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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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
AlcatorC-Mod Poloidal Flow Components
The poloidal flow pattern is composed of:
– A transport-driven part that
• Depends on magnetic topology
• Has finite divergence
– A drift-driven part that
• Depends on field direction
• Is divergence-free
vdrift
Bx∇B
AlcatorC-Mod Poloidal Flow Components
The poloidal flow pattern is composed of:
– A transport-driven part that
• Depends on magnetic topology
• Has finite divergence
– A drift-driven part that
• Depends on field direction
• Is divergence-free
We measure:
– A favorable drift direction flow pattern (Bx∇B towards x-point) : vfav = vtransp + vdrift
Bx∇B = +ΓrBx∇B
AlcatorC-Mod Poloidal Flow Components
The poloidal flow pattern is composed of:
– A transport-driven part that
• Depends on magnetic topology
• Has finite divergence
– A drift-driven part that
• Depends on field direction
• Is divergence-free
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
Drift-Driven Component
Bx∇B
Depth into SOL [mm]
nvθ/Bθ
(Ele
cD
ia)
[10
23T
m-2
s-1
]
LC
FS
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
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
Drift-Driven Component
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
Depth into SOL [mm]Depth into SOL [mm]
Para
llel F
low
[km
/s]
Co
-Cu
rre
nt
Dir
ec
tio
n
Drift-Driven
HFS LFS
Drift-Driven Component
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
Transport-Driven Component
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
Transport-Driven Component
HFS
S = 0S = 1
nvθ
Depth into SOL [mm]n
vθ
HF
S[1
02
2m
-2s
-1]
• Model transport-driven poloidal particle flux as sin(θ) on LFS
• Constrain with measured value of poloidal flux onHFS
LC
FS
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
nvr
Γr
Transport-Driven Component
HFSLFS
S = 0S = 1
nvr
nvθ
Depth into SOL [mm]Depth into SOL [mm]
LF
S L
imit
er
nv
rL
FS
[10
20m
-2s
-1]
nvθ
HF
S[1
02
2m
-2s
-1]
• Model transport-driven poloidal particle flux as sin(θ) on LFS
• Constrain with measured value of poloidal flux onHFS
• Calculate LFS radial particle flux implied by HFSpoloidal flux
LC
FS
LC
FS
Transport-Driven Flow Component:Should Agree with Measured Transport
S: Normalized poloidal distance from outer to inner divertor
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
Transport-Driven Component
HFSLFS
S: Normalized poloidal distance from outer to inner divertor
S = 0S = 1
nvr
nvrFluctuation-
induced
nvθ
Depth into SOL [mm]Depth into SOL [mm]
LF
S L
imit
er
nv
rL
FS
[10
20m
-2s
-1]
nvθ
HF
S[1
02
2m
-2s
-1]
• Model transport-driven poloidal particle flux as sin(θ) on LFS
• Constrain with measured value of poloidal flux onHFS
• 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
HFS ‘Ballooning’ Particle Pinch?
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
HFS ‘Ballooning’ Particle Pinch?
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
Evidence that Volume Recombination Plays a
Key Role in Closing Flow Loop
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
Evidence that Volume Recombination Plays a
Key Role in Closing Flow Loop
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.