D. Tskhakaya et al. 1 (13) PSI 18, Toledo 26 - 30 July 2008 Kinetic simulations of the parallel transport in the JET Scrape-off Layer D. Tskhakaya, R.

D. Tskhakaya et al. 1 (13) PSI 18, Toledo 26 - 30 July 2008

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

D. Tskhakaya et al. 2 (13) PSI 18, Toledo 26 - 30 July 2008

OUTLINE

Introduction

Description of the kinetic model

Discussion of simulations for JET

Extrapolations to ITER

conclusions

D. Tskhakaya et al. 3 (13) PSI 18, Toledo 26 - 30 July 2008

Introduction

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

What are the fluxes to the divertor?

How does plasma propagate along B?

Classical model can fail.

The reason:

low collisionality, inelastic and

short time scale processes

Resulting uncertainties might be critical for next generation tokamaks

Separatrix

SOL

Power loads to the JET divertor during the ELM 0 100 200 300 4000

50

100

150

200

250

300

MW

/m2

t [µs]

qdiv

Simulation

~50%

8 eT

e

D. Tskhakaya et al. 4 (13) PSI 18, Toledo 26 - 30 July 2008

Kinetic factors characterizing parallel transport in the stationary SOL

Introduction

5.3,2,

,52,1||

ie

e

TQ

TeM

Heat flux and viscosity limiters

1

||||

1

||

11,

11

nTTnVqq

BrTSH

Boundary conditions

at the divertor sheath

5.0,1.0

SOL

Can we really apply these models to the SOL?

D. Tskhakaya et al. 5 (13) PSI 18, Toledo 26 - 30 July 2008

1.5D kinetic model of the 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

Maxwellian particle source mimicking

cross field transport across separatrix

SOL

BIT1: 1.5D PIC/MC code

D. Tskhakaya et al. 6 (13) PSI 18, Toledo 26 - 30 July 2008

Stationary SOL: boundary conditions

Boundary conditions versus SOL collisionality

the model including el. radiation

Electron VDF at the divertor sheath

100

101

1021

2

3

4

5

6

i

e

the model including el. radiation and plasma recycling

Most boundary conditions

weekly depend on the SOL

parameters.

reduces by 40% with electron

radiation

-5 0 5

10-3

10-2

10-1

100

V||/V

T

Maxw.

Classic. Rad.

Rad./Rec.

fe(v

||)

D. Tskhakaya et al. 7 (13) PSI 18, Toledo 26 - 30 July 2008

Stationary SOL: flux and viscosity limiters

1

max||

11

qqq

SH

TnVqq TFS max

100

101

102

100

101

102

qSH

/q|| from PIC

qSH

=q||

Ion parallel heat flux versus SOL collisionality

s

Tqq SH

|||| Free streaming Maxwellian flux

f(v)

1.0

0 2 4 6 8

0

0.1

0.2

0.3

0.4

0.5

xpol

m

i

i

2 4 6 810

-2

10-1

100

101

xpol

m

e

e

D. Tskhakaya et al. 8 (13) PSI 18, Toledo 26 - 30 July 2008

Stationary SOL: flux and viscosity limiters

100

101

102

10-2

10-1

100

ae

ai

Heat flux and viscosity limiters versus SOL collisionality

Including el. radiation

Including el. Radiation and recycling

and 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!

,11

1

||

TnVqq

TSH

D. Tskhakaya et al. 9 (13) PSI 18, Toledo 26 - 30 July 2008

ELMy SOL

Previous model [Tskhakaya et al., EPS 07, CPP 08]

Main findings • Power to the divertors is curried mainly by ions

• 0.15 < WIR/WELM < 0.35

• We constructed fit functions describing BC and

power loads to the divertor during the ELMs at JET

qdiv(t), e,i(t) and (t)

SOL

0

ELM

t

SParticle source

No inelastic processes, stepwise ELM source

qdiv

tIR

WIR

D. Tskhakaya et al. 10 (13) PSI 18, Toledo 26 - 30 July 2008

ELMy SOL at JET

Model dependence of power loads to the divertor

Temporal shape of the ELM source

We need a reliable model for „reconnection“, or we can estimate it from measured power loads

power loads to the divertor

100

101

102

0

10

20

30

t [µs]

S(t) exp(-at)

stepwise

exp(-b(t-t0)2)

100

101

102

0

100

200

300

400

500

P [

MW

/m2]

t [µs]

stepwiseGauss.expon.

Power loads and boundary conditions strongly depend on the ELM model.

D. Tskhakaya et al. 11 (13) PSI 18, Toledo 26 - 30 July 2008

ELMy SOL at JET

Shot 62221 at JET WELM~ 0.4 MJ

Power flux to the outer divertor from IR

measurements (shot 62221, T. Eich) and from

PIC simulations (averaged over ~50 µs).

102

0

50

100

150

200

250

300

350

400

P [

MW

/m2]

t [µs]

JETstepwiseGauss.exp

102

0

100

200

300

P [

MW

/m2]

t [µs]

JETreferencerad.rad.+rec.

D. Tskhakaya et al. 12 (13) PSI 18, Toledo 26 - 30 July 2008

Extrapolations to ITER

0 100 200 3000

200

400

600

800

q div [

MW

/m2]

t [µs]

D+

T+

El.

,2/

exp1~

||

222

sELM

div

CL

ttttP

TTDD

peds MsMs

TC

2

Existing semi-analytic model well

describes power loads [Eich/Funamenski]

Power loads to the ITER outer divertor for 4 MJ ELM

0 100 200 3000

500

1000

1500

t [µs]

q div [

MW

/m2]

Analytic

PIC

D. Tskhakaya et al. 13 (13) PSI 18, Toledo 26 - 30 July 2008

CONCLUSIONS

Most of boundary conditions at the divertor weekly depend on (attached)

plasma parameters. The exception is , 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 < WIR/WELM < 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

Inter-ELM SOL

ELMy SOL

D. Tskhakaya et al. 14 (13) PSI 18, Toledo 26 - 30 July 2008

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t [µs]

q div [a

.u.]

taurec

50 µstau

rec 100 µs

taurec

150 µs

Energy loads to the divertors for

different (ELM energy is fixed)rec

D. Tskhakaya et al. 15 (13) PSI 18, Toledo 26 - 30 July 2008

10-2

10-1

100

101

102

103

10-1

100

101

102

E [eV]

PhelpsJanev

2/sin11ln4

1,2

aE

aE

aEd

Ed

Differential CS

implemented in BIT1

Choice of proper data

Implementation

Cross-sections for H2+ + H2 charge-

exchange collision from different sources.