I-05

Scrape-off layer plasma flow and drifts
in the tokamak divertor magnetic geometries
Nobuyuki Asakura
Japan Atomic Energy Agency, Naka
Acknowledgements:
R.A.Pitts (CRPP), W.Fundamenski, K.Erents (UKAEA),
B.LaBombard, B.Lipschultz (MIT), A. Loarte (EFDA), X.Bonnin(Univ. Paris) , K. Fujimoto, K. Shimizu and the JT-60 team (JAEA)

Joint Conference of 17th International Toki Conference on
Physics of Flows and Turbulence in Plasmas and16th International Stellarator/Heliotron Workshop 2007
Ceratopia Toki, Gifu, October 15-19, 2007

Contents1. Introduction:
Plasma flow in the tokamak and measurement
2. Scrape-off layer flow in tokamaks
3. Divertor particle flux and in-out asymmetry
4. Approach of SOL and divertor modelling
5. Conclusions

Parallel plasma flow in tokamak scrape-off layer
Parallel plasma flow is produced towards Plasma Facing Component
Plasma exhausted from core

1-D momentum transport
along SOL field lines

3-D plasma flow in tokamak

M =1

M ~0

M =1

B//

Bt Ip

Divertor

M// ~0.4

Divertor

SOL flow measurements at various poloidal
locations in tokamaks exhibit 2-3D flow pattern.
Multi physics processes (plasma drifts, diffusion,detachment, etc.) in tokamak divertor geometry.

Plasma flow plays important role on heat & particle transport inboundary plasmas:• Asymmetry in inner and outer divertors ⇒detachment, pumping flux
• Impurity shielding and exhaust, and long-range transport• Edge plasma formation and plasma energy confinement

SOL flow measurement using Mach probes"up-stream" SOL flow "down-stream"jsi-side

jse-side
single- or double-proberB// (~BT)
Ipz

Mach number of parallel flow is
calculated from js at i-side and e-sideusing Hutchinson's formula:M// = Mc ln[ jsi-side /jse-side ] ,where Mc = 0.4
I.H.Hutchinson, Phys. Rev. A37 (1988) 4358.

2. Scrape-off layer flow in tokamaks

SOL flow (M// ) profile changes at Low- and High-Field Sides-0.5
0

Plasma!top

0.5
1-1

-0.5
0!101
2
345
LFS SOL (Alcator C-MOD)1
towards HFS divertor
0.5

JET

Limiter
towards shadow
HFS!divertor

00.2 0.4 0.6 0.8 1AlcatorC-MOD

HFS SOL (JT-60U)

towards!HFS!divertor
1012
345
Distance from separatrix (cm)mapping to LFS midplane

HFSion !B drift
JT-60U

X-point
JT-60U

0!0.5

midplane LFS

BT (Ip)

HFS baffle
presheath

0.5

Alcator
C-MOD

JT-60U!100.2 0.4 0.6 0.8 1
LFS SOL (JT-60U)
1
towards HFS divertor
Midplane 0.5
0X-point!0.5
towards LFS divertor
!101
2
345
Distance from separatrix (cm)mapping to LFS midplane

Mach number-1!0.5

HFS SOL (Alcator C-MOD)

Mach number

Mach number

Mach number

0Mach number

Near separatrix: flow towards HFS divertor is large at LHS SOL.
Far SOL (r > λne~cm): flow towards HFS divertor increases at Top&HFS.
Top SOL (JET)
1
Combination of driving mechanisms
towards HFS divertor
0.5
determines the SOL flow profile.

Asakura et al. PPCF (2002) 2101, LaBombard, et al. NF 44 (2004) 1047, Erents et al. PPCF 46 (2004) 1757.

Key mechanisms to produce parallel flow in tokamak SOL:
(1) Asymmetrical diffusion, (2) Classical drifts, (3) Divertor detachment
Classical drifts
ErxB, ∇pxB

Poloidal projections
ExB poloidal drifts

EθxB(Eθ = −∇θT)
Parallel flow
Pfirsch-Schlüter flow
V//PS = 2qsV⊥cosθ, V⊥= (Er-∇pi)xb/B
Asymmetrical diffusion(particle & momentum & energy)
Divertor sink
Detachment, ∇//T, pre-sheath
Others: gas-puff, pumping, recycling
Fundamenski, et al JNM 337-330 (2005) 305, Pitts, et al. PPCF 45 (2005) B303

ion∇B ⇓Key mechanism (1): in-out asymmetry in diffusion
Single null divertor: comparable plasma pressure,but fast SOL flow towards HFS divertor
Double null divertor: showed low pe and flow stagnation at HFS SOLHFS SOL plasma (in single null) is transported from the LFS SOL
Lower Single Null Divertor

