1 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Comparison of 2D...

A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008 1 of 22

Comparison of 2D Models for the Plasma Edge with Experimental Measurements and Assessment of

Deficiencies

A.V.Chankin and D.P.Coster

Max-Planck-Institut für Plasmaphysik

Acknowledgements: L.K.Aho-Mantila, N.Asakura, X.Bonnin, G.D.Conway, G.Corrigan, R.Dux, S.K.Erents, A.Herrmann, Ch.Fuchs, W.Fundamenski, G.Haas, J.Horacek, L.D.Horton, A.Kallenbach, M.Kaufmann, Ch.Konz, V.Kotov, A.S.Kukushkin, T.Kurki-Suonio, B.Kurzan, K.Lackner, C.Maggi, H.W.Müller, J.Neuhauser, R.A.Pitts, R.Pugno, M.Reich, D.Reiter, V.Rohde, W.Schneider, S.K.Sipilä, P.C.Stangeby, M.Wischmeier, E.Wolfrum


Outline

Introduction: 2D edge fluid codes

Measurements and simulations of: - parallel ion flow in SOL - divertor and target parameters - Er in SOL

Possible causes of discrepancies between modelling and experiment

Summary


Computational grid and vessel structures

- Plasma description: collisional parallel transport model, with kinetic limiters for transp. coeff.; anomalous perp. coefficients, drifts included- Neutrals description: kinetic Monte-Carlo codes, inside and outside of computational grid

Main 2D edge fluid codes for SOL and divertor modelling

SOLPS: B2-Eirene (AUG), EDGE2D-Nimbus,Eirene (JET), UEDGE-DEGAS (DIII-D)

Physical and chemical sputtering from surfaces

Multiple impurity charged states

separatrix

inputpower

Consensus (prior to 2000): 2D edge fluid codes reproduce existing experiments within a factor of 2


JG04

.61-

30c

reciprocatingprobe

reciprocatingprobe

Parallel ion SOL flow in JET – comparison with EDGE2D[S.K.Erents et al., PPCF 2000 & 2004]

Normal Bt

Reversed Bt

Average

Distance from Separatrix (Mid-plane mm)

56723 Normal Field q95 = 2.9359737 Reverse Field q95 =3.0056723 Normal Field q95 = 2.75

56737 Reverse Field q95 = 2.8459723 Normal Field q95 =2.5456737 Reverse Field q95 = 2.67Average

ballooning

Parallel flow: ballooning + drift

Bt-independent(Average flow)

Bt-dependent


Normal Bt

Reversed Bt

Average

Distance from Separatrix (Mid-plane mm)

56723 Normal Field q95 = 2.9359737 Reverse Field q95 =3.0056723 Normal Field q95 = 2.75

56737 Reverse Field q95 = 2.8459723 Normal Field q95 =2.5456737 Reverse Field q95 = 2.67Average

0

0.1

0.05

-0.1

-0.2

-0.05

-0.15

-0.25

EDGE2D: Mach No.

Normal Bt

Reversed Bt

Mach number

Ohmic case,ns=5.3e18 m-3

0 0.01 0.02 0.03 0.04

Distance from separatrix [m]0 0.01 0.02 0.03 0.04

Distance from separatrix [m]

0

0.1

0.05

-0.1

-0.2

-0.05

-0.15

-0.25

EDGE2D: Mach No.

Normal Bt

Reversed Bt

Ohmic case,ns=7.3e18 m-3

JG04

.61-

30c

reciprocatingprobe

recipr.probe

Parallel ion SOL flow in JET – comparison with EDGE2D

EDGE2D underestimates effect of Bt reversal by factor ~ 3

UEDGE underestimates effect of Bt reversal in JT-60U by factor 2 [N.Asakura et al., 2004]


JT-60U: measured ion flow at outer midplane agrees with Pfirsch-Schlüter ion flow formula:

Parallel flows in JT- 60U and TCV: effect of Bt reversal

[N.Asakura, et al., PRL 2000]

Measured flows are consistent with P-S formula, when pi, Er … are taken from experiment

Same conclusion for TCV [R.A.Pitts et al., EPS-2007]

r

iPS|| enE

drdp

enBq2

sinθV


Parallel flow in SOLPS: simulating AUG Ohmic shots

Parallel flowat outer midpl.

