Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability
Scaling of the H-mode pedestal in tokamak plasmas with type I ELMs and dependence of the pedestal properties and the resulting divertor head load width with the plasma elongation and plasma current are investigated using the kinetic neoclassical XGC0 code for DIII-D and Alcator C-Mod tokamaks. The s...
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| Zitieren: | Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability / A.Y. Pan’kin, G.Y. Park, J. Cummings, C.S. Chang, G. Bateman, D. Bunner, R.J. Groebner, J.W. Hughes, B. LaBombard, J.L. Terry, A.H. Kritz, S. Ku, T. Rafiq, P.B. Snyder // Вопросы атомной науки и техники. — 2011. — № 1. — С. 8-12. — Бібліогр.: 6 назв. — англ. |
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irk-123456789-905922016-01-04T15:46:01Z Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability Pan’kin, A.Y. Park, G.Y. Cummings, J. Chang, C.S. Bateman, G. Bunner, D. Groebner, R.J. Hughes, J.W. LaBombard, B. Terry, J.L. Kritz, A.H. Ku, S. Rafiq, T. Snyder, P.B. Магнитное удержание Scaling of the H-mode pedestal in tokamak plasmas with type I ELMs and dependence of the pedestal properties and the resulting divertor head load width with the plasma elongation and plasma current are investigated using the kinetic neoclassical XGC0 code for DIII-D and Alcator C-Mod tokamaks. The simulations in this study use realistic diverted geometry and are self-consistent with the inclusion of kinetic neoclassical physics, theory-based anomalous transport models with the E×B flow shearing effects, as well as an MHD ELM triggering criterion. Scalings for the pedestal width and height are developed as a function of the scanned plasma parameters. The nonlinear interplay between anomalous and neoclassical effects motivates the development of a self-consistent simulation model that includes neoclassical and anomalous effects simultaneously. It is demonstrated that the divertor heat load width depend on the plasma currents. In the development of this dependence, effects of neutral collisions and anomalous transport are taken into account. Changes in the neoclassical divertor heat load fluxes associated with the introduction of the neutral collision and anomalous transport effects are described. За допомогою кінетичного неокласичного коду XGC0 для розрядів в токамаках DIII-D і Alcator C-Mod досліджено скейлінг п’єдесталу в плазмі, що перебуває в режимі поліпшеного утримання, з прикордонними локалізованими модами (ПЛМ) першого типу, властивості п’єдесталу і потоку тепла на дивертор в залежності від витягнутості плазми та струму плазми. У розрахунках використовуються: реалістична геометрія дивертора, кінетична модель для неокласичних ефектів, модель аномального транспорту, яка враховує ефекти шира (ExB)-потоків, і умови збудження ПЛМ-нестійкостей. У результаті розрахунків отримані скейлінгі для ширини і висоти п’єдесталу як функції параметрів плазми. Нелінійна взаємодія неокласичних ефектів і ефектів, пов'язаних з аномальним транспортом, є мотивацією для розробки самоузгодженої чисельної моделі, яка одночасно включає ефекти аномального і неокласичного транспорту. Показано, що потоки тепла на дивертор залежать від плазмових струмів. Також представлено результати дослідження залежності напівширини профілів тепла на дивертор від ефектів, пов'язаних з аномальним транспортом і зіткненнями з нейтральними частинками. С помощью кинетического неоклассического кода XGC0 для разрядов в токамаках DIII-D и Alcator C-Mod исследованы скэйлинг пьедестала в плазме, находящейся в режиме улучшенного удержания, с приграничными локализованными модами (ПЛМ) первого типа, и зависимость свойств пьедестала и потока тепла на дивертор от вытянутости плазмы и тока плазмы. В расчетах используются: реалистичная геометрия дивертора, кинетическая модель для неоклассических эффектов, модель