towards
divertor

Alcator C-MOD
LaBombard et al. NF 44 (2004) 1047

Double Null Divertor

Key mechanism (2) : Classical drifts in tokamak
Forward/ Reversal Bt: ΔM// direction above/ below average base-level<M//> ~0 (LFS midplane), ~0.2 (plasma top in JET)
Parallel flow is produced against ion ∇B direction.
M// (drift effect) decreases with ne.
Low-field-side midplane (JT-60U)
Gr0.4 ne/nion ∇B↓
0.23
0.2
0.46
0 0.44ΔM//<M >Mach number

towards
top//

+M//

ion ∇BΔM//-0.2-0.4 0.24

towards
divertor -1

Bt (I p)0123

ion ∇B↑
456

Distance to separatrix (cm)

Similar results were found in C-MOD, TCV, and limiter tokamak (ToreSupra)
JT-60U:Asakura et al. PRL 84 (2000) 3093, LaBombard et al. NF 44 (2004) 1047, Erents et al. PPCF 46(2004) 1757, TCV: Pitts et al. TCV.J.N.M. 363-365 (2007) 507, TS: Gunn et al, J.N.M. 363-365 (2007)484.

-Classical drifts in tokamak:
Upward parallel flow is driven for ion ∇B↓ by in-out asymmetry of drifts
Ion drift : V⊥ = (Er - ∇pi/eni)xb/B
large at LFS midplane

V//PS was evaluation fromEr ~∇(Vf +αTe), ∇Ti profiles∇ (Γ// + Γ⊥) = Si (~0)
small ion source
B×∇B↓"Pfirsch-Schlüter flow":
V//PS = 2qsV⊥cosθ
maximum at midplane

1 d(neTi)(kV/m)
Er, - ene dr

LFS midplane (JT-60U)
30Totalne = 1.5x1019 m-3
1 d(n T )20

- e ne dr e i B×∇B↓

1000Er123456Distance from separatrix (cm)Asakura et al. PRL 84 (2000) 3093
TCV: Pitts, et al. J.N.M. 363-365(2007)507"Pfirsch-Schlüter flow" is zero at plasma top & bottom.
V⊥ and V//PS are large at low density.

Evaluation of M// is smaller than measurement (using only ExB part):
better resolution of Ti profile will provide accurate evaluation of V//PS .
Classical drifts review: Chankin and Stangeby, PPCF 36 (1994) 1485 & 38 (1996) 839, NF 36 (1996) 839.

Key mechanism (3) : Influence of divertor detachment
Recombination process becomes
Mach number
dominant in dense and coldof SOL flow
divertor (< a few eV).
Plasma flow becomes Soniclevel at the recombination front.
Parallel flow at the upstream
SOL is increased.
2D divertor spectroscopy measurement(Dα- Dθ) determined recombination region
DαK. Fujimoto et al. submitted to PFR

Dβ/Dα

Ip=0.8MA,
Bt=3T,
ne~1.2x1019m-3
ne/nGW~0.47

Divertor detachment affects Subsonic-Sonic flow at HFS
M// in far SOL at HFS is enhanced when the divertor detachment occurs.
Static pressure is reduced
upstream M// increases to Sonic level
Bt (I p)ion ∇B+Recombination dominant area

Dβ/Dαne/nGW~0.47
Asakura et al. PPCF 44 (2002) 2101

3. Divertor particle flux and in-out asymmetryDrifts plays an important role near divertor null (X-point)• Heat and particle fluxes along B are separated in HFS/ LFS divertors• Change of in-out asymmetries in heat and particle fluxes was NOT
explained by parallel model (simulations)depending on Bt direction ⇒ Drifts (cross-field) transport in divertor
In-out asymmetry was reversed
at high ne (MARFE appears)
Projection of paralleltransport and neutrals

Projection ofpoloidal drifts

med. density D

high densityion∇B ⇓neutrals
EθxB= −∇θTxB

ErxB

Effects of drifts on heat transport: Fundamenski, et al JNM 337-330 (2005) 305

αSOL ion fluxes towards HFS&LFS divertors are evaluatedPoloidal components of convection flux (niv// Θ) and drift flux (nivdrExBΦ)are evaluated at the HFS and LFS SOLs (Mach probe locations):
Drift flux is large near the separatrix.
Net ion flux towards divertor: ΓpHFS/ LFS = 2π ∫ni [v// Θ ±vdrExBΦ]Rdr(HFS: - / LFS: + for ion ∇B drift towards divertor).
niV// ~ M// js /e , Θ = Bp/B// , Φ = Bp/B⊥~1, ni =ne.
Poloidal projection of particle fluxes

Asakura et al., JNM 313-316 (2003) 820.

