total flow vector in the c-mod sol filetotal flow vector in the c-mod sol n. smick, b. labombard mit...

AlcatorC-Mod

Total Flow Vector in the C-Mod SOL

N. Smick, B. LaBombard

MIT Plasma Science and Fusion Center

APS-DPP Annual Meeting

Atlanta, GA

November 3, 2009

AlcatorC-Mod Motivation and Goals

�� Detailed measurements of the total flow vector are needed to address these goals

Poloidal projection of parallel flows driven

by ballooning transport asymmetry in upper and lower single null

Γr

USN

LSN

Near Sonic Parallel Flows Observed

1. LaBombard, Brian, Nucl. Fusion 44 (2004)1047-1066

Measurements have revealed high parallel flow velocities in the High Field Side (HFS) SOL (approaching Mach 1)1 that appear to be driven by a strong ballooning-like transport asymmetry.

Goals of current investigation:

• Determine whether the measured parallel flows drive a net poloidal particle flux or are just part of toroidal rotation.

• Separate out transport and drift-driven components of poloidal flows.

• Identify mechanism for returning HFS poloidal particle flux to the core.

Γr

AlcatorC-Mod Plasma Flow Diagnostics in the C-Mod SOL

• C-Mod is equipped with two pneumatic

scanning probes on the low-field side

(LFS): a LFS midplane probe and a

vertical probe near the lower divertor.

• A key diagnostic is a new scanning

probe located near the HFS midplane.

• All scanning probes can measure the

total flow vector: v||, v⊥⊥⊥⊥, ExB and vr, nEθ

(from fluctuation-induced particle flux).

HFS Midplane

Scanning

Probe

Vertical

ScanningProbe

LFS

MidplaneScanning

Probe

~~

AlcatorC-Mod Poloidal Flow Components

The poloidal flow pattern is composed of:

– A transport-driven part that

• Depends on magnetic topology

• Has finite divergence

vtransp

Γr






– A drift-driven part that

• Depends on field direction

• Is divergence-free

vdrift

Bx∇B









We measure:

– A favorable drift direction flow pattern (Bx∇B towards x-point) : vfav = vtransp + vdrift

Bx∇B = +ΓrBx∇B









We measure:

– A favorable drift direction flow pattern (Bx∇B towards x-point): vfav = vtransp + vdrift

– An unfavorable drift direction flow pattern (Bx∇B away from x-point): vunfav = vtransp – vdrift

= -Bx∇B ΓrBx∇B

Bx∇B = +ΓrBx∇B

AlcatorC-Mod Flow Components on LFS and HFS midplanes

• Flow components have been extracted from probe data at the LFS and HFS midplanes.

• Parallel, transport-driven flow is dominant on HFS.

• Drift-driven flows are dominant on LFS.

HFS

HFS LFS

LFSBx∇B

Γr

Depth into SOL [mm]Depth into SOL [mm]

Po

loid

al

Flo

w [

km

/s]

To

wa

rds

In

ne

r D

ive

rto

r

Depth into SOL [mm] Depth into SOL [mm]

Po

loid

al

Flo

w [

km

/s]

Ele

ctr

on

Dia

ma

gn

eti

cD

irec

tio

n

Drift-Driven Part

Transport-Driven Part

Transport-Driven Component

Drift-Driven

Component

LC

FS

LC

FS

LC

FS

LC

FS

AlcatorC-Mod

Drift-Driven Flow Component:HFS/LFS comparison indicates divergence-free flow

HFS LFS

Drift-Driven Component

Bx∇B

Depth into SOL [mm]

nvθ/Bθ

(Ele

cD

ia)

[10

23T

m-2

s-1

]

LC

FS

• Total drift-driven flow is consistent with

divergence-free flow pattern as

expected from theory: similar profiles of

nvθ/B

θLFS to HFS.

AlcatorC-Mod

Drift-Driven Flow Component:HFS/LFS comparison indicates divergence-free flow

• Total drift-driven flow is consistent with

divergence-free flow pattern as

expected from theory: similar profiles of

nvθ/B

θLFS to HFS.

• This calculation uses total fluid motion,

not guiding center only; includes Parallel, ExB and Diamagnetic flow.