0

0.05

0.15

0.25

0.2

0.1

Mach number of parallel ion flow

SOLPS - direct

Pfirsch-Schluter..

1.3 0.8 0.5

Separatrix density (10 m )19 -3

SOLPS -

M||

But: simulated flows are below measured in AUG by factor 3 (as in JET)

Simulated flows are consistent with P-S formula (pi, Er … - from code)

r

iPS|| enE

drdp

enBq2

sinθV


Simulated vs. measured parallel ion flows

Both in the codes and experiments, flows are broadly consistent with Pfirsch-Schlüter formula (at outer midplane position)

But absolute values in codes < experimental by factors 2-3


SOLPS simulations of AUG divertor conditions

Fitting experimental outer midplane profiles by choice of D,e, i

0

1

2

3

4

5Edge Thomsonscattering

Lithium beam

SOLPS

0100

200

300

400

500

600

700

800

10-1

100

101

-0.02 0 0.02

SOLcore

Dperp.

e

i

i neoclassical

D: #17151 SOLPS: #12096

=

e

i

Ion temperature

Electrontemperature

[L.D.Horton et al., 2005]


H-mode #17151

Ohmic #18737 Ohmic #21320


SOLPS simulation of AUG divertor conditions - results

1.05 1.1 1.15 1.2 1.25 1.3

0.5

1.5

2.5

Ha,CIII emission at outer targetx 1020

0

1

2

3

s(m)

Ha exp.

Ha SOLPS

CIII exp. x 2

CIII SOLPS x 2

separatrix

distance along target (m)

1.05 1.1 1.15 1.2 1.25 1.301

2

34

1.05 1.1 1.15 1.2 1.25 1.305

10152025

sep.x 1019 Plasma density at outer target

Plasma temperatures at outer target

ne Langmuir probesne SOLPS

Te Langmuir probes

Te SOLPS

s(m)distance along target (m)

H-mode #17151: Ha,code > Ha,exp Ohmic #18737: Te,code < Te,exp , ne,code > n e,exp

Conclusion confirmed by available evidence: - target Langmuir probe data - divertor spectroscopy: Ha, CIII emissions - sub-divertor neutral flux - carbon content at plasma edge

At very low plasma ne, SOLPS predicts AUG target profiles reasonably well [M.Wischmeier et al., 2007]

For matching upstream profiles and boundary conditions, in medium to high density plasmas, SOLPS predicts colder and denser plasma in divertor than in experiment


SOLPS simulation of AUG divertor conditions - results

SOLPS fails to simulate large asymmetry between the targets, and detachment at inner target [M.Wischmeier, et al., 2007]

Talk by M.Wischmeier, next session, O-25


SOL flow and divertor discrepancies

parallel ion SOL flows-EDGE2D vs. JET-SOLPS vs. AUG-UEDGE vs. JT-60U

target Te

(ne, recycling)- SOLPS vs. AUG

SOL Er

- SOLPS vs. AUG- EDGE2D vs. JET

Debye sheath

Ion V|| compensatingErxB drift

Lower target Te in codes and flatter Te profiles expect lower Er in codes than in experiment: confirmed – see next

Radial electric field:

eEr 3 r

Te,target

enB

p

B

E

B

B

R

aV irPS

cos2||

Er underestimate in codes SOL flow underestimate


SOL Er discrepancy – code results

Flat SOL Vp profiles: eEr < |Te | low -eEr/ Te ratio

Vp (plasma potential) and Te profiles across SOL at outer midplaneSOLPS modelling ASDEX Upgrade, EDGE2D modelling JET plasmas [Chankin et

al.,NF 2007]

0 0.01 0.02 0.03 0.040

20

40

60SOLPS: Te and plasma pot.