Radiation peak (MARFE) stays near the X-point (LFS), anddetachment occurs at the down-stream of the MARFE.
2D divertor bolometer measurement
determined radiation peak location

Detachedne⇑3.2X1019

Field line length increased close to X-point,
comparable to one toroidal turn (~19m).

along the probe sweep

In private flux region under attached divertor condition,
large drift flow from LFS to HFS divertor is produced.
In common flux region, when LFS divertor is detached,large drift flow away from LFS divertor appears..

detachDrift flow awayfrom divertor
Drift flow towards HFS divertor

Attached div. in DIII-D: .A. Boedo, et.al.
Physics Plasma 7 (2000) 3093.

ΓpLFS=

Drift flow in the private region and divertor detachment play
an important role on producing in-out asymmetry in divertor.
LFS divertor is attached:Γp prv (drift flux in prv.) is added to ΓHFS
(HFS SOL flux), for ion ∇B drift towards the divertor
LFS divertor is detached:In-out asymmetry is determined by parallel flows
towards HFS & LFS divertors, Γi,//HFS < Γi,// LFS .
Γi//LFS
Γi//HFS
Boedo et al., PP 7 (2000) 1075,
Asakura et al., JNM 313-316(2003) 820.

4. Approach of SOL and divertor modellingApproach of SOL & divertor modelling with drifts & diffusion
2-D fluid codes (SOLPS, UEDGE, EDGE2D) include classical drift effects,
qualitatively reproduce normal/reversed Bt effects, but small M// (~0.1)[Bonnin et al, JNM 337-330 (2005) 301]

B×∇B↑

B×∇B↓

towards Top (HFS)

Modelling of potential and current
near separatrix may affect M// ?

LFS midplane (C-MOD - B2SOLPS)

Mach number(1) SOLPS for C-MOD (Bonnini, et al)
showed M// ~ 0.5 near separatrix.

SOL(2) Poloidal asymmetry models for D⊥, χ⊥1) Radial convection: EDGE2D(JET)
HFS⇒LFS for Norm-B (LFS⇒HFS for Rev-B.)
2) LFS-enhanced diffusion (D⊥~1/B),
in some cases, ΓRHFS enter confined plasma:

EDGE2D(JET), SOLPS(JET) ,UEDGE(C-MOD)
Large ΓRLFS/ΓRHFS(~50) explains fast M// ~0.5

Diffusion (1/B)/
transport (blob etc)
Convection

ΓRHFS

ΓRHFS

Bx!B drift

Plasma top (JET - EDGE2D)

Kirnev, et al JNM 337-339 (2005) 271, Coster et al. IAEA 2004, Pigarov et al. 10th PET 2005

Influence of intermittent/Blob radial transport on parallel flow
are implicated in 2D fluid simulations -- active area of study
Experiment results (C-MOD, DIII-D, TCV, JT-60U, ASDEX-U, JET, NSTX, etc):
2D fast imaging by blobs/ statistic analysis of fluctuations (skewness-flatnessof P.D.F.) show intermittent out-flux at LFS SOL such as ExB turbulence.

Alcator C-MOD
J.Terry, et al., J. Nucl.
Mater. 290-293, 757(2001).

• Non-linear simulation of the turbulencetransport can evaluate contribution ofoutflux to the fast SOL flow: <M//> ~ 0.1-0.2
for JETESEL for TCV LFS SOL: Garcia et al. PPCF 48 (2006) L1

Conclusions
Understanding of Flow pattern in SOL-Divertor has been progressed with
development of diagnostics to measure 2D profiles (Mach probes, etc.):

Flow pattern is produced by combination of main driving mechanisms:(1) Asymmetry in diffusion/ transport, (2) Classical drifts (Bt direction),(3) Divertor detachment, and other effects (recycling, intense-puff&pump)Those play an important role on formation of SOL & divertor plasmas:
Subsonic-Sonic SOL/divertor flow, in-out asymmetry in divertor plasma,Detachment and divertor MARFE etc.,

also influence on impurity transport (deposition, shielding from core)and energy confinement at edge (L-H transition, transport barrier).
All processes are important under reactor condition. Understanding ofboth // and ⊥ transport in tokamak magnetic geometry is urgent issue.
⇒ Quantitative determination of the SOL flow pattern BOTH fromexperiments (M// ) and simulation (appropriate modelling in realmagnetic configuration) are crucial for diveror design and operation.