pearson system includes Gaussian (c2 = c1 = 0), gamma (c1
(2)
0 and c2 = 0) and beta
distributions (when the roots for the equation c0 + c1x + c2x2 = 0 are real) respectively. Based on
the measured fast camera images, higher order moments of intensity fluctuations have been
analyzed and applied to deduce these numerical coefficients.
In this paper ECR heated Ohmic plasmas have been investigated by two dimensional tangential
fast imaging technique [15,18]. Inductively plasma current is driven in the initial ECR pre55
ionized slab annular plasma. At the beginning a closed magnetic surface (LCFS) appears from
the inboard side and it grows quickly. Helical perturbations, developed in the slab plasma phase,
are forced to bend due to the growing LCFS and moved outwards. Since ECRH is superposed
later, there exist two plasma source inputs to the SOL plasma. One is the core Ohmic plasma and
the other one is the ECR region vertically extended outside the LCFS. They serve as the possible
drives for the SOL fluctuations. Intermittent strong fluctuations dominated by blobs in the outer
SOL are investigated. Blob propagates not only along the field lines and but also radially
outward. Hence, in this work, we focus on the following two aspects of SOL fluctuations.
Statistical features of the background fluctuations and triggering mechanisms of blobs are
analyzed. Also, we attempt to discuss the plausible probability equation for the SOL fluctuations.
The paper is intended to demonstrate (1) universality of a simple relation between s and k in the
SOL, (2) re-alignment of this relation with the density gradient and its correspondence with the
non-linear damping of fluctuations and (3) the effect of stochastic force in the SOL turbulence
and associated PDFs.
Outline of the paper is as follows: the experimental setup is discussed next. Characteristics of the
SOL of Ohmic plasma are introduced in section 3. Section 4 provides an account of the statistical
analysis of the image data. A statistical model to characterize the PDFs and the physical
interpretation is described in section 5. Finally, some conclusions are drawn in section 6.
QUEST [23] is a medium sized spherical tokamak with major and minor radii of 0.68 and 0.4 m,
respectively. The diameters of the center stack and the outer wall are 0.2 and 1.4 m respectively
with flat divertor plates at D (= ±1 m) from the mid-plane. Hydrogen plasma is initiated by 2.45
GHz ECR pre-ionization. Then plasma current (Ip) is ramped up by Ohmic power. Finally ECR
heating (8.2 GHz) is performed on the Ohmic plasma near the fundamental resonance layer Rres
(~ 0.33 m). Fluctuation measurements in the wide SOL have been carried out in ECR heated
Ohmic configuration with Ip ~ 50 kA. Toroidal field Bt is maintained at 0.29 T at Rres. Ion
B
drift is directed downwards. Three radial regions are defined; the ‘plasma source’ region (Rs)
corresponding to the LCFS (R~0.57 m) and a ‘source-free’ region (Rsf) is at least 0.22 m far from
the LCFS in the outer SOL. An ‘intermediate’ region (Rim) is considered 0.1~0.2 m from the
56
LCFS as shown in figure 4.1. Rim and Rsf are characterized by a steep intensity gradient region
near the plasma boundary and a very weak intensity region or essentially vacuum with frequent
sweep by the helical perturbations respectively. Since both ECW power (~100 kW) and Ohmic
power (< 40 kW) are superposed, the plasma source along the vertical zone at R = Rres outside
the LCFS must be taken into account.
Figure 4.1: top view of QUEST showing the field of view of the fast camera along with other
diagnostics and sub-systems. The fundamental resonance (Rres), Rim and Rsf are shown as broken
circles.
The Photron Fastcam SA5 camera is used for tangential imaging (figure 4.1) on the mid-plane of
QUEST [24]. Spatial resolution on the tangency plane is 4.8 mm. The camera is operated from
the tokamak control room via Gigabit Ethernet, and image acquisition is initiated by an external
trigger synchronised with the tokamak operational sequence. Image is transferred away from the
view port by a 4.5 m long imaging fiber bundle manufactured by Schott. At the back end the
camera is connected with the fiber bundle through a 1:1 relay lens. Each frame is made up of 186
× 173 pixels, and framing rate is 50 kHz. Comparison with images using a H filter indicates that
the observed visible image is mainly due to the H emission as discussed in chapter 2. In order to
57
analyze temporal and spatial evolution of images it is assumed that the neutrals n0 are distributed
uniformly in the chamber and images are due to the local evolution of plasma or propagating
plasmoid whose electrons can excite the neutrals immediately [25,26]. The intensity I( ul) of a
spectral line of wavelength
-2 -1
ul
due to a transition from the upper level u to the lower level l is
-1
given (in photons m s sr ) by:
I
ul
1
4
x2
nu Aul dx
x1
1
4
x2
PEC exct ne , Te ne n g dx
(3)
x1
Here Aul is the spontaneous transition probability from upper to lower level and nu is the
population number density of the upper level u (= 3) of the emitting ion [27]. In the collisional
radiative approximation, ignoring recombination, the emissivity can be attributed to the
excitation of ground state atoms (ng) by electrons and the consequent photon emission. PECexct is
the ‘effective’ photon emission coefficient for the excitation of ground state atoms by the
electrons and is a function of ne and Te. The integration denotes the tangential line of sight for
each pixel that traverses through the plasma from x1 to x2. It has been shown that, at similar ne
and Te in TORPEX, the mean value of the light emission signal recorded with a tangential fast
camera depends linearly on ne at varying neutral hydrogen density and ECRH power [28]. Hence,
in our case too, it is reasonable to interpret the intensity fluctuations as density fluctuations,
although, it resembles plasma pressure fluctuations in a more precise way.
Figure 4.2 shows a typical time series of images showing evolution of the initial perturbations
into helical filaments. These filaments have the same pitch as that of the magnetic field lines.
They also move across field lines and eventually die off at the LFS. Few dark spots and scratches
on the images can be seen. Those are due to flaws in the fiber bundle and are excluded in further
statistical analyses.
58
Z (m)
0.4
362.98
363.00
363.02
363.04
363.06
363.08
363.10
363.12
0.2
0
-0.2
Z (m)
0.4
0.2
0
-0.2
0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8
R (m)
Figure 4.2: Formation and evolution of a helical perturbation (white arrow) are shown in false
color in the raw image series acquired at 50 kHz. The first image is superimposed with the
reconstructed magnetic surfaces (solid curves). The broken line denotes the center stack. Time
stamps are in ms.
10
0
-10
0.4
0.2
Z
(m
)a
l
g
on
fl
a
ux
rc
Intensity (AU)
Helical perturbations
0
0.384
0.3835
0.383
0.3825
(s)
Time
0.385
0.3845
Figure 4.3: Intensity fluctuations along a flux tube in the SOL (Rim < Rflux-tube < Rsf) from mid-plane
towards the top of the vessel. Time series is detrended and filtered with a low pass filter (<5 kHz).
Definite structures corresponding to the helical perturbations can be seen to flow along the flux
tube.