аномального транспорта, которая учитывает эффекты шира (ExB)-потоков, и условия возбуждения ПЛМ-неустойчивостей. В результате расчетов получены скэйлинги для ширины и высоты пьедестала как функции параметров плазмы. Нелинейное взаимодействие неоклассических эффектов и эффектов, связанных с аномальным транспортом, является мотивацией разработки самосогласованной численной модели, которая одновременно включает эффекты аномального и неоклассического транспорта. Показано, что потоки тепла на дивертор зависят от плазменных токов. Также представлены результаты исследования зависимости полуширины профилей тепла на дивертор от эффектов, связанных с аномальным транспортом и столкновениями с нейтральными частицами. 2011 Article Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability / A.Y. Pan’kin, G.Y. Park, J. Cummings, C.S. Chang, G. Bateman, D. Bunner, R.J. Groebner, J.W. Hughes, B. LaBombard, J.L. Terry, A.H. Kritz, S. Ku, T. Rafiq, P.B. Snyder // Вопросы атомной науки и техники. — 2011. — № 1. — С. 8-12. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.25.Xz, 52.35.Ra, 52.55.Fa, 52.65.Tt http://dspace.nbuv.gov.ua/handle/123456789/90592 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Магнитное удержание Магнитное удержание |
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Магнитное удержание Магнитное удержание Pan’kin, A.Y. Park, G.Y. Cummings, J. Chang, C.S. Bateman, G. Bunner, D. Groebner, R.J. Hughes, J.W. LaBombard, B. Terry, J.L. Kritz, A.H. Ku, S. Rafiq, T. Snyder, P.B. Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability Вопросы атомной науки и техники |
| description |
Scaling of the H-mode pedestal in tokamak plasmas with type I ELMs and dependence of the pedestal properties and the resulting divertor head load width with the plasma elongation and plasma current are investigated using the kinetic neoclassical XGC0 code for DIII-D and Alcator C-Mod tokamaks. The simulations in this study use realistic diverted geometry and are self-consistent with the inclusion of kinetic neoclassical physics, theory-based anomalous transport models with the E×B flow shearing effects, as well as an MHD ELM triggering criterion. Scalings for the pedestal width and height are developed as a function of the scanned plasma parameters. The nonlinear interplay between anomalous and neoclassical effects motivates the development of a self-consistent simulation model that includes neoclassical and anomalous effects simultaneously. It is demonstrated that the divertor heat load width depend on the plasma currents. In the development of this dependence, effects of neutral collisions and anomalous transport are taken into account. Changes in the neoclassical divertor heat load fluxes associated with the introduction of the neutral collision and anomalous transport effects are described. |
| format |
Article |
| author |
Pan’kin, A.Y. Park, G.Y. Cummings, J. Chang, C.S. Bateman, G. Bunner, D. Groebner, R.J. Hughes, J.W. LaBombard, B. Terry, J.L. Kritz, A.H. Ku, S. Rafiq, T. Snyder, P.B. |
| author_facet |
Pan’kin, A.Y. Park, G.Y. Cummings, J. Chang, C.S. Bateman, G. Bunner, D. Groebner, R.J. Hughes, J.W. LaBombard, B. Terry, J.L. Kritz, A.H. Ku, S. Rafiq, T. Snyder, P.B. |
| author_sort |
Pan’kin, A.Y. |
| title |
Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability |
| title_short |
Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability |
| title_full |
Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability |
| title_fullStr |
Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability |
| title_full_unstemmed |
Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability |
| title_sort |
kinetic modeling of h-mode pedestal with effects from anomalous transport and mhd stability |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2011 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/90592 |
| citation_txt |
Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability / A.Y. Pan’kin, G.Y. Park, J. Cummings, C.S. Chang, G. Bateman, D. Bunner, R.J. Groebner, J.W. Hughes, B. LaBombard, J.L. Terry, A.H. Kritz, S. Ku, T. Rafiq, P.B. Snyder // Вопросы атомной науки и техники. — 2011. — № 1. — С. 8-12. — Бібліогр.: 6 назв. — англ. |
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KINETIC MODELING OF H-MODE PEDESTAL WITH EFFECTS
FROM ANOMALOUS TRANSPORT AND MHD STABILITY
A.Y. Pan’kin1,2, G.Y. Park3, J. Cummings4, C.S. Chang4,5, G. Bateman1, D. Bunner6,
R.J. Groebner7, J.W. Hughes6, B. LaBombard6, J.L. Terry6,
A.H. Kritz1, S. Ku4, T. Rafiq1, P.B. Snyder7
1Lehigh University, Bethlehem, PA, USA;
2Institute for Nuclear Research, Kiev, Ukraine;
3New York University, New York, NY, USA;
4Caltech, Pasadena, CA, USA;
5Korea Advanced Institute of Science and Technology, Daejeon, Korea;
6MIT Plasma Science and Fusion Center, Cambridge, MA, USA;
7General Atomics, San Diego, CA, USA
E-mail: pankin@lehigh.edu
Scaling of the H-mode pedestal in tokamak plasmas with type I ELMs and dependence of the pedestal properties
and the resulting divertor head load width with the plasma elongation and plasma current are investigated using the
kinetic neoclassical XGC0 code for DIII-D and Alcator C-Mod tokamaks. The simulations in this study use realistic
diverted geometry and are self-consistent with the inclusion of kinetic neoclassical physics, theory-based anomalous
transport models with the E×B flow shearing effects, as well as an MHD ELM triggering criterion. Scalings for the
pedestal width and height are developed as a function of the scanned plasma parameters. The nonlinear interplay
between anomalous and neoclassical effects motivates the development of a self-consistent simulation model that
includes neoclassical and anomalous effects simultaneously. It is demonstrated that the divertor heat load width depend
on the plasma currents. In the development of this dependence, effects of neutral collisions and anomalous transport are
taken into account. Changes in the neoclassical divertor heat load fluxes associated with the introduction of the neutral
collision and anomalous transport effects are described.
PACS: 52.25.Xz, 52.35.Ra, 52.55.Fa, 52.65.Tt
1. INTRODUCTION
For the basic kinetic neoclassical behavior, the XGC0
kinetic guiding-center code [1] is used with a realistic
diverted geometry. For the anomalous transport, a radial
random-walk is superposed in the Lagrangian neoclassical
particle motion, using the FMCFM interface to the
theory-based MMM95 and GLF23 models. These
anomalous models include transport driven by drift-wave
instabilities, such as the electron and ion temperature
gradient driven modes and trapped electron modes. The
MMM95 model includes a resistive ballooning
component that is particularly important near the plasma
edge. The sheared E×B flows result in a reduction of
anomalous transport, which leads to the formation of an
edge transport barrier and the transition to the H-mode
improved confinement in tokamaks. The effect of E×B
flow shear quenching is implemented through a flow
shear suppression factor [2]: Fs=1/(1+(τc ωE×B) ), where τ
2. STUDY OF H-MODE PEDESTAL WIDTH
AND HEIGHT SCALING
The study of DIII-D discharges includes a scan with
respect to plasma shaping. Three DIII-D discharges are
analyzed in this section. The DIII-D discharge 136674 has
high elongation, κ≈1.7, which is typical for most DIII-D
discharges, but rather low triangularity δ≈0.1. The DIII-D
discharge 136693 has almost circular geometry with the
elongation κ≈1.2 and triangularity δ≈0.03. The third DIII-
D discharges studied in this section, DIII-D discharge
136705, has very small elongation, κ≈1.3, but relatively
high triangularity, δ≈0.3. Thus, the elongation is been
varied by a factor of 1.4 and the triangularity is being
varied by a factor of 10 in this study.
