Simulation of convective cross-field transport, toroidal plasma flows, and dust dynamics in NSTX with UEDGE and DUSTT codes

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Simulation of convective cross-field transport,
toroidal plasma flows, and dust dynamics in NSTX
with UEDGE and DUSTT codes

• A.Yu. Pigarov, S.I. Krasheninnikov, J.A. Boedo

University of California at San Diego, La Jolla CA
R. Bell, S. Paul, A. Roquemore PPPL, Princeton
NJ V. Soukhanovskii LLNL, Livermore CA R.
Maingi, C. Bush ORNL, Oak Ridge TN
Presented at the 47th DPP APS Meeting, October
24-26, Denver Colorado 2005
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Abstract
Fast intermittent convective cross-field
transport has been observed in the outer SOL of
NSTX and other tokamaks. It is expected that such
kind of transport has ballooning like asymmetry
and can be a cause of large parallel plasma flows
in SOL. With UEDGE code, we perform
multi-species fluid simulations in the LSN
magnetic configuration of NSTX L-mode plasma
using poloidally asymmetric profiles for
anomalous transport coefficients and convective
velocities and for some boundary conditions on
the chamber wall. We present modeling results
on SOL plasma flows originating from outer
mid-plane, moving into inner divertor, and
reaching M1 at inner mid-plane. The UEDGE
analysis of experimental NSTX data with newly
developed 3D diagnostic tools (e.g. for
bolometry) will be given. Also, as measured,
dust particulates of micron size are unavoidably
present in NSTX. We present results on simulation
of dust dynamics, transport, and ablation with
DUSTT code. The possible effect of dust on NSTX
divertor plasma profiles is discussed. The
research was supported by DoE Grants NRG5025 and
DE-FG02-04ER54739 at UCSD.
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Simulation of large parallel plasma flows in the
SOL of NSTX tokamak
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Large parallel plasma flows have been observed
experimentally in the SOL of several tokamaks. It
is expected that such flows have crucial effect
on edge plasma parameters in NSTX

1. Parallel plasma flows cause the 1st order
   effect on edge plasma parameters by filling up
   the inner divertor by particles and energy
2. The flows can be the byproduct of natural
   asymmetries in0 magnetic configuration and
   cross-field transport. If so, the flows should be
   expected in ITER, as well.
3. The physics mechanisms of flow generation and
   acceleration/de-acceleration should be understood
   , e.g. for the flow control purposes.
4. These flows carry and re-deposit the material,
   tritium, and can push dust into core or at wall
   as a bullet.

• .

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Driving mechanisms for near-sonic plasma flows in
the tokamak SOL

1. Classical plasma drifts
2. Cross-field transport asymmetry
3. Magnetic configuration

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2D diffusive-and-convective model for cross-field
plasma transport suggests the in/out asymmetry
Anomalous cross-field plasma flux
G-(?,?) D-(?,?) ?n/?r n V-conv (?,?)
The edge physics code adjusts D-(?,?) , ?-(?,?)
, V-conv (?,?) profiles to match a set of
experimental data.
Poloidal profiles of D-(?,?) , ?-(?,?) , V-conv
(?,?) are asymmetric. They mimic the ballooning
type of cross-field transport Vconv, D?, ??
vary poloidally (3-10)X and are peaked at the
outer mid-plane.
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Asymmetries in LSN magnetic configuration of NSTX
In the Lower Single Null magnetic configuration,
the surface area connected to the inboard SOL is
much (10X) smaller than the area connected to
the outboard SOL. Total magnetic field strength
at the inner SOL mid-plane is 8-10X higher than
at the outer SOL mid-plane.
Shot 109033
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UEDGE model

1. multi-species (DC)
2. Anomalous cross-field transport
3. Ballooning-like asymmetry is prescribed to
   cross-field diffusivities (D, ?, ?, ?)
4. Intermittent (e.g. blobs) transport effect is
   modeled by means of anomalous convective
   velocity Vconv for ion species. The 2D profile
   prescribed Vconv is ballooning like.
5. Ion charge states have different sign and
   amplitude of Vconv.
6. Diffusive transport dominates on confined
   magnetic flux surfaces, whereas convection
   dominates in the SOL
7. No classical drifts were switched on in these
   calculations.

Ballooning-like profile for transport
coefficient (TC) 1) is given in magnetic flux
coordinates (?,?) 2) is characterized by
asymmetry parameter
?asTC(LFS)/TC(HFS) 3) is peaked at the outer
mid-plane 4) is constant along mfl at the HFS
5) is given by radial profile prescribed at
outer mid-plane
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Experimental data for typical medium density
L-mode shot in NSTX is reasonably well fitted by
UEDGE in the case when all transport
diffusivities/velocities are strongly HFS/LFS
asymmetric
In the obtained UEDGE solution Cross-field
transport at the LFS mid-plane is predominantly
convective Vconv(sep)6m/s, Vconv(wall)100m/s HF
S/LFS asymmetry factor of TC is
?as1/20 Real flux asymmetry at the separatrix
is ?LFS/?HFS33, ?LFS1350A, ?HFS40A.
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To match experimental data, anomalous transport
coefficients D?, ??, and Vconv? should vary also
radially in the ?N-space
D? is a weakly increasing with ? . It is
typically around 0.6m2/s at ?1. ? ? is strongly
decreasing function by factor 5. In L-mode,
typically ?15-20 m2/s at ?0.7. Vconv strongly
increases with ? (in L-mode, from zero at ?0.7
to 10-40m/s at ?1 and further to 100-200m/s at
the wall.
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Important features of NSTX edge plasma are well
reproduced with UEDGE