59
Line of sight (LOS) integration effect due to the tangential view may hinder the fluctuation
assessments. A quantitative evaluation of this effect is carried out under the framework of the
TITR code [16,29]. It is seen that the effect is negligible in the edge and SOL of the plasma as
compared to the plasma core as the density and hence the intensity is appreciably smaller in that
region. Hence, statistical analysis inside the LCFS seems inconclusive and fluctuation
characteristics only at the SOL are reported.
Ohmic plasma is evolved from the inboard side when the inductive field (< 5V/m) is induced. As
Ip is ramped-up the LCFS grows and the initial ECR pre-ionized slab plasma is bent outwards
significantly. Fluctuations appear at the SOL and the amplitude grows with the increase in Ip. At
Ip ~ 50 kA, when ECRH is switched on the outboard fluctuation in the outer SOL shows strong
helical perturbations. An individual blob event right from the birth till it fades out in the far SOL is
shown in the image sequence in figure 4.2. The pitch of these perturbations seems to be the same
as that of magnetic field lines in the outer SOL. Since 100 kW ECWs are injected and it interacts
with the SOL plasma at the top and bottom region outside the LCFS along the vertical line at R =
Rres, the plasma source due to ECWs is considered to dominate this SOL region. Intensity
fluctuations along a flux surface in the Rsf are shown from the mid-plane towards the top divertor
plate in figure 4.3. Intermittent helical perturbations can be traced along the flux surface. The
trajectory is directed from the top towards bottom (ion
B drift direction) and also bulges out
radially. The frequency of blob generation is ~2 kHz.
60
Mean
75 0.5
0.5
70
0.4
65
0.3
60
Z (m)
0.2
55
0.1
50
0
45
-0.1
40
-0.2
35
-0.3
Standard Deviation
0.4
7
0.3
6
0.2
5
0.1
4
0
3
-0.1
2
-0.2
1
-0.3
30
0.5 0.6 0.7 0.8
R (m)
8
0.5 0.6 0.7 0.8
R (m)
0
Figure 4.4: Mean and standard deviation of the intensity fluctuations. The black curve denotes the
plasma boundary as shown in the mean contour.
Skewness
Skewness
0.5
0.5
15 0.5
0.4
2
0.4
0.4
0.3
1.5
0.2
Z (m)
Kurtosis
Excess
Kurtosis
2.5
0.3
1
0.5
0
-0.1
0
-0.2
-0.5
-0.3
0.5 0.6 0.7 0.8
R (m)
-1
10
8
0.3
10
0.2
0.1
Inverse
Inverse scale
scale length
length
0.1
6
0.2
0.1
0
4
0
5
-0.1
-0.2
-0.2
-0.3
-0.3
0.5 0.6 0.7 0.8
R (m)
0
2
-0.1
0
0.5 0.6 0.7 0.8
R (m)
-2
Figure 4.5: Higher order moments s and k of p(x). Inverse gradient scale length of intensity is
shown in the third panel.
It has been reported that the density and potential fluctuations in the SOL show typical nonGaussian statistics, that is, the skewness s is negative or zero in the core, positive in the SOL and
tends to increase with the distance from the LCFS [19-21]. In this work the statistics of intensity
61
fluctuations featuring blobs at the wide SOL of the Ohmic plasma is investigated with respect to
the radial regions of Rim and Rsf. R-Z contours of the mean ( ) and standard deviation (
2
)
are shown in figure 4.4. The black solid curve indicates the flux contour along the approximate
plasma boundary as seen in
seen that
contour. For most of the pixels
shows a non-zero value. It can be
drops off quickly beyond Rim to less than half of the peak intensity while
shows a
sharp increase in that region due to the existence of the intermittent bursts at the boundary.
Contours of higher order moments (s and k) and the inverse gradient scale length of intensity
( L p1
R
ln
) are shown in figure 4.5. Comparing the flux surfaces (Fig. 2) it can be seen
that both s and k are functions of the length of the flux tubes from the top towards the bottom of the
vessel in the SOL. Both s and k at Rsf are consistently higher at the lower half of the poloidal crosssection, signifying that the blobs are traversing from the top towards the bottom of the vessel along
with their cross-field motion. s values remained low up to Rim and thereafter it shows a steep
positive gradient. k values and Lp-1 remain very low or close to 0 till Rim and then increase rapidly
at the immediate vicinity of Rim on the LFS. These suggest that the p(x) is close to the Gaussian
distribution on the left of Rim and sharply deviates just beyond it. However, near the LCFS and
inside the core, the shape of p(x) is inconclusive from the present observations due to the LOS
integration effect of the tangential images.
A radial slice of the moments are plotted in figure 4.6 at the mid-plane (Z = 0
0.014 m) to have
a closer look at the statistical features. The Rim and Rsf regions are shown with dark and faded
bars respectively. The mean intensity has a steep negative gradient in the Rim region. This region
is also characterized with k ~0 and maximum Lp-1. Hence, this analysis reveals that the Rim region
with maximum Lp-1, sharply varying s and minimum k may be the most probable location for
blob generation. Further, rapid growth can also be observed in the radial profiles of / in figure
4.6. Similar observations were reported earlier in case of slab plasma [16]. This ratio can be
interpreted as the ratio of the stochastic to the deterministic terms in the nonlinear Langevin
equation as discussed in section 5.
62
max
0.8
/
0.6
s
0.4
2
1
0
10
k
5
/
0
0.2
0.1
0
0.4
0.5
0.6
R (m)
0.7
0.8
0.9
Figure 4.6: Radial profiles (at Z = 0 0.014 m) of the normalized mean intensity, s, k and /
respectively. Blob-generation (Rim) and propagation (Rsf) regions are shown with the dark and
light shaded bars.
The relation between s and k is plotted for the SOL in figure 4.7. Data show a well defined
distribution around a simple quadratic curve as observed earlier in slab plasma [16]. The blue
cross and red circles represent the s vs. k relation at, Rim (R = 0.73
(R = 0.79
0.02 m at mid-plane) and Rsf
0.2 m at mid-plane) along flux contours respectively. kim and ksf are shifted by +5 and
+10 to show the variation in the parabolic fit (green and magenta curves of Rim and Rsf
respectively). The black dots represent data from the wide SOL. The scattered points are fitted to
a parabolic relation ( k
As 2
C ), and the coefficients A and C are determined. Data from Rim
and Rsf clearly segregate in the s axis representing two different parabolas with the coefficient A
as 1.31 1nd 1.64 respectively. It can be seen that A can assume values both greater than and less
than the earlier reported [20] value (A=3/2). C was found to be ~0 in both cases.
The PDE mentioned in the introduction is examined substituting observed quantities ( , s, and k)
into equation (2). The coefficients c0, c1 and c2 of the denominator are derived and shown in figure
4.8. c0 is large positive (> 3) in Rim and Rsf and relatively smaller values (~1) from the LCFS to Rim.