HFS LFS


Bx∇B

Depth into SOL [mm]

nvθ/Bθ

(Ele

cD

ia)

[10

23T

m-2

s-1

]

LC

FS


Po

loid

al

Flo

w [

km

/s]

Ele

ctr

on

Dia

ma

gn

eti

cD

irec

tio

n

Drift-Driven

AlcatorC-Mod

• We can now unambiguously

decompose the drift-drivenparallel flow into Pfirsch-Schlüter and toroidal rotation components.

Drift-Driven Flow Component:Toroidal rotation and Pfirsch-Schlüter contributions

HFS LFS


Bx∇B

V rot, ||V Pfirsch-Schlüter

BV⊥⊥⊥⊥, ExB

(Inferred from ∇∇∇∇Φ)

V⊥⊥⊥⊥, Diamagnetic(Inferred from ∇∇∇∇p)

Vφ

Net Fluid Flow

Measured v||Net poloidal

flow, vθ

φ

θ

AlcatorC-Mod

• We can now unambiguously

decompose the drift-drivenparallel flow into Pfirsch-Schlüter and toroidal rotation components.

• Data confirm expectation that

these components should

cancel on closed field lines.

Drift-Driven Flow Component:Toroidal rotation and Pfirsch-Schlüter contributions


Para

llel F

low

[km

/s]

Co

-Cu

rre

nt

Dir

ec

tio

n

Drift-Driven

HFS LFS


Bx∇B

V rot, ||V Pfirsch-Schlüter

BV⊥⊥⊥⊥, ExB

(Inferred from ∇∇∇∇Φ)

V⊥⊥⊥⊥, Diamagnetic(Inferred from ∇∇∇∇p)

Vφ

Net Fluid Flow

Measured v||Net poloidal

flow, vθ

φ

θ

AlcatorC-Mod

HFS LFS

S

nvθ/Bθ Toward

Inner Divertor

HF

S

LF

S

Γr


S = 0S = 1

• Model transport-driven poloidal particle flux as sin(θ) on LFS

Transport-Driven Flow Component:Should Agree with Measured Transport

S: Normalized poloidal distance from outer to inner divertor

AlcatorC-Mod

HFS LFS

S

nvθ/Bθ Toward

Inner Divertor

HF

S

LF

S

Γr


HFS

S = 0S = 1

nvθ

Depth into SOL [mm]n

vθ

HF

S[1

02

2m

-2s

-1]


• Constrain with measured value of poloidal flux onHFS

LC

FS



AlcatorC-Mod

HFS LFS

S

nvθ/Bθ Toward

Inner Divertor

HF

S

LF

S

nvr

Γr


HFSLFS

S = 0S = 1

nvr

nvθ


LF

S L

imit

er

nv

rL

FS

[10

20m

-2s

-1]

nvθ

HF

S[1

02

2m

-2s

-1]



• Calculate LFS radial particle flux implied by HFSpoloidal flux

LC

FS

LC

FS



AlcatorC-Mod

Transport-Driven Flow Component:Consistent with LFS fluctuation-induced radial flux data

HFS LFS

S

nvθ/Bθ Toward

Inner Divertor

HF

S

LF

S

nvr

Γr


HFSLFS


S = 0S = 1

nvr

nvrFluctuation-

induced

nvθ


LF

S L

imit

er

nv

rL

FS

[10

20m

-2s

-1]

nvθ

HF

S[1

02

2m

-2s

-1]



• Calculate LFS radial particle flux implied by HFSpoloidal flux

• Result shows agreement with measurements of fluctuation-induced particle flux on the LFSthrough

θEn~

~

LC

FS

LC

FS

AlcatorC-Mod

• There must be an efficient particle sink

on the HFS to sustain pressure

gradients driving near-sonic transport-driven parallel flows.

• Could particles be returning to the core

via a HFS convective pinch? This is a

solution commonly employed by 2-D

edge codes to explain HFS flows.2,3,4

2A.Y. Pigarov et al. Contrib. Plasma Phys. 48 (2008) 82-883J.D. Elder et al. J. Nucl. Mater. 390-391 (2009) 376-3794G.S. Kirnev et al. J. Nucl. Mater. 337 (2005) 271-275

-Γr

HFS ‘Ballooning’ Particle Pinch?

