Comparative Divertor-Transport Study
for W7-AS and LHD
Y. Feng, M. Kobayashi, N. Ashikawa, L. Giannone, P. Grigull, K. Ida, J. Kisslinger,A. Komori, R. König, LHD experimental group, S. Masuzaki, K. McCormick, J.
Miyazawa, T. Morisaki, S. Morita, O. Motojima, Y. Nakamura, K. Narihara, N.
Ohyabu, B.J. Peterson, F. Sardei, K. Sato, M. Shoji, N. Tamura, H. Thomsen, M.
Tokitani, F. Wagner, U. Wenzel, H. Yamada, I. Yamada- Max-Planck-Institut für Plasmaphysik, Euratom Association, Germany- National Institute for Fusion Science, Toki, Japan• Common SOL-transport features• Impurity and neutral screening• Stability of detached plasmas• On the way to W7-X

W7-AS island divertor vs LHD helical divertor
W7-ASLHD

•
••

•
•

Helical divertor (HD)Island divertor (ID)Shear:
large
Field structure: stochastic (multi-island chain)
SOL thickness:~10 cmLc:
several m -> several km
Targets:
4 continuous plates
Divertor structure:openlow
single island chain~4 cm~100 m
10 discontinuous modules
open

Θ=dr/dl 10-4-10-3 (0.1 in tokamak) → Significant contribution of ⊥-transport

SOL-transport guided by low-order islands
LHD HD

W7-AS ID

* ThomsonTe

EMC3-EIRENE

EMC3/EIRENE

10/6

radial

10/7
10/8

Poloidal ½ field period

Lc contour + Poincaré plot

Inboardmidplane=>Transport governed by low-order islands(W7-AS: 5/m, LHD: 10/m)=> No remarkable stochastic effects on SOLtransport even in LHD
outboard
midplaneViscous momentum loss between opposite flows
Parallel momentum balance:()p 1+ M 2 = 2 pup − D ∫⎛ mnVII ⎞mnVII⎜ 2 ⎟ Lcdl2pD=−up2⎜ ∆ ⎟∆⊥⎝ ⊥ ⎠Small ∆⊥ and large Lc→ large momentum loss

0-

Poloidal several mradial friction

+nVII

∆⊥ ~4

Radial several cm

W7-AScm(EMC3/EIRENE)∆⊥~1-2cm?

LHD

poloidal friction=> break up parallel pressure conservation

No high recycling regime(tokamak high recycling regime: ned ~ nes3, Γrec~nes2)

W7-AS
EMC3/EIRENE

LHD
Langmuir probes• No evidence for high recycling: ned, Isat ∝ nes, ne up to rollover• Rollover of recycling flux:nes↑ ⇒ Ted ↓ and Prad ↑ ⇒ inward shift of ionization zone when Ted < Eion
⇒ larger recycling zone ⇒ momentum loss↑ ⇒ Γrecy , ned ↓Island screening effects on intrinsic impurities

PFC• Core plasma in both W7-AS and LHD surrounded by island
chains of several cm thickness

λSOL ∝ Lc
Large Lc → thick SOL

CoreCX-neutral
im pu r ity• Reduction of physical sputtering yield (impurity source)

qSOL = γTΓrecyc :↑ Γrecyc →↓ T

• Impurity retention (impurity transport)→ high SOL density needed!

Island screening effect on CX-neutrals
LHD
10Total Fe production rate / 1019 /s

5Total Fe yield / a.u.
1
1W7-AS(EMC3/EIRENE)

D=0.5 m2/s, peaked ne-profile
D~1/nes, peaked ne-profile
D=0.5 m2/s, flat ne-profile
D~1/nes, flat ne-profile

4

3

2

1

todetach.
nLCMS/1019 m-3

10002

nes / 1019 m-3

4High densities shift CX-neutrals to low energy range in two ways:
1) by lowering the SOL temperature2) by reducing the neutral penetration length6

SOL impurity transport
Simplified force balance between friction
and ion thermal force

τ ZimZZ 2 ∇ II TiLCMS

From 1D radial continuity fortarget-released impurities:

Θ = drdl

Θ2dTi/drRecycling⎛ target ΘVZ II ⎞nIs / nId = exp⎜⎜ − ∫dr ⎟⎟⎠⎝ LCMS DZ ⊥Impurity retention if VzII>0 i.e. Vi II > CiTi

τ ZimZΘViII
core

SOLtargetV Z II = Vi II + C ir

Z 2∇ II Ti

5 / 2 niTiVi IIfriction>1~
5/ 2thermal force κ iTi ∇ IITi
→ reducing II-conductive heat flux is the key to reduce thermal forces

Reduction of II-conductive heat flux by ⊥-transport
1D radial energy transport for ions:

LCMS⊥IIIf Θ is small (long connection length),⊥-heatconduction makes significant contributions.

coreCondition for significant reductionof parallel ion heat conduction:

nTi

>
5/ 2

Θ 2κ iUse Bohm-condition nTi3/2 ∼ qi:

χiTi

w/o ⊥

Θ = drdlw⊥
targetdTi
25 / 2 dTi
5 / 2ΘnTiViII − nχ i− Θ κ iTi= qi
drdrSOLr

Note that Θ ∼ 10−4−10−3 in W7-AS and LHD
and ∼ 0.1 in tokamaks!