63
c1 shows a clear boundary corresponding to Rim. Inside Rim, c1 is ~0 while beyond Rim it is, 1<c1<3.
c2 is ~0 in the entire region. These 2D contours of the numerical coefficients of PDE are consistent
with argument that p(x) is Gaussian in the region up to Rim and thereby it shifts towards gamma
distribution. A sharp boundary in the statistical nature of the fluctuations is found to be the Rim.
25
2
ksf = 1.6355ssf+0.059583
2
kim = 1.3088sim +1.6702e-012
20
2
Kurtosis k
kall = 1.6566sall+1.1786e-011
15
10
5
0
-0.5
0
0.5
1
1.5
Skewness s
2
2.5
3
Figure 4.7: k as a function of s from the wide SOL (black dots) is fitted (solid cyan line) to the
parabolic relation ( k As 2 C ). The blue cross and red circles represent the s vs. k relation at,
Rim (R = 0.73 0.02 m at mid-plane) and Rsf (R = 0.79 0.2 m at mid-plane) along flux contours
respectively. kim and ksf are shifted by +5 and +10 to show the variation in the parabolic fit (dashdot green and broken magenta curves for Rim and Rsf respectively).
Pearson coefficient c0
0.5
2.5
0.5
3
0.5
0.2
0.4
2
0.4
2.5
0.4
0.15
0.3
0.1
0.2
0.05
0.1
0
0.3
1.5
Z (m)
0.2
0.3
2
0.2
1
0.1
0.5
0
-0.1
0
-0.2
-0.5
-0.3
1.5
0.1
1
0
-0.1
0.5 -0.1
-0.2
-0.2
0
-0.3
0.6
0.8
R (m)
-1
0
-0.05
-0.1
-0.15
-0.3
0.6
0.8
R (m)
-0.5
0.6
0.8
R (m)
-0.2
64
Figure 4.8: Pearson’s coefficients c0, c1 and c2. The black solid curve is same as shown in figure 4.4
and 5.
4.5 Discussions
PDF of the fluctuations at Rim and beyond deviates from the Gaussian and becomes positively
skewed. At this point we attempt to understand the physical basis of the increased level of
fluctuations and blob ejection with steep density gradient at Rim. Assuming that the intensity
fluctuations in our case resembles the plasma density fluctuations as stated in section 2, a simple
nonlinear Langevin equation [30-32] for a random variable x, representing the plasma density, is:
dx
dt
where,
x bx 1
x
(4)
t
is the linear growth rate and b is the nonlinear damping amplitude. (t) represents a -
correlated Gaussian process with amplitude Q,
t'
t
Q t t ' . (1+ ) is the exponent of
nonlinear damping. However, it can be noted that identifying the terms in equation (4) with exact
physical processes is clearly not trivial from the present dataset and hence, the model represents
nonlinear systems in general. The corresponding Fokker-Planck equation is:
p
t
x
x bx 1
Steady-state solution of equation (5) p 0
p0 x
Nx
1 2
Q
exp
Q 2 2
x p
2 x2
1
Qx p
2
t
(5)
0 yields the expression,
2b x
Q
where, N is the suitable normalization constant, N
(6)
2b Q
2
Q
1
2
Q .
First two terms on the right hand side of the stochastic differential equation (4) denotes the
deterministic part of this process, while the last term represents the stochastic part. Observed /
65
of the intensity fluctuations (section 4) resembles the ratio of the stochastic to the deterministic
contribution of equation (4) as discussed earlier [16]. Hence, the rapid growth of / at Rim with
the steep density gradient signifies a sudden increase in the stochastic forces. This increased
stochasticity can broaden the PDF, while maintaining the Gaussian distribution. However, the
PDF is observed to deviate from Gaussian from Rim towards the far SOL. This may happen only
when the multiplicative nature of the noise term in equation (4) is considered. The plausible
explanation may be that at Rim, there is a steep density gradient which in turn may have increased
the stochastic forces and also coupled the density fluctuations with the noise term. In figure
4.9(a), the PDF is Gaussian when Q = 1 (<<2 ) but deviates with the increasing Q. Here
is
taken as 16. Thus if the stochastic force is enhanced, the deviation of p(x) from Gaussian can be
inferred as seen at R
Rim. When Q = 2 , the PDF changes abruptly. Thereafter as Q assumes
values > 2 , the exponent of x in equation (6) turns negative and p0(x) is represented by x-n
(where n~1 as Q~ ) superposed with the exponential decay as shown in figure 4.9(a). However,
such a situation is unlikely and Q is expected to be < 2 in our case.
Equation (4) is similar to the Pearson PDE, as shown in equation (1). For example, when the
damping exponent = 1, expression (4) assumes the gamma distribution [33] of the form:
p0 x
Where
Nx
1
exp
= 2 /Q and
x
(7)
= 2b/Q. Parabolic relation between s and k for the class of PDFs
represented by equation (6) are shown in figure 4.9(b) for different values of . The coefficient A
in the fitted parabolic relation for SOL fluctuations stays on either side of 3/2 for Rim and Rsf
respectively. For
= 1, A can be precisely 3/2 for the gamma distribution as shown in figure
4.9(b). However, if > 1 ( < 1), A can attain values < 3/2 (> 3/2). Hence, a situation with greater
(less) than second order nonlinear damping may be envisaged in our case at Rim (Rsf).
66
1
14
Q=1
10
Kurtosis k
0.6
pP
0(x)
0
x2
12
0.8
Q=50
0.4
Q=32
a
0
0
8
2
4
x
6
x4
6
x5
4
2
0.2
x3
k=1.5s2
b
0
8
-2
0
0.5
1
1.5
2
Skewness s
2.5
3
Figure 4.9: (a): PDFs given by equation (6) for = 16 and different values of Q. The broken curve
indicates Gaussian PDF with Q = 1, while the red curve denotes the abrupt change in PDF shape
for Q = 2 ; (b): parabolic relation between s and k with different values of the non-linear damping
exponent.
4.6 Conclusions
Statistical features of SOL fluctuations are investigated using the fast camera imaging technique
in the Ohmic plasma. Tangential fast imaging provided the unique opportunity to characterize
the SOL fluctuation and follow the blob trajectories along a wide region in 2D. Intermittency,
dominated by blobs, is observed in the SOL. SOL fluctuations are seen to have similar features
as the slab plasma [16]. At the immediate vicinity of Rim towards LCFS, p(x) can be described
well by Gaussian distribution. A simple quadratic relation exists between s and k, and the
deviation of the p(x) from Gaussian is significant beyond Rim towards the far SOL. The deviation
of p(x) and hence the enhanced intermittent blob transport is considered to be caused by
enhanced ‘stochastic force’ due to the
using a simple logistic model.
Acknowledgements
This work is supported by a Grant-in-aid for Scientific Research (S24226020). This work is also
performed with the support and under the auspices of the NIFS Collaboration Research Program
(NIFS07KOAR009, NIFS08KUTR024) and the Sasagawa Scientific Research Grant (25-203)
from The Japan Science Society.