These simulations do not include the effects associated
with the anomalous transport. The anomalous transport
was selected at small residual level through the whole
edge region for all DIII-D discharges that are investigated
in this section. The electron and ion thermal diffusivity
have been selected to be 0.02 m2/s in the pedestal region
and 0.4 m2/s in the SOL region and the particle diffusivity
has been selected to be 0.01 m2/s in the pedestal region
and 0.05 m2/s in the SOL region. Motivation of the
selection of anomalous transport coefficients at a small
residual level is that the focus of this study is the
neoclassical and MHD effects on the H-mode pedestal
structure. However, a residual anomalous transport was
still necessary in these simulations. Without the
anomalous transport, the plasma density becomes too low
in the near outer separatrix region. The plasma density
B
2
c
is the correlation time of fluctuations for the case without
flow and ωE×BB is the normalized E×B flow shear rate:
ωE×B≡|R BB θ /Bϕ B ∂/∂r (Er /R Bθ )|. Growth of the pedestal by
neutral penetration and ionization is limited by an ELM
instability criterion computed by the ELITE MHD
stability code [3]. H-mode pedestal profiles for DIII-D
and Alcator C-Mod tokamaks are considered: DIII-D for
low B-field, low-density, high temperature plasmas; and
Alcator C-Mod for a high B-field, high-density plasmas.
8 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2011. № 1.
Series: Plasma Physics (17), p. 8-12.
mailto:pankin@lehigh.edu
depletion leads to unrealistic ion and electron temperature
profiles. These changes to the plasma profiles might occur
before the H-mode pedestal develops enough to trigger
the peeling or ballooning instabilities that would lead to
an ELM crash.
Fig. 1. Normalized plasma density profiles as a function of
normalized poloidal flux for DIII-D discharges with
different elongations and similar triangularities. Here, n100
and n95 are the plasma densities at the separatrix and at
95% of the normalized poloidal flux, respectively
Fig. 2. Normalized electron temperature profiles as a
function of normalized poloidal flux for DIII-D discharges
with different triangularities and similar elongations.
Here, Te
100 and Te
99 are the electron temperatures at the
separatrix and at 98.8% of the normalized poloidal flux,
respectively
The simulation results illustrate a scaling that is
qualitatively similar to some experimental observations.
Fig. 1 shows the normalized plasma density profiles as a
function of the normalized poloidal flux for high and low
elongation DIII-D discharges. Fig. 2 shows the
normalized electron temperature profiles for low and high
trinagularity DIII-D discharges. In XGC-0 kinetic
simulations, it has been found that the pedestal width is
smaller for high elongation and high triangularity
discharges. In the discharges considered in this study, the
effect of increased elongation manifests itself in the
plasma density profiles first, while the effect of increased
triangularity manifests itself in the electron temperature
profiles first. It has also been found that the pedestal
width for the ion temperature profile is much wider than
the pedestal width for the electron temperature and
plasma density profiles. The pedestal height is found to be
significantly larger in the discharges with larger
elongation.
9
While the neoclassical effect together with the MHD
stability conditions can explain some experimental trends,
the question about the contributions of the anomalous
transport in the pedestal and SOL regions remains. This
question will be partially addressed in the next section.
3. STUDY OF THE EFFECTS ASSOCIATED
WITH THE ANOMALOUS TRANSPORT
The anomalous transport in the plasma edge region has
been previously analyzed in a number of studies. In
particular, it has been pointed out that particle pinches
might play an important role in the pedestal region [4,5].
Experimental observations and some analytical models
suggest that anomalous transport in SOL can be
significantly larger than in the pedestal region and
intermittent. Studies of the anomalous transport in the
plasma edge region are typically based on the analysis of
experimental data that should include a robust model for
the neoclassical transport. Particle and thermal fluxes
obtained from analysis of experimental data include
contributions from both the anomalous and neoclassical
transport so that the neoclassical transport needs to be
deducted to get the correct anomalous fluxes and effective
diffusivities. Effects associated with neutral collisions and
recycling are other factors that can affect the total particle
fluxes and should be carefully taken into consideration.
