1. Mechanisms Controlling Parallel Flows in the SOL
A.V.Chankin
Max Planck Institute for Plasma Physics,
EURATOM Association, Garching, Germany
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

2. Outline mechanisms determining parallel flow pattern in the SOL
Experimental evidence and theoretical explanation of the main
mechanisms determining parallel flow pattern in the SOL
JET data on flows, impurity behaviour, location of surface
layers; code modelling results, unresolved issues
Summary
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

3. Impurity Control Limiter Experiment in DITE (Matthews et al.,1988)
As part of this experiment:
set of Langmuir probes on both ion (i)
and electron (e) drift sides of limiter
parallel plasma flows can be measured:
(use either ;
or for the Mach
number M of parallel ion flow)
Independent reversal of Bt, Ip
(4 combinations in total) to study
the nature of plasma flows Bt
Interpretation of Asymmetries in the SOL of DITE
through combination of
ion Pfirsch-Schlüter flow and
asymmetric (outboard enhanced) perpendicular
turbulent transport (“ballooning”)
(Hugill,1992)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

4. Ion Pfirsch-Schlüter Flow in the SOL
Perpendicular Ion Drift Flow:
Ion
Pfirsh-Schlüter
Flow
(reverses with
Bt reversal) R
EB drift ion diamagnetic flux
In the SOL, due to Debye sheath drop:
(plasma – target  3Te /e)
eEr  -3dTe /dr > 0 
poloidal EB drift adds to ion diamagnetic flux 
Finite (non-zero) ion poloidal flow
High recycling tends to reduce parallel ion flows in the divertor
Divergence of this flow in toroidal
geometry (B-var., R-var.) generates:
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

5. ||  Poloidally Asymmetric Turbulent Transport (“Ballooning”) R
Outboard enhanced perpendicular transport is closed (partly) by parallel Ion flows away from the midplane position  R
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

6. Poloidal SOL Asymmetries and Toroidal Flow in DITE (Pitts et al.,1990)
a number of Langmuir probes imbedded into both
ion (i) and electron (e) drift sides of poloidal limiters
provided good poloidal coverage of the SOL
Interpretation of Asymmetries in the SOL
of DITE through combination of
net toroidal rotation of the edge plasma in
the direction of the main plasma current
and
- enhanced particle diffusion at the outside
midplane (“Ballooning”, same as Hugill’s)
P-S flow
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

7. Rotation + Ballooning in the SOL
T-10 (Vershkov et al.,1989)
Effects of Rotation & Ballooning also
observed in many other experiments
Qualitatively, the same conclusion as in
Pitts’ work, has been obtained on T-10
(Pfirsch - Schlüter flows don’t contribute at the top
and bottom of the magnetic configuration, but
large parallel/toroidal ion flows were routinely
measured there)
P-S flow
Toroidal rotation present in the output from
EDGE2D and B2.5 codes
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

8. Toroidal Rotation in the SOL Driven by Poloidal EB Drift
First related to baffling of poloidal EB flow by target plates in (Tendler & Rozhansky, 1990) R
EB flow
High recycling
EB flow R
“baffle”
“baffle”
High recycling
Poloidal EB Drift + Parallel Flow = Toroidal Flow
(along Ip, as in exper.)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

9. Toroidal Rotation in the SOL Driven by Poloidal EB drift (cont.)
The same conclusion for EB flow in the
divertor: compensating parallel flows
should result in toroidal rotation
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

10. Parallel Flux Pattern in the SOL (so far …)
Parallel Ion
Pfirsh-Schlüter
Flow
(reverses with
Bt reversal) R
“uniform”
Flow due to
“Ballooning”
(Does not !
reverse with
Can be modelled by 2D codes without
additional assumptions
Requires assumptions
about perp. transport
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

11. Toroidal Rotation vs. Pfirsch-Schlüter Flow
(only exists in toroidal geometry, ~ r/R)
(present in cylindrical geometry) 
(rough theoretical estimate)
Toroidal
Rotation R
Pfirsch-
Schlüter
However, owing to the factor 2 in
and the sum of dpi/dr and Er terms,
and can be very
close near the midplane
The two mechanisms can be easily confused when measuring ion velocity
only near outer midplane
(accuracy in experimental evaluation of Er is poor)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

12. Toroidal Rotation vs. Pfirsch-Schlüter Flow (cont.)
JT-60U: Reversal of ion parallel flow near outer midplane with Bt reversal
(Asakura
et al., 2000)
Ion B
“Natural
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

13. Toroidal Rotation vs. Pfirsch-Schlüter Flow (cont.)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

14. Toroidal Rotation vs. Pfirsch-Schlüter Flow (cont.)
Alcator C-Mod
with
“Toroidal rotation as an explanation for plasma flow observations in the
Alcator C-Mod scrape-off layer” (LaBombard et al., 2003)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