67
References
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S, Ryoukai T and QUEST group 2011 J. Nucl. Mater. 415 S624
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[18] Liu H Q et al 2010 J. Plasma and Fusion Research series 9 33
[19] Sattin F et al 2009 Plasma Phys. Contr. Fusion 51 055013
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M 2007 Phys. Rev. Lett. 98 255002
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70
CHAPTER FIVE
ECW induced scrape
off layer (SOL) flow
5.1 Introduction
5.2 Experimental details
5.3 Spectral characteristics of intensity fluctuations
5.4 Estimation of poloidal component of parallel velocity
5.5 Particle image velocimetry through orthogonal dynamic programming
(ODP)
5.7 Conclusions
References
ECW induced SOL flow
5.1 Introduction:
Plasma flow along the magnetic field lines in the scrape-off layer (SOL) is believed to play vital
roles in the regulation of instabilities, L-H transition as well as divertor power handling due to
the reduction of heat flux e-folding length in the SOL by high flow velocities. [1-6]. Parallel flow
in the SOL has been measured in many tokamaks [4,7]. Several mechanisms are cited to drive
these flows like toroidal rotation, ionization imbalances, Pfirsch-Schlüter (PS) flow, cross-field
drift and ballooning transport. Comprehensive information of the poloidal flow is crucial for the
reconstruction of the total flow pattern in the SOL [4] and thereby improving plasma performance.
Flow induced by RF is being explored recently. RF (ICRH and LHCD) induced toroidal flow
drive and modified SOL flow are observed in Alcator C-Mod [4,8-10]. Sheared poloidal flow
generation in the confined plasma has been observed in ion Bernstein wave (IBW) heated
discharges in PBX-M and TFTR [11,12]. Poloidal rotation measurement has also been reported
with ECRH in Heliotron E [13]. However, direct observation of ECW (ECRH/ECCD) induced
poloidal flow is not reported experimentally in tokamak SOL to date. It can be noted that
electron cyclotron wave (ECW), which is capable of highly localized power deposition, is
indispensible both on existing tokamaks and future fusion reactors. Experimental demonstration
of SOL flow induced by ECW can provide an effective tool to modify the plasma pressure
profile and also edge turbulence characteristics.
Cyclotron wave heating is characterized by the increase in perpendicular kinetic energy of the
resonant particles. This may lead to particle loss through outward particle flux [14]. In the
collision-less regime the perpendicular kick also piles up the resonant species toward the lowfield side (LFS) in the toroidal magnetic well and gets them trapped. A poloidally varying
electrostatic potential is expected to rise and saturate at a level that balances the trapping effect
due to the magnetic well and the RF heating [15-17]. During ECRH, the scenario is even more
intriguing with electrons being the resonant particles. It is envisaged that the poloidal
accumulation of the electrons also triggers the redistribution of the ions along the magnetic
surface, resulting in a poloidally asymmetric ion source [14,15].
~
For an asymmetric ion source, S
cos ( being the poloidal direction), i.e. peaked in the LFS,
a parallel flow with a poloidal varying part u~||
sin would be produced to avoid poloidally
72
~
localized accumulation of ions in the confined plasma. As a consequence of the S in the
proximity of the last closed flux surface (LCFS), strong parallel flow can be driven by
ballooning-like cross field transport [4] in the LFS SOL. Such a situation appears when the LFS
and HFS are magnetically connected like in the single-null (SN) configuration.
We report here the direct observation of the poloidal component of ECW induced parallel flow
(u|| ) in the SOL of the spherical tokamak QUEST [18], using tangential fast visible images. In
the SOL u|| can be inferred non-intrusively and comprehensively in 2D from this diagnostic, but
the core rotation measurements are rather inconclusive due to line of sight integration effect [19].
This observation is further supported by a set of Langmuir probes accessing the SOL from the
LFS. Such an observation of ECW induced SOL flow is being reported for the first time in
tokamaks.
5.2 Experimental details:
In this experiment plasma start up by 8.2 GHz ECRH, is followed by an Ohmic (OH) phase
where, plasma current (Ip) value is fed back (FB) to the OH coil power supply in order to
maintain Ip flat-top at -30 kA. At the declining OH phase again heating is performed (R = 0.33
m) with ECRH (30 kW). Simultaneously 8.2 GHz ECCD (30 kW) is applied with a phased array
antenna [20] to drive Ip thereafter. We focus on this second OHFB-ECW phase as strong edge
turbulence and SOL flow are observed. Toroidal magnetic field (Bt) is kept constant (0.29 T at R
= 0.33m). Typical plasma parameters at the core are line averaged ne ~ 6 1017 m
3
and Te ~ 40
eV. Such discharges are obtained routinely at very high reproducibility in QUEST with minor
variations in discharge parameters. Figure 5.1 shows the change in plasma configuration and the
typical discharge parameters with the ECW phase starting at t = 2.0s.
73
Shot number: 18963
0.4
1.95 s
2.16 s
0.2
0.2
0
0
-0.2
-0.2
a
-0.4
0.5
R (m)
-3.5
b
-0.4
1
0.5
R (m)
Ip
-3
-2.5
-2
OH
-1.5
-1
-0.5
1.5
7
5
e
OH, I
p
ne
1
3
n
Z (m)
0.4
1
c
ECW pulse
2
2.5
-1
3
Time (s)
Figure 5.1: (a-b) plasma shape reconstructed from flux loop signals showing HFS limiter (1.95s)
and inboard poloidal null-like (2.16s) configurations for a typical shot; (c) Ip ( 10 kA), line
averaged density ne ( 1e17 m-3) and OH coil current ( 2 kA) are shown. The vertical shaded bar
denotes the fast image recording window.
A Photron Fastcam SA5 camera is used for tangential imaging at 20 kHz on the mid-plane of
QUEST [21]. Spatial resolution achieved on the tangency plane is 3.7 mm in both radial (R) and
~
vertical (Z) directions. Intensity fluctuations ( I ) in the images are shown in fig. 5.2(a) along the
9th flux contour (as numbered in fig. 5.2b), from mid-plane towards the top of the vessel, and as
a function of time. Propagation of a coherent mode is evident as shown by the solid arrows with
respect to the dotted lines, denoting the time when the intensity peaks are crossing ~mid-plane.
An axially rotatable ceramic probe head consisting of seven tungsten probe tips of diameter 1
mm and length 2 mm each is inserted radially below mid-plane. Schematic of the probe head is
shown in the inset of figure 5.9. In order to avoid damage due to hot electrons in the ECW phase,
probes can be inserted only up to 20 cm from the vessel wall. Hence, only the far-SOL (FSOL)
can be scanned in a shot by shot basis in reproducible discharges to measure floating potential
FSOL
) at 50 kHz.