The kinetic XGC0 code is designed for the first-principle
neoclassical computations and includes several advanced
models for neutral collisions including the DEGAS2
model. Also, the XGC0 code takes into consideration the
recycling and other particle effects that contribute to the
total particle fluxes. Thus, the XGC0 code can be used for
the analysis of experimental fluxes in order to derive the
effective diffusivities. These anomalous effective
diffusivities can be also used for comparisons with the
analytical models for anomalous transport. In particular, it
is important to understand the origin of particle and
thermal pinches in the pedestal region. While the origin of
particle and thermal pinches is not studied in this work, it
is worth mentioning that there are several physical effects
that can be associated with the pinches in the pedestal
area such as curvature effects and parallel compression.
The purpose of the study described in this section is to
derive the anomalous effective diffusivities that can
reproduce the experimental profiles when they are used in
the neoclassical kinetic XGC0 code. These profiles will
be used in the next section of this paper for the
computation of the divertor heat load fluxes. There are
three regions of constant diffusivites that are separated by
two narrow transitional regions that use tanh-fit. The
levels of anomalous transport in all three regions,
locations of transitional regions and their widths are
adjustable parameters. The diffusivity profiles are
adjusted to find a steady state solution that reproduces the
experimental profiles. A series of four DIII-D discharges
that represent plasma current scan [6] is analyzed in this
study. In this series of DIII-D discharges, the total plasma
current is varied from 0.51 to 1.50 MA with an
approximately fixed toroidal magnetic field (BBT≈2.1 T),
plasma shape (δ≈0.55), and normalized toroidal beta
(βn≈2.1…2.4). The discharges differ by total plasma
current, and auxiliary heating power that are given in the
Table below. The plasma density is also different in these
discharges. The plasma density at the top of the pedestal
varies in the ranges from approximately
for the high plasma density DIII-D discharge 132016 to
for the low plasma density DIII-D
discharge 132018.
DIII-D discharges analyzed in this study and their
parameters
Discharge # EFIT time,
ms
Plasma
current, MA
Auxiliary
heating power,
MW
132016 3023 1.50 8.12
132014 3023 1.17 7.36
132017 2998 0.85 8.50
132018 1948 0.51 7.10
10
The anomalous diffusivity profiles are selected so that the
resulting profiles remains close to the experimental
profiles at least up to eight ion transit periods (see Fig. 3).
Fig. 3. Simulation results of the plasma density profile
in the DIII-D discharge 132016 for the first eight ion
transit periods. The experimental plasma density
profile is shown in red
There is a clear evidence of strong pinches in the particle
and thermal channels of anomalous transport. While the
mechanisms that result in these pinches are not the subject
of this study, we have analyzed the anomalous transport
in the DIII-D discharges, which are described in the
Table, with the drift wave anomalous transport model
MMM95 that is implemented in the XGC0 code.
Fig. 4. Ion thermal diffusivity profiles predicted with drift-
wave transport model MMM95 for the DIII-D discharge
132016 at five ion transit periods. Contributions to the
anomalous thermal transport from ITG and RB modes are
shown in red and in blue correspondingly. The smoothed
total ion thermal diffusivity that is used in the XGC0
simulations is shown in black
It has been found that the largest contribution to the
anomalous transport in the outer pedestal region comes
from the turbulence driven by the resistive-ballooning
instabilities (see Fig. 4). The resistive-ballooning model
gives somewhat larger contribution for the lower plasma
current and lower plasma density discharges 132017 and
132018 comparing to the contributions to the anomalous
transport for the higher plasma current and higher density
discharges 132014 and 132016.
Fig. 5. The heat load widths for four DIII-D discharges
(first panel) and one Alcator C-Mod discharge (second
panel) as functions of plasma current scaling factor
There are no physical effects in the resistive-ballooning
model that can explain the particle and thermal pinches
that are found to be important in the analyzed discharges.