15. Toroidal Rotation vs. Pfirsch-Schlüter Flow (cont.)
Competition between the two flows
is expected on the inboard side,
where they have different directions
In JT-60U, an Inner Mach Probe
was recently installed to establish
the flow pattern in the SOL
(Asakura et al., 2002)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

16. Toroidal Rotation vs. Pfirsch-Schlüter Flow (cont.)
Expected behaviour of the old probes, but:
In normal field plasmas, the Inner Mach Probe
showed the ion flow towards divertor, opposite
to the Pfirsch-Schlüter Flow across most of
the SOL (could also be affected, apart from the
Er/B toroidal rotation, by the sink to the target
due to its proximity to the divertor ?)
Near the separatrix, however, the flow reversed,
and was in the direction of the Pfirsch-Schlüter
Flow. This could be due to:
a) its “competitor” has zeroed (Er=0 at the
separatrix), or
b) “ionization driven flow reversal” (2D effect)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

17. Experiments on JET Erents et al., 2000 Normal Bt Rev. Bt
P-S flow
Normal Bt
Rotation
Flow towards inner divertor
Ballo-oning
Rev. Bt
Flow towards outer divertor
Large parallel velocity toward inner divertor in normal Bt plasmas
Reversal of the flow direction in reversed Bt plasma, but the flow is much smaller
Deposition of impurities (with formation of loosely bound surface layers) on the
inner target and large build up of carbon (and trapped tritium) at the inner divertor
louvers (Coad et al., 2001)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

18. Is There a Link Between the Flow and Impurity Deposition ?
Operation mostly in Normal
field configuration (with large
parallel flow)
Outer target – clean
Can large parallel ion flow
scoop impurities towards
the inner target by parallel
friction force ?
Pe=Pi=2.5MW
Prad=0.77MW
ns=1.11019m-3
Midplane coeff.
(constant in flux
space):
D=0.1 m2s-1
e=i=1 m2s
Vpinch=3 ms-1
Input parameters and computational grid for the modelled EDGE2D case 
Match with experimental target ne and
Te profiles achieved
All drift flows included
Modelling with EDGE2D code
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

19. Modelling with EDGE2D (drifts included)
Experiment
Code Modelling
Normal Bt
Rev. Bt
Reversal of the flow direction with Bt reversal can be modelled (attributed to both
toroidal rotation and Pfirsch-Schlüter flows)
More symmetric flow reversal than in experiment: Ballooning transport was not
incorporated into the code
Modelled Mach numbers are much smaller than in experiment. This includes the
difference in M’s between normal and reversed field directions
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

20. Modelling with EDGE2D (cont.)
EDGE2D so far can not reproduce large Mach numbers of parallel ion flow velocity measured in JET and other experiments (the same is true for JT-60U and UEDGE code results (Asakura et al., 2002)):
Neither the “ballooning” introduced into the code later,
No drift effects
result in sufficiently high flow velocities
More code work is required
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

21. ||  More theoretical work is required
Even if all radial particle flux goes throught
outer side, Mach numbers will be rather low
due to low sink to divertor (“baffle” on the
figure)
How can high M|| due to “ballooning” transport be generated ?
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

22. ||  More theoretical work is required (cont.)
M|| due to “ballooning” can be much higher if
the flux on the inside is negative, directed
inside the plasma
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

23. More theoretical work is required (cont.)
Scenario that could generate negative radial particle flux on the inboard side: blobs originating on the outboard side but propagating along field lines to the inboard side
EB drift
EB drift
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

24. Does this agree with experiment
Impact of the Flows on the Impurity Migration
It is clear that:
Neither the Rotation (which is toroidal)
No the Pfirsch-Schlüter Flow, which connects top and bottom of the flux surface
(along the field lines)
Can be responsible for impurity migration from outer to inner divertor (if there is one) R
Parallel Ion
Flow due to
“Ballooning”
(Does not !
reverse with
Bt reversal)
Only the flow caused by “ballooning” has the potential of dragging impurities from the outside to inside
This flow has the same direction for normal and reversed Bt.
Hence, IF only the above 3 mechanisms for
plasma flows are considered
AND IF we relate target impurity
deposition with SOL plasma flows
THEN we must expect a similar in-out
deposition asymmetry in reversed
as in normal field configuration
Does this agree with experiment
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

25. New JET Data (field reversal experiments) (Pitts et al., 2003)
Norm-Rev. field averaged flow: from outside to inside as before ( ballooning ?)
The difference (M_nor.Bt - M_rev.Bt) is the same as in earlier experiments
Shape of the M-number profile has been established; Field reversal (drift?) effects
small near the separatrix. Can be understood by assuming :
Er  0 at sep. (reducing rotation with Er/B),
Pfirsch-Schlüter Flow  0 at sep. (no P-S flow in the core + effect of viscosity)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