( f) and ion saturation current ( I sat
74
Intensity (AU)
a
20
0
-20
0.4
0.3
0.2
0.1
0
2.091
2.092
2.093
2.094
2.095
Time (s)
0.4
Z (m)
0.2
Mid-plane
0
-0.2
b
0.2
0.4
0.6
0.8
R (m)
1
Z (m) along 7th flux arc
0.8
7 8 9
6
0.4
0.6
0.2
0.4
0
0.2
-0.2
-0.4
0
c
500
1000 1500
Frequency (Hz)
2000
0
~
Figure 5.2: (a) Time series of I from the mid plane to the top along the 9th flux contour as shown
in figure 5.2(b). Tilt between the solid arrows and broken lines shows the flow. (b) Raw image
superimposed with flux contours in the SOL. Reference pixel for C is highlighted in white
(R=0.69m and Z=0.2m); (c) C of all the pixels along the 7th flux contour.
5.3 Spectral characteristics of intensity fluctuations:
Spectral characteristics at the SOL are determined by the magnitude squared coherence estimate
~
(C) of I along the flux contours shown in figure 5.2(b). C is a function of the power spectral
densities (Pr ef,r ef( ) and Pr,r( )) of the reference pixel (r ef) and any other pixel (r = [R,Z])
along the flux arc and the cross power spectral density (Pr ef,r( )). Figure 5.2(c) shows the
contour plot of C of all pixels along the 7th flux contour with that of r ef at R=0.69m and Z=0.2m.
A distinct mode appears at 0.78 kHz, much lower than the ion cyclotron frequency (2
i~4.4
75
MHz) and remains across the flux contours suggesting long range correlations. Coherence length
is 40 cm along and 10 cm across the flux surfaces. When the probe head is inserted at an angle of
45 so that the tips (5~7) are aligned poloidally, the same mode appears at 0.78 kHz during the
ECW injection as shown in figure 5.3. Radial density profile from Thomson scattering data
obtained from a series of similar discharges shows that ne peaks at R = 0.48 m and 0.65 m (~2nd
harmonic) before and during ECW injection respectively, suggesting higher rise in LFS edge ne
as compared to core and steepening of the pressure profile near LFS SOL during ECW (figure
5.4). Thus the coherent fluctuations in density, potential and optical emissions suggest the
instabilities may be of pressure-gradient-driven drift-interchange type which is generally
Cross power magnitude (tips 5,6)
observed near the outer plasma edge [19,22].
-4
8
x 10
Peak at 781 Hz
6
Before ECW
During ECW
4
2
0
2000
4000
6000
8000
Frequency (Hz)
10000
12000
Figure 5.3: Cross power spectra of f at tips 5 and 6 before and during the ECW phase. The
distinct mode at 781 Hz appears during the ECW phase.
~
~
The spatiotemporal features of I are determined by a two-point two-time correlation [23] of I
in the range of
1 kHz (a low pass filter is applied) along the flux contours. The correlation
function between the intensities at two different points in space and time is defined as:
N
ef
, ,
I
ef
I2
,t
,t I
I2
,t
ef
,t
(1)
76
where is the time lag, I (r, t) is the intensity time series of the camera pixel sampling plasma at
r and
indicates the temporal averaging defined as:
xt
1
T
T
x t dt
(2)
T
1.8s
2.0s
2.1s
ne (normalized)
1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
R (m)
0.8
1
Figure 5.4: ne profiles measured by Thomson scattering before (<2.0s) and during ECW injection
( 2.0s) shows peak shift towards LFS during ECW phase. Profiles are normalized to the peak
value at 2.1s.
~
Figure 5.5 shows contour plots of the correlations of I from all the pixels starting from mid-
plane towards the top and along the 6th, 7th, 8th and 9th flux contours (see figure 5.2b) with that of
r ef at Z = 0.3 m on the 8th flux contour. The fluctuations have long range correlation along the
flux surfaces, suggesting long poloidal wave lengths. Fluctuation structure appears to propagate
from bottom (negative ) to top (positive ) divertor plate in a non-diffusive manner. Propagation
velocity along the 6th contour is ~0.6 kms-1 and increases across the flux contours towards LFS to
cover larger radii of curvature. Fluctuations also appear to propagate radially (shown by the
broken arrow through the maximum correlation with increasing Z) across the flux surfaces at the
same time when the fluctuating structure flows poloidally. However, from the tangential view it
77
is not possible to differentiate between the propagation of the fluctuations with respect to the
plasma and the plasma rotation itself and the observed flow may be a combination of both.
~
Figure 5.5 shows contour plots of the correlations of I from all the pixels starting from mid-
plane towards the top divertor plate and along the 6th, 7th, 8th and 9th flux contours (see figure
5.2b) with that of the reference pixel (r ef) at Z = 0.3 m on the 8th flux contour. The fluctuations
have a long range correlation along the flux surfaces, suggesting long poloidal wave lengths. The
fluctuation structure appears to propagate from bottom (negative ) to top (positive ) divertor
plate in a non-diffusive manner. Propagation velocity along the 6th contour is ~0.6 kms-1 and
increases across the flux contours towards LFS to cover larger radii of curvature. Fluctuations
also appear to propagate radially (shown by the broken arrow through the maximum correlation
with increasing Z) across the flux surfaces at the same time when the fluctuating structure flows
poloidally.
With 6th flux contour
0.5
0.4
0.4
0.3
0.3
1
0.5
1
0.5
0.4
0.2
B
0.5
0.3
0.2
0.2
0
0.1
-2
-1
0
(ms)
0
1
-1
-0.5
0
(ms)
0
1
0.5
0.5
0
0
0.2
0
0.1
-2 2
1
0.3
0
0.1
1
0.4
0.5
A
Z (m) along flux arc
0.5
0.1
-2
2
-1
-0.5
0
(ms)
0
1
-2 2
-1
-0.5
0
(ms)
1
2
-0.5
Figure 5.5: Cross correlation of a reference pixel at Z = 0.3 m on the 8th flux contour (see Fig:
2b) and all the pixels from mid-plane (A) to top of the vessel (B) along a single flux contour. For
each flux contour the cross correlation lags at A and leads at B. Also, across the flux contours (6
to 9 and so on), the maximum correlation moves from A towards B.
5.4 Estimation of poloidal component of parallel velocity:
Next we attempt to evaluate the mean poloidal velocity along the flux surfaces. The correlation
technique described above is extended to the entire SOL that has appreciable signal to noise ratio
(SNR). Each flux contour is divided into regular poloidal intervals. The reference pixel is chosen at
the middle of each interval and the velocity for that interval is calculated from the difference in
78
lags among the extreme points of the interval and the poloidal distance between them. Once
velocity along a flux contour is evaluated, same procedure is repeated for the next contour and so
on. Finally, SOL poloidal velocity u|| is mapped by smoothening out the velocity field as shown
in figure 5.6(a). u|| remains positive (+
towards top) all along the flux contours showing
unidirectional flow in the SOL from the bottom towards the top divertor plate and reaches
maximum of ~0.85 kms-1 around mid-plane. Further, flux surface averaged u|| shows a positive
gradient along the radius (figure 5.6b). Local sound speed Cs (
Te mi , mi being the ion mass) in
the SOL is estimated to be ~15 kms-1. Field pitch (Bt/B ) ~4.5 suggests parallel Mach number of
~0.3 for the SOL flow. Negative u|| in the far SOL is due to low intensity and thereby poor SNR
away from the LCFS.