Normal BtReversed Bt

Ohmic

0 0.01 0.02 0.03 0.040

20

40

60 TeeVp

0 0.01 0.02 0.03 0.040

50Te

0 0.01 0.02 0.03 0.040

50

100


Te

ns=1.3e19 m-3

Ohmicns=8e18 m

-3

Ohmicns=5e18 m

-3

H-modens=1.6e19 m-3

eVp

eVp

0 0.01 0.02 0.03 0.04 0.050

20

40

60

EDGE2D: Te and plasma pot.

0 0.01 0.02 0.03 0.04 0.050

20

40

60

0 0.01 0.02 0.03 0.04 0.050

50

100

150


Normal BtReversed Bt

Ohmic

H-mode

TeeVp

Te

Te

eVp

eVp

ns=7.3e18 m-3

Ohmicns=5.3e18 m-3

ns=1.4e19 m-3


Experimental -eEr/ rTe ratios in the SOL significantly exceed code predicted values

Er from Langmuir probe measurements

Tokamak comments

ASDEX

Upgrade* 3.1standard Ohmic shot [H-W.Müller, 2007]

JET 1.6average over Ohmic, L-mode, H-mode shots [K.Erents et al., 2004]

JT-60U 2.4L-mode, middle of density scan range [N.Asakura 2007]

TCV 3.3 – 5.0

Ohmic, middle of density scan range [R.A.Pitts, I.Horacek, 2007]

Alcator C-Mod 1.7 – 1.8

Ohmic L-mode [B.LaBombard et al., 2004]

*Similar values - from Doppler reflectometer measurements, when using probe Te

-eEr/ rTe


Potential causes of discrepancies

Neutrals

Plasma

role of fluctuations; problem of time-averaging (ab a b)

non-local kinetic effects of parallel transport

[W.Fundamenski 2006, S.I.Krasheninnikov 2007]

||7/2

downe,7/2

upe,||e )/LTk(Tq

||7/2downe,

7/2upe,||e )/LTTk(q

excessive ionisation due to low perp. mobility in codes


Non-local kinetic effects in SOL and divertor

Present 2D edge fluid codes (SOLPS/B2, EDGE2D, UEDGE) assume classical (Spitzer-Härm/Braginskii) heat flow along field lines for ions and electrons

However, real heat conduction starts to deviate from classical collisional formula(s) beginning with Lm.p.f. /LTe > 0.01 (typically ~ 0.1 in SOLs existing experiments, and expected in ITER)

The deviation is due to: most of the parallel heat flux being carried by supra-thermal electrons

with velocities: Weakly collisional: Lm.p.f.

Contributions of electrons with different velocities v to the heat flux qe

eee mT /53v

4ve

Standard corrections for kinetic effects in fluid codes, introduction of “kinetic flux limiters” – far insufficient (see later)

(Focus on electrons since e|| >> i||)

Kinetic effects: - may increase parallel heat flux in divertor, Debye sheath - affect atomic physics rates (ionisation, excitation)


Example of existing kinetic codes

ALLA [Batishchev et al., 1996-1999]: Fokker-Planck code for ions and electrons, with full Coulomb collision operator, kinetic neutrals, “logical sheath” condition

1D in physical space, adaptive mesh

2D in velocity space (energies E||, E), adaptive mesh

400

300

200

100

0-300 -200 -100 0 100 200 300

Axis

Cells

v 0.08

00 0.08

ET

E||/T

2

ET

E||/T

|

|

)&(v

v ....

||

||

|||| sourcescollisionsC

f

m

Eq

l

f

t

f

ieα ,

symmetryplane

plasma core

heat flux

0 L

neutrals

||

divertorplate


Kinetic code results on

parallel e In upstream SOL plasma, depletion of supra-thermal electron population use of flux limiters for heat fluxes in fluid codes is justified. Their values depend on plasma conditions and geometry of experiment (variation 0.03 – 0.8 reported)