26. New JET Data (cont.) In reversed Bt plasmas, deposition of
impurities (creating surface layers) is found
on the outer target ! While the inner target
is clean
How important are SOL flows for
impurity behaviour in the divertor?
Can it be that in-out asymmetries in
the divertor itself play a crucial role?
Survace layers tend to be formed in
low Te plasmas
Divertor target can be cleaned of impurities in
high Te plasmas (by sputtering)
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

27. Divertor/Target Asymmetries
Expected even without drifts
Due to a number of factors: (geometrical: larger outer surface,
Shafranov shift, larger turbulence at low field side (ballooning)
more power goes to the SOL through outer surface, leading to
Te,inner < Te,outer
Pressure conservation along the field lines:
pe,inner = pe,outer 
ne,inner > ne,outer
Particle flux to the target target~ne(Te)1/2~pe(Te)-1/2
inner > outer
Inner target must be denser and cooler  more prone to impurity deposition
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

28. ne Influence of Bt Direction on Divertor Asymmetries – Major Trends:
Agreement between Experiment and Modelling with Drifts Included
ne distribution (from EDGE2D code)
normal Bt
reversed Bt ne
ne,inner > ne,outer
Te,i,inner < Te,i,outer
More symmetric distribution
of ne and Te
Drift effects (mainly EB dirft: (Stangeby et al, 1996) ) result in:
- further cooling of the inner divertor in normal Bt plasmas
- cooling of the outer divertor in reversed Bt plasmas more symmetric
distribution
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

29. Expected Formation of Surface Layersne
normal Bt:
on the inner target ne
reversed Bt:
not clear…
Reversal of asymmetries reported (JT-60U (Itami et al., 1992) ), but in JET, generally, they do not reverse
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

30. Helium Enrichment Studies in JET (Lehnen, Pitts et al., 2003)
Result of puffing He
Normal Bt:
more He reaches INNER
divertor
Reversed Bt:
more He reaches OUTER
Normal Bt data Not surprising:
Denser plasma at INNER target,
with higher recycling
Reversed Bt data: why more He
at OUTER target ?
He subdivertor pressure measured
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

31. Helium Enrichment Studies in JET (cont.)
Is there higher particle flux/ neutral recycling at OUTER target in reversed Bt ?
(Pitts et al., 2003)
Fairly symmetric recycling,
if not larger at the INNER
target
So what is pushing He
towards the OUTER target ?
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

32. Summary
SOL flow pattern is well established and the driving mechanisms are
reasonably well understood (at least, qualitatively)
More efforts are required to correctly model SOL flows with 2D codes (both on
the computational side and understanding underlying physics, including
turbulence)
No direct or indirect evidence exists that SOL flows are primarely responsible
for asymmetries in impurity target deposition / surface layer formation,
between INNER and OUTER targets
Results of reversed field experiments in JET with surface layer formation and
preferential He accummulation at the OUTER divertor target are not
understood. Better understanding of divertor asymmetries and related effects
may provide a clue
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

33. On the Results of Reversed Field Experiments
There is no obvious explanation why either impurity accumulation or surface
layers formation should occur at the OUTER target in reversed field
configurations, when the INNER target remains clean
Asymmetries between inner and outer divertor plasma parameters in these
particular experiments should be studied in more detail to see if the OUTER
target was denser and/or cooler than the inner one
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

34. SOL Flows Caused by Divertor Asymmetries
Higher recycling in the INNER divertor in normal Bt plasmas  neutrals flow from inner to outer divertor (Kukushkin et al., 2001)
Mass conservation results in the SOL plasma flow towards INNER and away from OUTER divertor  extra drag force on impurities towards inner divertor. The SOL flow can be increased by pumping (Asakura et al., 2002: in JT-60 detached plasmas with pumping, M|| at the entrance to inner divertor reached 0.7)
Can this flow reverse in reversed
Bt plasmas ? / Can the asymmetry
of neutrals recycling reverse ?
Neutral flux is not too large (only ~ 0.06 of recycled neutrals)
It can be blocked by a septum, and conflicting evidence exists on the role of septum in JET:
a) Maggi et al., 1999: septum can influence
divertor asymmetry - EDGE2D modelling
b) Rapp et al., 2003: septum doesn’t affect
plasma detachment at targets - experiment
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany

35. Toroidal Rotation in the SOL Driven by Poloidal EB drift (cont.)
The same conclusion for EB flow in the
divertor: compensating parallel flows
should result in toroidal rotation
Diamagnetic flows don’t contribute to
net toroidal rotation of the SOL
Larmor gyration
Vertical B and
Centrifugal drifts
A.V.Chankin, Zinnowitz Theory Meeting, – , Zinnowitz, Germany