It can be noted that tangential camera images only detect the poloidal projection of the total
plasma flow, u||
_total.
This may be arising from various parallel flow components like PS ion flow
(u||PS), E B (u|| ot) and the flow driven by ballooning-like cross-field transport (u||t ans) to restore
particle balance [4]. Ion
B drift is directed + . u||PS and u|| ot are estimated from the ne and Te
profiles from Thomson scattering and E profile extrapolated to LCFS from the probe
measurements in FSOL. u||PS is directed - and co-Ip and is estimated to be ~ 0.6Cs. u|| ot is directed
+ , counter-Ip and is ~0.3Cs. Hence, combination of these two flows may not account for the
measured flow magnitude and direction and u||t ans seems to be playing a vital role in deciding
u||
_total.
In view of such an inference we try track the plasma eddies born from ballooning-like
transport and u||
_ed
( u||
_t ans)
due to their propagation by the particle image velocimetry (PIV)
technique [24-26]. PIV relies on optical alignments of various types of patterns as a global
transformation between consecutive image strips and thereby it is most likely to track the eddy
propagation. u||
_ed
is ~0.15 kms-1 and shows up-down anti-symmetry (Z= 0.2m in figure 5.6c).
Around mid-plane u||
_ed also
attains maximum value of ~0.6 kms-1. This suggests that the newly-
born eddies flow towards HFS SOL along the shortest path. However, orientation of eddies and
interplay among flow components on either side of the mid-plane may be significant in precise
determination of u||
_ed.
79
Both u||PS and u|| ot are estimated to be decreasing function of R on the mid-plane as seen on other
devices [5,27], while u||t ans is an increasing function of R as seen in both LFS and HFS SOL (~1
cm) of Alcator C-Mod SN discharges [4] similar to u||
_total
in our case. Plausible explanation may
be the shortening of the parallel connection length (L|| = bBt/Bz; b being the distance of flat divertor
plates from mid-plane and Bz is the vertical field) [19] going further away from the LCFS. There
the field lines connect the top-bottom flat divertor plates rather than terminating on the center stack,
as seen in the near SOL.
ms-1
ms-1
800
a
0.3
600 0.3
Z (m)
200 0.1
0.1
Bt
Ip
0
-0.1
0
200
u||PS
100
0
-200 -0.1
0
u||rot
-100
-400 -0.2
-0.2
0.6
Mean u (ms-1)
300
400 0.2
0.2
600
400
c
0.8
R (m)
1
-600
0.6
0.8
R (m)
1
-200
b
400
200
0.76 0.78 0.8 0.82 0.84 0.86
R(m) at mid-plane
u||trans
Inboard poloidal null configuration
Figure 5.6: (a): Poloidal velocity u|| _ in the SOL constructed from equation (1); (b) poloidal
mean of u|| across flux surfaces; error bars represent standard deviation of the data along flux
surface; (c) u|| _ed constructed using PIV.
5.5 Particle image velocimetry through orthogonal dynamic programming (ODP)
The procedure is essentially the search of a transformation that relates the consecutive image
with the previous image in a time series and minimizes the Minkowski distance Ln
80
I 0 i, j
i
I 1 i, j
n
between them. Details of the algorithm are discussed in Ref. [24-26] and
j
can be outline here in the following steps:
(1) Each image of the temporally displaced pair is sliced into several parallel overlapping strips
(here along R direction).
(2) Then, for every pair of strips, an optimal match is searched for with displacements allowed
only in the slicing direction and identical for all the pixels in the same column in the
orthogonal direction (here along Z direction). With the help of dynamic programming a dense
field of displacement is computed for every pair of strips by minimizing the distance L1
between them. The velocity is estimated from the distortion or transformation, in the slicing
direction, necessary to minimize the calculated intensity difference. The spatial resolution on
the tangency plane and the temporal resolution serve as factors to denote this velocity with
respect to real co-ordinates.
(3) The displacement field found in the first step is used to deform the second image relative to
the first one. An image I (i, j) is reconstructed from the (vR(i, j ), vZ(i, j )) displacement field
and the image I1(i, j) as I (i, j) = I1(i + vZ(i, j), j + vR(i, j)). The image I (i, j ) instead of I1(i, j )
is compared and now aligned to I0(i, j ).
(4) Then, all the above steps are repeated with the slicing performed in the orthogonal (Z)
direction and the alignment results are used to update and refine the (vR(i, j ), vZ(i, j ))
displacement field.
(5) The whole process is reiterated several times to achieve higher spatial resolution similar to
the actual pixel resolution of the image. The width of the strips and the corresponding
overlaps are reduced by about 2 in each iteration.
The code is first tested with simulated pairs of images. The images contain some patterns which
are different in intensities than the background. In the second image the patterns are shifted with
known number of pixels (analogous to velocity of the patterns) in both R and Z directions. Figure
5.7 shows example of such a pair of images and the estimated pixel shifts with the ODP
algorithm. Satisfactory match between the simulated shifts and the calculated shifts is obtained.
81
Image 1
Image 2
1
2
3
4
5
a
b
Pixel shift in 2nd image
15
10
5
0
-5
-10
-15
0
c
1
2
3
4
Pattern number
5
6
Figure 5.7: (a) and (b) shows the pair of images with the patterns numbered as 1~5. In the second
image, the patterns are shifted, with the original positions shown in broken rectangles. (c) Dotted
and broken lines show the actual shifts in R and Z directions respectively. Squares and circles in
the plot represent mean shift for all the pixels within that pattern and the error bars are the
within the pattern in R and Z directions respectively.
The image sequence used in this experiment comprises of 3500 images taken at 20 kHz. The
ODP algorithm is extended to the entire time series by selectively taking two consecutive images
at each instance. Thus 3499 frames of turbulent velocity field are computed from the intensity
images. Figure 5.8 shows the turbulent velocity maps superimposed on the intensity fluctuations
for 8 consecutive frames. The arrows represent magnitude and direction of velocities at a super
pixel (5
5 pixels) area for the sake of clarity in representation. Velocity field estimation from a
pair of images takes <10 s on a Windows® 7 laptop equipped with Intel® coreTM i5 processor and
4 GB RAM.
82
Z (m)
Z (m)
0.26
0.26
0.26
0.26
0.24
0.24
0.24
0.24
0.22
0.22
0.22
0.22
0.2
0.2
0.2
0.2
0.18
0.18
0.18
0.18
0.16
0.16
0.16
0.16
0.14
0.14
0.14
0.14
0.12
0.12
0.12
0.12
0.1
0.26 0.75
0.1
0.26
0.9 0.75
0.1
0.26
0.9 0.75
0.8
0.85
0.8
0.85
0.8
0.85
0.1
0.26 0.75
0.9
0.24
0.24
0.24
0.24
0.22
0.22
0.22
0.22
0.2
0.2
0.2
0.2
0.18
0.18
0.18
0.18
0.16
0.16
0.16
0.16
0.14
0.14
0.14
0.14
0.12
0.12
0.12
0.12
0.1
0.1
0.1
0.75
0.8
R (m)
0.85
0.9 0.75
0.8
R (m)
0.85
0.9 0.75
0.8
0.85
0.9
0.85
0.9
0.1
0.8
R (m)
0.85
0.9 0.75
0.8
R (m)
Figure 5.8: 2D turbulent velocity maps superimposed on the intensity image. Length and
orientation of the arrows denote magnitude and direction of the velocity respectively. Each arrow
represents velocity at a super-pixel (~3.4 cm2) for clarity of representation. The frames start at
2.07815 s, run from left to right and top to bottom and the consecutive images are 50 s apart.