As result, the effective diffusivities computed with the
MMM95 model are found to be overpredicted and the
corresponding plasma profiles are found to be under-
predicted compared to the experimental profiles and
profiles computed with the diffusivities derived in the
analysis mode. The computations of the divertor heat
fluxes that are presented in the next section of this report
use the diffusivities obtained in the analysis mode. It
should be pointed out that the theory-based reduced
model for the resistive-ballooning modes might need a
significant revision that would extend its validity to the
SOL and near separatrix regions.
4. DIVERTOR HEAT LOAD STUDIES
FOR THE DIII-D AND ALCATOR C-MOD
TOKAMAKS
Understanding physical effects that contribute to
divertor heat load fluxes is important for experiment
planning, design of future tokamaks, and development of
new models for the SOL region. In this study, the
neoclassical effects and effects related to neutral
collisions and anomalous transport are investigated. Four
DIII-D discharges described in the Table above are
analyzed here. In addition, one Alcator C-Mod discharge
1100212024 that was a part of Alcator C-Mod/DIII-D
similarity campaign is analyzed. The divertor heat load
widths, , for four DIII-D
discharges and one Alcator C-Mod discharge as functions
of the poloidal magnetic field amplification factor CBp are
shown on Fig. 5. This scaling factor is an internal
numerical multiplier introduced in the XGC0 code in
order to alter the initial equilibrium by scaling the
poloidal flux. If the toroidal flux is not modified,
, where ψ is the normalized poloidal
flux. Thus, the amplification factor CBp can be also
considered as a scaling factor for the total plasma current
Ipl. It has been found that the neoclassical heat load width
for all four DIII-D discharges follows approximately the
1/Ip dependence. There is neither anomalous transport nor
neutral effects included in these simulations. The
difference in the slopes of divertor heat load widths for
different DIII-D discharges might be attributed to
different collisionality in these discharges. The difference
in slopes is especially noticeable if two set of discharges
with lower (DIII-D discharges 132017 and 132018) and
higher plasma densities (DIII-D discharges 132014 and
132016) are compared. This computational result on the
effect of collisionality on divertor heat fluxes still needs
to be confirmed in further computational and analytical
analysis. Meantime, there is no doubt that the neoclassical
divertor heat load width is decreasing with increasing
plasma current for all DIII-D discharges studied in this
research. Simulation results that are shown on Fig. 6
demonstrate the effects of neutral collisions and
anomalous transport. The dependence of the divertor heat
load width is weakly affected by neutral collisions, but it
can be completely modified when the anomalous
transport is introduced and is applied uniformly for all
poloidal angles. Changes to the divertor heat load width
scaling related to the ballooning nature of resistive-
ballooning modes, that are likely to be major players in
the region near the separatrix, are shown as purple curve
on Fig. 6. In these simulations, the anomalous transport is
applied in the region within 45○ from the midplane. The
neoclassical dependence of the divertor heat load width
on the total plasma current is preserved for the high-
density DIII-D discharge 132016 and is almost vanished
for the low-density DIII-D discharge 132018 (not shown
on Fig. 6). The dependence of divertor heat load width on
the current density was weakest for the DIII-D discharge
132018 among discharges studied in this research (see
Fig. 5). The introduction of anomalous transport effects
typically widens the divertor heat load width. This
observation becomes evident, when red and purple plots
on Fig. 6 are compared.
5. CONCLUSIONS
The dependence of H-mode pedestal width and height
on plasma shaping is investigated in coupled XGC0-
ELITE simulations. The initial plasma profiles from
equilibria reconstructed from three DIII-D experiments, where
the elongation and triangularity have been significantly varied,
are evolved in the kinetic neoclassical XGC0 code.