Γr

?

Sink for Transport-Driven Flow

AlcatorC-Mod

• There must be an efficient particle sink

on the HFS to sustain pressure

gradients driving near-sonic transport-driven parallel flows.

• Could particles be returning to the core

via a HFS convective pinch? This is a

solution commonly employed by 2-D

edge codes to explain HFS flows.2,3,4

• Could a volume recombination zone

be present in the far SOL of the inner

divertor leg, returning particles to the

core as neutrals?

2A.Y. Pigarov et al. Contrib. Plasma Phys. 48 (2008) 82-883J.D. Elder et al. J. Nucl. Mater. 390-391 (2009) 376-3794G.S. Kirnev et al. J. Nucl. Mater. 337 (2005) 271-275

Volume Recombination Zone?

Γr

Γn

Sink for Transport-Driven Flow

AlcatorC-Mod Measurement of HFS Pinch Velocity

• HFS radial particle flux is robustly zero.

• Hint of pinch near LCFS from 2007 data was

shown by improved statistics to be

anomalous.

HFS

LFS

DIV

-Γr


Γr

?

DIV

LFS

HFS

Depth into SOL [mm]

Γr/n

e[m

/s]

AlcatorC-Mod

• HFS radial particle flux is robustly zero.

• Hint of pinch near LCFS from 2007 data was

shown by improved statistics to be

anomalous.

XHFS

LFS

DIV

-Γr


Γr

DIV

LFS

HFS

Depth into SOL [mm]

Γr/n

e[m

/s]

Measurement of HFS Pinch Velocity

AlcatorC-Mod

Evidence that Volume Recombination Plays a

Key Role in Closing Flow Loop

Strong flow to partially-detached inner divertor

USN, No MARFE

HFS Probe

Location

Parallel Mach #1.0

-1.0

0

0 10

LC

FS

[mm] into SOL

Electron Pressure

0 10

LC

FS

0

60

[mm] into SOL

neT

e[1

020

eV

m-3

]

[mm] into SOL

HFS HFS

To Divertor

AlcatorC-Mod



Strong flow to partially-detached inner divertor.

USN, No MARFE USN, MARFE in Lower Chamber

HFS Probe

Location

~ no plasma makes it around MARFE to populate HFS. Residual flow is towards MARFE (recombination zone).

Parallel Mach #1.0

-1.0

0

0 10

LC

FS

[mm] into SOL

Electron Pressure

0 10

LC

FS

0

60

[mm] into SOL

neT

e[1

020

eV

m-3

]

[mm] into SOL

Electron Pressure

0 10

LC

FS

0

60

[mm] into SOL

neT

e[1

020

eV

m-3

]

Parallel Mach #1.0

-1.0

0

0 10

LC

FS

[mm] into SOL

HFS HFS HFS HFS

To Divertor

To MARFE

MARFE

AlcatorC-Mod



USN, No MARFE USN, MARFE in Lower Chamber

HFS Probe

Location

Parallel Mach #1.0

-1.0

0

0 10

LC

FS

[mm] into SOL

Electron Pressure

0 10

LC

FS

0

60

[mm] into SOL

neT

e[1

020

eV

m-3

]

[mm] into SOL

Electron Pressure

0 10

LC

FS

0

60

[mm] into SOL

neT

e[1

020

eV

m-3

]

Parallel Mach #1.0

-1.0

0

0 10

LC

FS

[mm] into SOL

HFS HFS HFS HFS

To Divertor

To MARFE

MARFE closes the flow loop. Calls for careful modeling of inner divertor recycling / recombination effects.

MARFE

AlcatorC-Mod Conclusions

• ExB flow data show that transport-driven parallel flows

are responsible for net poloidal motion of HFS plasma toward active x-point.

• Measured drift-driven flows are divergence-free.

• Transport-driven poloidal particle flux is consistent with

measured LFS fluctuation-induced radial particle flux.

• HFS particle pinch is zero; this is not the mechanism that

closes the mass flow loop on the HFS.

• Recycling / recombination physics in inner divertor leg is

a strong candidate to close mass flow loop.

total flow vector in the c-mod sol filetotal flow vector in the c-mod sol n. smick, b. labombard mit...

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