Kinetic simulations of the parallel transport in the

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Kinetic simulations of the parallel transport in
the JET Scrape-off Layer
D. Tskhakaya, R. A. Pitts, W. Fundamenski,
T.Eich, S.kuhn and JET EFDA Contributors
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OUTLINE

• Introduction
• Description of the kinetic model
• Discussion of simulations for JET
• Extrapolations to ITER
• conclusions

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Introduction
What is the aim of parallel transport study in
the SOL?
Separatrix

SOL
How does plasma propagate along B?
What are the fluxes to the divertor?
Classical model can fail. The reason low
collisionality, inelastic and short time scale
processes
Resulting uncertainties might be critical for
next generation tokamaks
Power loads to the JET divertor during the ELM
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Introduction
Kinetic factors characterizing parallel transport
in the stationary SOL
Boundary conditions at the divertor sheath
Heat flux and viscosity limiters
SOL
Can we really apply these models to the SOL?
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1.5D kinetic model of the SOL
BIT1 1.5D PIC/MC code
Maxwellian particle source mimicking cross field
transport across separatrix

SOL

• Full resolution of particle motion, 1d3V
  plasma particles, 2d3V neutrals
• Electric field is calculated
  self-consistently, magnetic field is fixed
• Nonlinear collision model for arbitrary
  number of plasma and neutral particle
  species
• Plasma recycling (nonlinear model). New
• Electron radiation (linear model with fixed
  impurity profiles). New
• Arbitrary diagnostics

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Stationary SOL boundary conditions
Most boundary conditions weekly depend on the SOL
parameters. j reduces by 40 with electron
radiation
the model including el. radiation and
plasma recycling
Boundary conditions versus SOL collisionality
Electron VDF at the divertor sheath
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Stationary SOL flux and viscosity limiters
Free streaming Maxwellian flux
Ion parallel heat flux versus SOL collisionality
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Stationary SOL flux and viscosity limiters
a and b are strongly nonuniform, have wrong
dependence on SOL collisionality and are too
sensitive to inelastic processes! The solution
for relatively high collisional SOL no limiting
at all!
Heat flux and viscosity limiters versus SOL
collisionality
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ELMy SOL
Previous model Tskhakaya et al., EPS 07, CPP 08
No inelastic processes, stepwise ELM source
S
Particle source
t
0

• Main findings
• Power to the divertors is curried mainly by
  ions
• 0.15 lt WIR/WELM lt 0.35
• We constructed fit functions describing BC
  and power loads to the divertor during the ELMs
  at JET
• qdiv(t), ge,i(t) and j(t)

WIR
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ELMy SOL at JET
Model dependence of power loads to the divertor
Temporal shape of the ELM source
Power loads and boundary conditions strongly
depend on the ELM model.
power loads to the divertor
We need a reliable model for reconnection, or
we can estimate it from measured power loads
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ELMy SOL at JET
Power flux to the outer divertor from IR
measurements (shot 62221, T. Eich) and from PIC
simulations (averaged over 50 µs).
Shot 62221 at JET WELM 0.4 MJ
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Extrapolations to ITER
Power loads to the ITER outer divertor for 4 MJ
ELM
Existing semi-analytic model well describes power
loads Eich/Funamenski
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CONCLUSIONS
Inter-ELM SOL

• Most of boundary conditions at the divertor
  weekly depend on (attached) plasma parameters.
  The exception is j, reducing by 40 with
  electron radiation.
• Heat flux and ion viscosity limiters are strongly
  nonuniform along the field lines and too
  sensitive to plasma conditions in the SOL
• All kinetic factors strongly depend on the choice
  of ELM model. Best agreement with the experiment
  at JET gives the complete PIC model with stepwise
  ELM reconnection
• Two parameters are model-independent ions curry
  main part of power to the divertors and 0.15 lt
  WIR/WELM lt 0.35
• No surprises from (simplified) ITER simulations
• power loads to the divertor correspond to the
  energy propagation with Cs
• and can be described by existing analytic
  functions
• main power to the divertors is curried by ions,
  WIR 0.35

ELMy SOL
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Energy loads to the divertors for different
(ELM energy is fixed)
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Choice of proper data
Cross-sections for H2 H2 charge-exchange
collision from different sources.
Implementation
Differential CS implemented in BIT1