Fig. 6. Effects of neutral collisions and anomalous
transport on the divertor heat load width scaling in the
XGC0 simulations of the DIII-D discharge 132016. The
red curve shows the neoclassical scaling that does not
include the effects of neutral collision and anomalous
transport. The green curve shows the effect of neutral
collisions. The anomalous transport that is applied
uniformly for all poloidal angles in used in the
simulations resulted in the blue curve. The purple curve
shows the divertor heat load width scaling when the
anomalous transport is applied within 45○ from the
midplane
11
As plasma profiles evolve, the ideal MHD stability
ELITE code is used to check if peeling-ballooning
stability conditions are violated. These conditions set
maximum H-mode pedestal height. In this research, it has
been found that the neoclassical effects and MHD
stability conditions alone can explain some
experimentally observed trends. In particular, it has been
found that the pedestal height is the largest in the DIII-D
discharges with the largest elongation. The effect of
triangularity is found to be somewhat weaker comparing
to the effect of elongation. As result, it might be more
difficult to reach specific pedestal height and width by
altering the triangularity and keeping the elongation fixed.
It has been also found that the H-mode pedestal width for
electron temperature and plasma density is affected
differently by elongation and triangularity. The effect of
elongation reveals itself on the plasma density profiles
first, while the effect of triangularity reveals itself on the
electron temperature profiles first. Pedestal width for the
plasma density profiles decreases with the elongation and
is almost independent of triangularity, while the pedestal
width for the electron temperature profiles decreases with
the triangularity and is almost independent of elongation.
It should be pointed out that these conclusions might
change if the anomalous transport is included in this
analysis. The theory-based MMM95 model has been
tested for several DIII-D discharges that represent plasma
current scan. The anomalous transport driven by the
resistive ballooning modes is found to be one of the major
contributors to the total anomalous transport in the near
separatrix region. However, it is also found that the
resistive-ballooning component of MMM95 produces too
much transport if compared with effective diffusivites
computed in the analysis mode using the XGC0 code. In
addition, there are strong indications of particle and
thermal pinches in the pedestal regions of Alcator C-Mod
and DIII-D discharges, while the resistive-ballooning
model does not predict particle and thermal pinches in
12
these plasma regions. There is an urgent need for an
improved resistive-ballooning model that can be applied
for predictive modeling in the H-mode pedestal and SOL
regions.
The neoclassical scaling of divertor heat load width
with the plasma current in DIII-D and Alcator C-Mod
discharges is studied in this report. It has been found that
the divertor heat load width is broader for lower plasma
currents for all discharges simulated in this work. The
effect of neutral collisions does not significantly modify
this dependence, while the inclusion of anomalous
transport is typically widen the divertor heat load width
and enhances the heat load fluxes on the divertor.
ACKNOWLEDGEMENTS
This work supported by the U.S. Department of Energy
under grants DE-SC0000692, DE-FC02-08ER54985, DE-
FG02-06ER54845, DE-FG02-92ER54141, DE-FG03-
98ER54461, DE-FG02-94ER54084, DE-FC02-04ER54698,
DE-FC02-99ER54512.
REFERENCES
1. C.S. Chang, et al. Numerical study of neoclassical
plasma pedestal in a tokamak geometry // Phys.
Plasmas. 2004, v. 11, p. 2649.
2. T.S. Hahm, and K.H. Burrell. Flow shear induced
fluctuation suppression in finite aspect ratio shaped
tokamak plasma // Phys. Plasmas. 1995, v. 2,
p. 1648.
3. P.B. Snyder, et al. Edge localized modes and the
pedestal: A model based on coupled peeling–
ballooning modes // Phys. Plasmas. 2002, v. 9, p.
2037.
4. M.E. Rensink, et al. Particle transport studies for
single-null divertor discharges in DIII-D // Phys.
Fluids B. 1993, v. 5, p. 2165.
5. W.M. Stacey. The effects of rotation, electric field,
and recycling neutrals on determining the edge
pedestal density profile // Phys. Plasmas. 2010, v. 17,
p. 052506.
