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Project P1
Kinetic theory and simulation of plasma and
impurity transport in the SOL
S. Kuhn
24th Association Day, Association
EURATOM-ÖAW Vienna, 5 June 2009
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Group members
Profs. (2) S. Kuhn (head) D.D. Tskhakaya
(sr.) Drs. (4) U. Holzmüller-Steinacker N.
Jelic N. Schupfer D. Tskhakaya (jr.) PhD
Students (3/6) F. Bint-e-Munir (finished Jan.
2009) A. Din M. Kamran D. Kupelwieser A.
Schneider (just finishing) J. Seebacher (just
finishing now in P8)
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Collaborations
NIFS, Toki
Czech Republic IPP, Prague Finland
TEKES, Helsinki France CNRS,
Paris Germany IPP, UNI, Greifswald
IPP, Garching, FZ, Jülich Italy DEP, Torino,
Romania UNI, Iasi Slovenia LECAD,
Ljubljana Switzerland CRPP, Lausanne UK JET,
Culham Austria Other groups Task forces (TF)
and large EU projects TF-ITM, TF-E, TTG,
EUFORIA
U.C. Berkeley
ITER, Cadarache
New 2008/2009 EU Projects Deisa, HPC-FF
Spain BSC, Barcelona UK
HECTOR, Edinburgh Finland UNI, Turku
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Topics (P1)

• Studies of the plasma-wall transition (PWT)
  layer
• 1.5D plasma, 2D neutral/impurity transport in
  the SOL
• Code development
• Anomalous impurity diffusion
• Probe theory
• Coordinate singularities near separatrices and
  X-points

Publications (06.2008 - 05.2009)
4 Invited talks at large institutes and
Universities 6 Refereed papers 5 Conference
contributions
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Studies of the plasma-wall transition layer (PWT)

• Applied studies
• We have completed development of the boundary
  condition module for ITM TF task ITM-08-IMP3-T13
  D. Tskhakaya, 2008.
• The module incorporates boundary conditions for
  particle, momentum and energy fluxes at the
  divertors in the stationary and ELMy SOLs.

• Fundamental studies
• Main goal Conceptually correct and consistent
  theoretical description of the plasma-wall
  transition
• Will ultimately result in more consistent PWT
  theories and codes,
• requiring substantially fewer free parameters
  than is the case at present
• Most obvious application for fusion plasmas
  improved boundary conditions for fluid codes
  simulating the SOL (see above!)

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Studies of the plasma-wall transition layer (PWT)

• Schneider,
• Comprehensive and detailed studies of the
  intermediate regio between the sheath and the
  presheath
• (PhD thesis, June 2009)

The Intermediate scale was re-derived following
K. U.- Riemannbut more precisely.
Comprehensive investigations of the sheath edge
singularitiesof the electric potential, the
electron density and the ion velocityhave been
performed.
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Studies of the plasma-wall transition layer (PWT)
Correct fluid treatment of the collisionless
Tonks-Langmuir model with a cold ion source
(M. Kamran and S. Kuhn)

• In 1, a fluid treatment of a collisionless
  Tonks-Langmuir model with a cold ion source was
  given, with the ion temperature assumed to be
  zero.

• In reality, however, the ions have a finite
  effective temperature even if the source is cold.

• Normalized basic equations

1 K. U. Riemann, J. Seebacher, D. D. Tskhakaya
(Sr.) and S. Kuhn, Plasma Phys. Control. Fusion
47, 1949 (2005).
2 K. U. Riemann, Phys. Plasmas, 13, 063508
(2006).
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Studies of the plasma-wall transition layer (PWT)
Conclusions
We conclude that proper choice of the ion
polytropic coefficient is extremely important for
a fluid model to be realistic.
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Studies of the plasma-wall transition layer (PWT)
N. Jelic, L. Kos, J. Krek, J. Duhovnik and S.
Kuhn PIC simulations of a collisionless
Tonks-Langmuir model discharge with a warm ion
source
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Modelling of Edge-Localised Modes
Type I ELM-ing H-mode is baseline ITER scenario
JET 62218