During ECW the plasma center is pushed towards LFS by 0.095
0.007 m (from R ~ 0.42 m to
0.51 m) as calculated from plasma shape reconstruction using flux loops [28]. This happens due
to the reducing OH current and increased plasma pressure. Plasma configuration tends to change
from the initial HFS limiter towards an inboard poloidal null-like (IPN) featuring significant
magnetic connection (figure 5.6) between the LFS and HFS in the near SOL [29]. Such change
in configuration features increase in line averaged ne (figure 5.1) by a factor of ~2.5, while the
cross field particle flux
FSOL
, calculated from I sat increases by a factor of ~3.5. Hence, during
the ECW phase there is at least 25% degradation of the particle confinement ( p) due to enhanced
FSOL
cross-field transport. Both radially chord integrated H emission and I sat at tip 7 are enhanced
FSOL
as shown in figure 5.9, indicating increased outward particle flux. I sat fluctuation level also
increases by a factor of 10. In this shot, the probe head is inserted 17 cm from the LFS wall and
rotated by 45 . Difference in
f
(
f
E .) at tips 5 and 6 increases sharply at the ECW injection
83
as shown in figure 5.9 showing induced poloidal asymmetry of particles. Hence, the driftinterchange instability, excited by ECW, accompanied by poloidally asymmetric ion source at
the LFS is most likely responsible for the enhanced cross-field transport [22]. The sudden
particle spill-over from cross-field transport in the LFS SOL thereby tends to fill-in the HFS
SOL through parallel flows along the field lines.
Shot number: 19007
1.5
H
1
0.5
1
0
f
(probe 5 - 6)
0
-1
FSOL
Isat at probe 7
0
x 10
-4
-1
-2
-3
-4
1
1
2
5
6
7
1.5
4
3
2
2.5
3
Time (s)
Figure 5.9: H ,
f
FSOL
and I sat
profiles before and during (shaded) ECW injection. Probe
FSOL
, with tips 5~7 oriented along the poloidal direction.
orientation is shown in inset of I sat
5.7 Conclusion:
In conclusion, the unique Shafranov shifted IPN-like plasma configuration in QUEST has
allowed the first experimental demonstration of ECW induced SOL flow. SOL flow has now
been recognized to have direct bearing on at least two major impediments towards realization of
steady state reactor-grade plasma operation: regulation of instabilities for improved confinement
and divertor heat loads due to high parallel flow velocities (~0.5Cs). Therefore this phenomenon
84
may find its major application in modifying the edge turbulence and SOL flow pattern by ECW
which is the most versatile auxiliary heating system on future fusion reactors. This opens up the
possibility of developing new operation scenarios with modified SOL flow patterns and edge
turbulence by relatively low EC power.
85
References:
[1] Biglari H, Diamond P H and Terry P W 1990 Phys. Fluids B 2 1
[2] Terry P W 2000 Rev. Mod. Phys. 72 109
[3] Loarte A et al 2007 Nucl. Fusion 47 S203
[4] LaBombard B et al 2004 Nucl. Fusion 44 1047
[5] Goldston R J 2012 Nucl. Fusion 52 013009
[6] Lipschultz B et al 2007 Nucl. Fusion 47 1189
[7] Sangwan D, Jha R, Brotankova J and Gopalkrishna M V 2012 Phys. Plasmas 19 092507
[8] Wallace G M et al in Proceedings of the 37th EPS Conference on Plasma Physics, Dublin,
Ireland, June 2010, P5.193
[9] Ince-Cushman A et al 2009 Phys. Rev. Lett. 102 035002
[10] Lin Y et al 2008 Phys. Rev. Lett. 101 235002
[11] LeBlanc B B et al 1995 Phys. Plasmas 2 741
[12] Wilson J R et al 1998 Phys. Plasmas 5 1721
[13] Obiki T in Proceedings of the Twelfth IAEA International Conference on Plasma Physics
and Controlled Nuclear Fusion Research, Nice, France, October 1988.
[14] Castejón F, Eguilior S, Calvo I, López-Bruna D and García-Regana J M 2008 Phys.
Plasmas 15 012504
[15] Liu C, Qian S and Wan H 1998 Phys. Plasmas 5 2642
[16] Hsu J Y, Chan V S, Harvey R W, Prater R and Wong S K 1984 Phys. Rev. Lett. 53 564
[17] Zushi H, Mizuuchi T, Nagasaki K, Nakayama T and Peterson B J 1996 Plasma Phys.
Cont ol. Fusion 38 1307
[18] Hanada K et al 2010 Plasma Fusion Res. 5 S1007
[19] Banerjee S et al 2012 Nucl. Fusion 52 123016
[20] Idei H et al 2011 AIP Conf. P oc. 1406 473
[21] Banerjee S et al 2012 Rev. Sci. Inst um. 83 10E524
[22] Poli F M, Ricci P, Fasoli A and Podestà M 2008 Phys. Plasmas 15 032104
[23] Inagaki S et al 2012 Nucl. Fusion 52 023022
[24] Quénot G M, Pakleza J and Kowalewski T A 1998 Exp. Fluids 25 177
[25] McKee G R, Fonck R J, Gupta D K, Schlossberg D J, Shafer M W, Holland C and Tynan G
2004 Rev. Sci. Instum. 75 3490
86
[26] Banerjee S et al 2013 in press Plasma Fusion Res.
[27] Asakura N, Sakurai S, Shimada M, Koide Y, Hosogane N and Itami K 2000 Phys. Rev. Lett.
84 3093
[28] Hasegawa M et al 2012 IEEJ T ans.FM 132 477
[29] Zushi H et al in Proceedings of the Twenty forth IAEA Fusion Energy Conference, San
Diego, USA, October 2012.
87
CHAPTER SIX
Conclusions and
future scope
6.1 Conclusions
6.2 Future scope
Conclusions and futu e scope
6.1 Conclusions
Light intensity fluctuations from the slab annular plasma sustained with ECR power (at 2.45
GHz and 8.2 GHz) are studied in the QUEST device with fast imaging technique at high
temporal and spatial resolutions respectively. These plasmas provide the unique opportunity to
study fluctuations, blob formation and propagation with the tangential fast imaging diagnostic
technique, owing to the wide SOL-like region beyond the steep density gradient towards the LFS.