6. R. Groebner, et al. Progress towards a predictive
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Article received 29.09.10
КИНЕТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПЬЕДЕСТАЛА В РЕЖИМЕ УЛУЧШЕННОГО УДЕРЖАНИЯ
ПЛАЗМЫ С ЭФФЕКТАМИ АНОМАЛЬНОГО ТРАНСПОРТА И МГД-УСТОЙЧИВОСТИ
А.Ю. Панькин, G.Y. Park, J. Cummings, C.S. Chang, G. Bateman, D. Bunner, R.J. Groebner, J.W. Hughes,
B. LaBombard, J.L. Terry, A.H. Kritz, S. Ku, T. Rafiq, P.B. Snyder
С помощью кинетического неоклассического кода XGC0 для разрядов в токамаках DIII-D и Alcator C-Mod
исследованы скэйлинг пьедестала в плазме, находящейся в режиме улучшенного удержания, с приграничными
локализованными модами (ПЛМ) первого типа, и зависимость свойств пьедестала и потока тепла на дивертор
от вытянутости плазмы и тока плазмы. В расчетах используются: реалистичная геометрия дивертора,
кинетическая модель для неоклассических эффектов, модель аномального транспорта, которая учитывает
эффекты шира (ExB)-потоков, и условия возбуждения ПЛМ-неустойчивостей. В результате расчетов получены
скэйлинги для ширины и высоты пьедестала как функции параметров плазмы. Нелинейное взаимодействие
неоклассических эффектов и эффектов, связанных с аномальным транспортом, является мотивацией разработки
самосогласованной численной модели, которая одновременно включает эффекты аномального и
неоклассического транспорта. Показано, что потоки тепла на дивертор зависят от плазменных токов. Также
представлены результаты исследования зависимости полуширины профилей тепла на дивертор от эффектов,
связанных с аномальным транспортом и столкновениями с нейтральными частицами.
КІНЕТИЧНЕ МОДЕЛЮВАННЯ П’ЄДЕСТАЛУ В РЕЖИМІ ПОЛІПШЕНОГО УТРИМАННЯ ПЛАЗМИ
З ЕФЕКТАМИ АНОМАЛЬНОГО ТРАНСПОРТУ І МГД- СТІЙКОСТІ
О.Ю. Панькін, G.Y. Park, J. Cummings, C.S. Chang, G. Bateman, D. Bunner, R.J. Groebner, J.W. Hughes,
B. LaBombard, J.L. Terry, A.H. Kritz, S. Ku, T. Rafiq, P.B. Snyder
За допомогою кінетичного неокласичного коду XGC0 для розрядів в токамаках DIII-D і Alcator C-Mod
досліджено скейлінг п’єдесталу в плазмі, що перебуває в режимі поліпшеного утримання, з прикордонними
локалізованими модами (ПЛМ) першого типу, властивості п’єдесталу і потоку тепла на дивертор в залежності
від витягнутості плазми та струму плазми. У розрахунках використовуються: реалістична геометрія дивертора,
кінетична модель для неокласичних ефектів, модель аномального транспорту, яка враховує ефекти шира (ExB)-
потоків, і умови збудження ПЛМ-нестійкостей. У результаті розрахунків отримані скейлінгі для ширини і
висоти п’єдесталу як функції параметрів плазми. Нелінійна взаємодія неокласичних ефектів і ефектів,
пов'язаних з аномальним транспортом, є мотивацією для розробки самоузгодженої чисельної моделі, яка
одночасно включає ефекти аномального і неокласичного транспорту. Показано, що потоки тепла на дивертор
залежать від плазмових струмів. Також представлено результати дослідження залежності напівширини профілів
тепла на дивертор від ефектів, пов'язаних з аномальним транспортом і зіткненнями з нейтральними частинками.
1. INTRODUCTION
2. STUDY OF H-MODE PEDESTAL WIDTH AND HEIGHT SCALING
3. STUDY OF THE EFFECTS ASSOCIATED WITH THE ANOMALOUS TRANSPORT
4. DIVERTOR HEAT LOAD STUDIES FOR THE DIII-D AND ALCATOR C-MOD TOKAMAKS
5. CONCLUSIONS
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