In divertor, parallel heat flux may exceeds classical instead of flux limiters, flux enhancements

e > e,Braginskii/Spitzer-Härm

[K.Lackner, et al., 1984]*[R.Chodura, 1988][A.S.Kukushkin, A.M.Runov, 1994][K.Kupfer et al., 1996][O.V.Batishchev et al., 1997][W.Fundamenski, 2005] (review)*Used a fit to kinetic results

by Luciani et al., 1983


Progress in the ITER Physics Basis [Nucl. Fusion 47 (2007) S1-S413]Chapter 4: Power and particle controlSection 2: Experimental basis

Parallel energy transport is determined by classical conduction and convection, with kinetic corrections to heat diffusivities at low (separatrix) collisionalities

ei,||χei,ν

Consensus view reflected in:

Kinetic code results on parallel

e (cont.)

?


Kinetic simulations for SOL of ASDEX Upgrade H-mode

ASCOT code, adapted for kinetic electron transport in SOL of AUG H-mode shot #17151 [L.Aho-Mantila et al., 2008]

Test electrons are launched at outer midplane with local Maxwellian distribution consistent with Te of the background generated by SOLPS. Electrons collide with the background plasma and traced down to targets.

Test electron energy distributions at the targets are recorded and compared with the target Te

of the background (SOLPS) plasma.

Fraction of total target electron heat flux carried by supra-thermal electrons: 70 % near outer strike point

Helsinki University of Technology & IPP Garching


ITER H-mode scenario:

ne,sep = 4x1019m-3

Te,sep = 150 eVq95 = 3R=6.3 m

AUG standard Ohmic #18737:

ne,sep = 1.3x1019m-3

Te,sep = 47 eVq95 = 4R=1.7 m

ee = 13.8 ee = 11.6

Yes: Ohmic plasmas in AUG at low-medium densities have similar separatrix electron collisionality as that expected in ITER

Are kinetic effects in SOL of AUG relevant for ITER ?


Discrepancies between 2D fluid edge codes and experiments: - parallel ion SOL flow - divertor parameters, target asymmetries - Er in the SOL

Outer target, Er and ion SOL flow discrepancies are related to each other and caused by the codes tendency to underestimate divertor Te and overestimate ne Cause of the discrepancies is unknown, presently under investigation: - neutrals treatment by kinetic Monte-Carlo codes - role of fluctuations, present in experiments but missing in codes - non-local kinetic effects of parallel electron transport

Summary


Spares


0

1

2

3

4

5Edge Thomsonscattering

Lithium beam

SOLPS

0100

200

300

400

500

600

700

800

10-1

100

101

-0.02 0 0.02

SOLcore

Dperp.

e

i

i neoclassical

D: #17151 SOLPS: #12096

=

e

i

Ion temperature

Electrontemperature

[L.D.Horton et al., 2005]


H-mode #17151

SOLPS simulation of AUG divertor conditions (cont.)Satisfy experimental boundary conditions:

- Input power into the grid

- Particle balance: Gas puff, NBI source,

cryo-pump efficiency

- Power to target: determine separatrix position, density

Inputpower

Pumping

Gas puff,NBI source


Some results (Batishchev et al. 1996-1999)

cold

hot

Braginskii

1

0.80.60.40.2

0-0.2-0.4-0.6

0 2 4 6 8 10 12 14E/T

v v f2||

Parallel electron heat flux density, for case Te/Te = 10 (upstream to target Te ratio)Lm.p.f. /L = 0.1, typical for the SOL of ASDEX Upgrade:

At hot end, depletion of energetic electrons

At cold end, large surplus of energetic electrons flux enhancement needed (rather than flux limit)

Solution for IPP: develop kinetic module for SOLPS(B2) for parallel electron heat flux (later – also for ions)

e > e,Spitzer-

Harm

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