Three radial locations are defined; the plasma source region bounded by a relatively sharp
boundary, the intermediate and the source-free regions respectively. Rim is characterized by a
steep intensity gradient near the plasma boundary and Rsf by very weak intensity or essentially
vacuum. Two different studies are undertaken in this configuration. In the first, magnetic field
pitch Bz/Bt (at the ECR layer) is varied from -1.7% to 7.8% to investigate fluctuations of the
source plasma that presumably drives the edge and SOL fluctuations and consequently the
triggering mechanism of the coherent convective structures i.e. the so called ‘blobs’. With the
increase in Bz/Bt progressive enhancement of fluctuations and consequent blob generation and
propagation are observed. Amplitude and waiting time of the blobs attain a maximum for highest
Bz/Bt (=7.8%). Blob formation location is identified precisely to be the density gradient region
(Rim). s and k follow the parabolic constraint for all Bz/Bt with the coefficient A always remaining
<3/2. This may be due to the varied degree of non-linearity in the damping mechanisms of
fluctuations. Segregation of s was observed for Rs, Rim and Rsf respectively with increase in Bz/Bt.
High radial blobs velocities (~1700 ± 200 m/s) are observed. Accelerated radial propagation was
observed for large sized blobs, emphasizing the need to revisit the blob propagation scalings
proposed so far.
In the second part of the studies in slab plasma, the magnetic field curvature and hence the mirror
ratio is changed by changing the PF coil pairs. Thereby, the strength of Bz is also varied at a
constant Bt. Fluctuation characteristics are quite different for PF17, 26 and 35 with high,
moderate and low magnetic shear respectively. Highest fluctuations and blobs are recorded for
intermediate S (PF26) and shallow PF well. Coherent mode at ~ 4 kHz appears for deep PF well
(PF35) beyond Bz~13 mT. It was not apparent for either of PF17 and 26.
88
After the slab plasma with open magnetic field lines, Ohmic plasma which features a well
defined LCFS is studied. Statistical features of SOL fluctuations are investigated using the fast
camera. Tangential fast imaging provided the unique opportunity to characterize the SOL
fluctuation and follow the blob trajectories again along a wide region in 2D. Intermittency,
dominated by blobs, is observed in the SOL. SOL fluctuations are seen to have similar features
as the slab plasma. At the immediate vicinity of Rim towards LCFS, p(x) can be described well by
Gaussian distribution. A simple quadratic relation exists between s and k, and the deviation of
the p(x) from Gaussian is significant beyond Rim towards the far SOL. The deviation of p(x) and
hence the enhanced intermittent blob transport is considered to be caused by enhanced
‘stochastic force’ due to the
using a simple logistic model.
Finally, poloidal component of the parallel flow, induced by ECW injection, is measured in the
QUEST SOL. In this experiment plasma start up by 8.2 GHz ECRH, is followed by an Ohmic
(OH) phase where, plasma current (Ip) value is fed back (FB) to the OH coil power supply in
order to maintain Ip flat-top at -30 kA. Towards the end of the OH phase again central heating (R
= 0.33 m) is performed with ECRH (30 kW). Simultaneously 8.2 GHz ECCD (30 kW) is applied
with a phased array antenna to drive Ip thereafter under the ECCD – electron Bernstein wave
(EBW) mode conversion scenario. We focus on this second OHFB-ECW phase as strong edge
turbulence and SOL flow are observed. This may be an indirect manifestation of the destabilized
Stringer rotation in the core due to ECW induced poloidally localized accumulation of particles
on the LFS. Definite flow structures with long range radial and poloidal correlation and a distinct
mode at 781 Hz are observed. Cross correlation of intensity shows poloidal spin-up and radial
FSOL
suggests density pump-out even though there is an increase in
out-flow. Increase in H and I sat
ne. This strong cross-field transport may be driving the SOL parallel flow under the unique
scenario of ECW induced inboard poloidal null configuration in QUEST.
In conclusion, this study has provided deeper insights in the generation mechanisms and
propagation dynamics of the coherent convective structures (blobs). The effect of field pitch and
curvature may provide better controls on the intermittent transport across the plasma edge in
tokamaks and thereby improve the performance of the plasma core. Further, the unique
Shafranov shifted IPN-like plasma configuration in QUEST has allowed the first experimental
89
demonstration of ECW induced SOL flow. SOL flow has now been recognized to have direct
bearing on at least two major impediments towards realization of steady state reactor-grade
plasma operation: regulation of instabilities for improved confinement and divertor heat loads
due to high parallel flow velocities. Therefore this phenomenon may find its major application in
modifying the edge turbulence and SOL flow pattern by ECW which is the most versatile
auxiliary heating system on future fusion reactors. This opens up the possibility of developing
new operation scenarios with modified SOL flow patterns and better regulation of instabilities by
relatively low EC power.
6.2 Future scope
So far the blob propagation and frequency of blob generation can be studied in details from the
fast images. Effect of field pitch and curvature has also been addressed. Accelerated radial
propagation was observed for large sized blobs. However, the physical reason behind such
accelerated propagation, in contrast with the proposed velocity scalings, cannot be inferred as the
E
B velocity cannot be estimated so far due to lack of local measurements. Blob generation
mechanism cannot be inferred comprehensively as well. This can be done when the fast image
acquisition can be complemented by Langmuir probe measurements.
Another important study is to characterize the plasma flow in the SOL in the ECCD-EBW mode
conversion scenario. Strong plasma flow has been observed in the SOL in the fast visible images.
ECW induced plasma flow has not been reported in tokamaks till date. Comprehensive
knowledge of the electric field and particle flux is necessary to interpret the driving mechanisms
of such flows. Better insight of the driving mechanisms of the SOL flow which is vital for the
performance of the plasma core, will enable access to better confinement regimes. It can be
noted that the imaging diagnostics can only provide line of sight integrated information and
cannot provide any local measurements. A scanning multi-pin Langmuir probe needs to be
installed to complement the fast imaging measurements with local measurements of plasma
potential and density fluctuations. This will enable us to measure the components of the electric
field (E , E and E ). Here, , and
are the radial, poloidal and toroidal directions respectively.
Measurements of the electric field components in the SOL is essential to reconstruct the
90
complete flow pattern and for the estimation of the E
B velocity. Finally, the velocity field
calculated from the fast images can be compared with the local measurements with the probe.
Another aspect that needs to be addressed from the point of view of better plasma confinement is
the intrinsic toroidal rotation. With the help of Helium ion (He II) edge filters (red and blue edge)
toroidal rotational velocity of the plasma (puffed with Helium) can be obtained from the Doppler
shift in the fast images. Simultaneous measurement of the red-shift and blue-shift images along
with a broadband He II filter for image calibration is required for effective measurement of the
toroidal velocity from the same shot. This in turn can be done by splitting the light carried by the
imaging fiber bundle into three parts by partial mirrors and applying suitable filters for each part.
Finally, three separate images can be recorded simultaneously on the fast camera using a three to
one transition fiber bundle.
91

Experimental Studies of Edge Turbulence, Convective Transport

Transcription

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