• t 19.05 s,
• before-ELM

Edge Localized Modes (ELMs) are periodic bursts
of particles and energy into the SOL
ELMs curry 10 of the pedestal energy and at
least 60 of it is deposited to the divertor
plates eroding the plate surface
Damage caused by ELMs (Loarte TF-S1, 2006)
R.A. Pitts, EPS 2005
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Modelling of Edge-Localised Modes
Due to low collisionality, inelastic and short
time-scale processes in the ELMy SOL, it is
necessary to use kinetic modeling
Agreement of BIT1 results with experiment in
existing Tokamaks (JET, TCV) D. Tskhakaya,
13th EU-US TTFW 2008
WIR
Definition of
qdiv
tIR
WIR defines the damage caused by ELMs
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Predictions for ITER
Pdiv
Power and particle fluxes to the divertors during
the 4 MJ ELM D. Tskhakaya, TTFW 2008
Important result impurity radiation during
theITER ELM is negligible!
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Code development
Requirements for full size self-consistent 1.5D
kinetic simulations of the SOL. 4 scale lengths
in the SOL
Number of cells gt 10 000
CPU hours for serial code gt1000
It is necessary to develope a parallel code
suitable for simulations on HPC
Participation in largest HPC projects in the EU
ITM EUFORIA, DEISA, HPC-FF
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Code development
Speed up of simulations vs. number of processors
for new parallel BIT1 code
Parallel BIT1 is suitable for simulations up to
gt1000 processors
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Code development
Parallel BIT1 is Implemented in largest HPC
facilities in the EU MareNostrum (Barc.), HECToR
(Einb.), IBM power6 (Gar.)
Poloidal profiles of the plasma temperature in
the JET SOL. Simulations are perfored with 512
processors on MN HPC in Barcelona. Number of
simulated cells (in 1D) 12 000.
First (worldwide!) full kinetic simulations of
the SOL on HPC
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Anomalous impurity diffusion
A new mechanism for radial electric-field
generation in the tokamak edge plasma

• Assumptions (based on numerical modelling Krlin
  PPCF 1999 )
• the impurity (e.g. C) suffer anomalous
  diffusion in fluctuative
• plasma potential.
• is the ion Debye length, V is ion
  velocity

Then, for the resulting radial electric field we
find
S. Kuhn 24st Association
day, Wien, 5 June 2009
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I-V characteristic of a spherical emissive probe
A Din and S. Kuhn

• Species considered in the PPT region
• ? Electrons and ions entering the collisionless
  plasma-probe transition (PPT) region at the
  presheath-entrance sphere (PSES) 1.
• ? New Half Maxwellian electrons emitted from
  the probe surface.

• Collisionless trajectories within the PPT
  region
• (1) Trajectories entering at the PSES.
• (2) Trajectories entering at the probe surface.
• (3) Trajectories confined within the PPT region.

• Solution scheme
• ? The ion velocity distribution function (VDF)
  in the PPT region has been calculated via
  trajectory integration of the Vlasov equation.
• ? Solution of Poisson's equation for this
  two-species system within the PPT region
  with suitable boundary conditions is under way.
• ? Next step Inclusion of electrons emitted from
  the probe.
• 1. Ira B. Bernstein and Irving Rabinowitz,
  Physics of Fluids, 2(2), 112 (1959).

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Coordinate singularities near separatrices and
X-points
D. Kupelwieser, S. Kuhn and K. Lackner (PhD
project)

• Many codes for the numerical simulation of a
  fusion plasma (MHD or kinetic) depend on
  magnetic coordinates (Hamada or Boozer), in which
  the magnetic field lines appear straightened,
  in order to decrease computing time.
• In a diverted toroidal plasma, magnetic
  coordinates become singular at the X-point of
  the separatrix, where the poloidal component of
  the magnetic field vanishes, thus thwarting
  numerical calculations close to this point.
• To date, attempts at resolving this issue have
  not been fully satisfactory
• Cutting off the plasma close to the separatrix
  (CASTOR, diverging results depending on the
  cut-off location)
• Use of hybrid finite elements (KINX, higher
  number of dimensions)
• Envisaged ways of improvement
• Detailed description of the particles' motion
  close to the X-point, evaluation of the
  applicability of gyro-averaging
• Analytical construction of a coordinate system
  which is naturally and optimally adapted to
  magnetic field and particle motion
• Improvement of existing numerical schemes (such
  as CASTOR) to better include the separatrix
  and application also to resistive MHD.

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Conclusions

• We have completed development of boundary
  condition module for the ITM TF
• On PWT, several applied and fundamental
  developments
• We have developed a model predicting particle and
  energy loads to the ITER divertors.
• We have developed a highly scalable parallel
  version of the BIT1 code. First (worldwide!)
  kinetic ELM simulations on the HPC are
  successful.
• We have found the radial electric field caused by
  impurity ion diffusion.
• A new generation of fundamental plasma physics
  problems has been tackled and is under way.

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Future plans

• Implement kinetic factors obtained by us in large
  fluid codes (JET work programme 2009)
• Develop a new method of adaptive processor load,
  for optimization of HPC kinetic simulations of
  strongly nonuniform plasmas (e.g. SOL)
• Continue parallel PIC SOL simulations on the
  largest HPCs.
• To develop a full 2D kinetic model of the SOL
  including impurity transport (for 2010-2011).
• Other plans