(only representative)Θ 2κ in8 / 3> Const ⋅
5/ 3
χiqi
→ For a given power qi, there is threshold density to switch off the thermal forceImpurity retention: 3D code predictions

Increasing neLHD

W7-AS

nLCFS = 2 x 1019 m-3

4 x 1019 m-3
nes = 1.5 x 1019 m-3
K. McCormick 15th ISWS

5.0 x 1019 m-3

Relevance to experiments:
nLCFS~3e19 m-3

8 102

2e19 m-3

HDH
NC

H*2X

HDH
Density ramp

• Low τimp measured for HDH (R. Burhenn)mechanism not yet understood

6 102
4e19 m-3
4 102timeDetails -> I-07 Kobayashi

Detachment stability(experiments)#56846#56848

LHD

800

0.8

diaWpstable

600

0.6

4000.4

P(kJ)

E /kJ

W7-ASWP

radPradGeometry-related detachment stability:• large islands and field-line pitch →stable partial detachment• small islands or field-line pitch →unstable complete detachment• Sharp transition to detachment

tot

00

1

time

0.2

/P

1.1

1.2

1.3

1.4

time (s)• no stable partial detachment found• quasi-stable complete detachment(Serpens mode) with a rotatingradiation belt inside LCFS
• Sharp transition to detachment

totP/MWp/PPNBI

rad200Radiation distributions of detached plasmas(code results)

W7-ASLarge
IslandLHDSmallIsland

Carbon radiation intensity• X-point radiation• radiation belt outside LCFS
• large island (stable partial detach.)-inboard side radiation-good neutral screening• small island (unstable completedetach.)-divertor radiation-week neutral screening• O-points of remnant islands• solutions found with radiation belt outsideLCFS• no significant in/out asymmetry, neither
among the islands• week neutral screening• experimentally not yet accessible as thedivertor radiation case in W7-AS- due to loss of neutral screening?

From W7-AS to W7-X
W7-X
W7-AS

•

•

•

•
•

Similarities:• SOL transport governed
by low-order islands• Large Lc, small Θ• 10 open divertor modules• Neutral baffling

Differences:• lower poloidal mode number (4,5,6),
larger a → larger poloidal distance• larger islands

Moderate poloidal viscous transport
W7-AS

W7-X+nVII0
Standard divertor
configuration withIcc = 25 kA(vacuum field)Poloidally-contacted-

divertor shadow trapping remains
radialtarget

shadowtargetΘ

to upstreamhelicalPoloidally-isolated→ more ‘localized’ flows→ impurity screening?

Density rise along island fans expected
Preliminary EMC3/EIRENE results→ improved neutral screening ?
→ detachment shifted to lower densities ?

Transition to friction-dominated impurity transport(preliminary EMC3/EIRENE results)

Carbon (test impurity) density distributions as function of nes
ViII=0Existence of large stagnation region → impurity leakage?
(especially for wall-released impurities)SummaryDespite the large differences in divertor configuration and concept between W7-AS andLHD, there are common features in terms of SOL transport and divertor function:• Transport governed by low-order islands• Large Lc (small Θ) increases significantly the ⊥/‖-transport ratio• Viscous transport causes significant momentum loss
• No high recycling regime as found in tokamaks• High nes for detachment transition• Dense, cold islands reduce influx of intrinsic impurities:- reduce impurity yield from CX-neutrals- reduce thermal forces so that frictional plasma flow drives
impurities outwards (friction-dominated impurity transport regime)(These code results need further experimental confirmations)Differences in detached plasmas:• Stable partial detachment for large islands and field line pitch
W7-AS - inboard side radiation outside LCFS
• Unstable complete detachment for small islands and field line pitch- Marfe-like radiation inside LCFS
LHD • Quasi-stable complete detachment (Serpens mode)- Rotating radiation belt inside LCFS
W7-X : Systematic numerical parameter pre-studies under way

Physics model in EMC3/EIRENEBackground plasma (fluid, EMC3: Y. Feng et al., J. Nucl. Mater. 1999):∇ ⋅ (niViII b − Db⊥ b⊥ ⋅ ∇ni ) = S p∇ ⋅ (mi niViIIViII b − ηII bb ⋅ ∇ViII − miViII Db⊥ b⊥ ⋅ ∇ni − η ⊥ b⊥ b⊥ ⋅ ∇ViII ) = − b ⋅ ∇p + S m∇ ⋅ ( 52 neTeViII b − κ e bb ⋅ ∇Te − 52 Te Db⊥ b⊥ ⋅ ∇ne − χ e ne b⊥ b⊥ ⋅ ∇Te ) = − k (Te − Ti ) + S ee + Simp
∇ ⋅ ( 52 niTiViII b − κ i bb ⋅ ∇Ti − 52 Ti Db⊥ b⊥ ⋅ ∇ni − χ i ni b⊥ b⊥ ⋅ ∇Ti ) = + k (Te − Ti ) + S ei

Impurities (fluid, EMC3:Y. Feng et al., Plasma Phys. Control. Fusion 2002):∇ ⋅ (n IzVIIIz b − DIz b⊥ b⊥ ⋅ ∇n Iz ) = S z −1→ z − S z → z +1 + Rz +1→ z − Rz → z −1

U Iiz (VIIIz − ViII ) = − b ⋅ ∇n IzTIz + n Iz ZeEII + n Iz Z 2Ce b ⋅ ∇Te + n Iz Ci b ⋅ ∇Tib ⋅ ∇neTe + ne eEII + neCe b ⋅ ∇Te = 0TIz = Ti
Neutrals (kinetic, EIRENE: D. Reiter et al., Fusion Sci. Technol. 2005):
Boltzmann equation
Plasma-surface and neutral-surface interaction:
Particle and energy reflection and sputtering models integrated in Eirene code