• Intense gas puff provides deep core plasma
  fueling at the rate higher than NBI fueling rate
  consistent with observed core density increase
• 2) Strong in/out asymmetry in radial plasma
  profiles and in plasma heat flows
• 3) Far-SOL shoulders and large mid-plane
  pressure indicative of main chamber recycling

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The plasma flow up to M0.8 is predicted by UEDGE
at the inner mid-plane of NSTX
At the inner mid-plane, plasma in the entire SOL
is moving toward the inner divertor
plate. Parallel plasma velocity V is 10-25
km/s. V and MV/sqrt(teti)/mD are
increasing toward the chamber wall. In the far
SOL, M increases mostly because of increase in
V. V attained at inner mid-plane doesnt
depend on boundary conditions at the divertor
plates.
Here magnetic flux surfaces are mapped to the
outboard mid-plane. The inner SOL is 2.5X
broader.
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Parallel plasma flow in the SOL at the inner
mid-plane carries significant particle flux
The averaged flux density is Flux 7 kA/m tends
to be constant over the SOL width. The integral
flux corresponds to few hundred Amperes flowing
toward the inner divertor. It is much higher than
the separatrix flux coupled to the inboard. The
high M flow is near the wall. The higher the
Btot, the higher the M. Plasma temperature in
the far SOL is relatively flat due to fast
cross-field convection, so M increases
primarily due to increase in V.
Here magnetic flux surfaces are mapped to the
outboard mid-plane. The inner SOL is 2.5X
broader.
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At the outboard mid-plane, the parallel flow is
directed to inboard but is relatively quiescent
ltVgt2.5km/s, ltMgt0.03
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Parallel plasma velocity increases all the way
from the outer to the inner mid-plane. In
spherical tori, the maximum of M is around the
inner mid-plane
Inner midplane
Outer mid-plane
Top
Inner divertor
Outer divertor
?1.78 cm
?0.5 cm
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Plasma flow ends at the inner divertor plates.
The equivalent amount of neutral particles leaks
from the inner divertor into the core through the
separatrix.
Leakage from inner divertor
Recycling at the outboard chamber wall
Gas puff and associated recycling
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Flow direction pattern in the case of large flows
typically contains stationary zonal flows.
Counter clockwise
Counter clockwise
Clockwise
Clockwise
Attached inner divertor
Detached inner divertor
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In C-MOD, plasma pressure is constant along mfls
in HFS. Pressure hill at LFS midplane is due to
ballooning transport in the far SOL, it
accelerates plasma toward the plates. Similar
profiles are in NSTX.
Near separatrix
Far SOL
Inner plate
Outer plate
Outer midplane
Inner midplane
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V and M is peaked at the inner mid-plane in
spherical torus NSTX. This can be attributed to
peculiarities of magnetic configuration causing
nozzle-like effects
Inner mid-plane position
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Magnetic configuration affects the far SOL flow.
V and M closely follow the Btotal variation
NSTX
C-Mod
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Cylindrical symmetry tends to wash out plasma
flows (i.e. the case of small flow asymmetry and
constant flux tube cross-section).
Real tokamak magnetic field
Cylindrical case (constant toroidal field)
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Big picture of large plasma flows in LSN

• Based on UEDGE simulations of edge plasma
  transport in the single-null magnetic
  configuration of C-Mod, DIII-D, NSTX tokamaks, we
  obtain the following "big picture" of the origin
  of near-sonic flows in the SOL
• ?The strong ballooning-like transport causes
  large cross-field plasma fluxes at the outer side
  that results in HFS/LFS asymmetry of plasma
  parameters.
• ? A key component is intermittent convective
  transport (e.g. blobs), which brings plasma
  density, energy, and momentum into the far SOL
  region.
• ? Since plasma in divertor regions connected to
  the far SOL is weak, it does not build up a high
  pressure due to recycling processes (as plasma
  near separatrix does) and does not cause
  stagnation of plasma flow.
• Therefore, plasma ejected into the far SOL on the
  LFS flows almost freely into the inner and outer
  divertors with Mach about unity.
• The tokamak magnetic configuration also affected
  the parallel plasma flow. The HFS/LFS asymmetry
  in magnetic field causes variation of the
  cross-section of effective magnetic tube in the
  SOL and the corresponding change in the parallel
  flow velocity.
• Combined effects of cross-field transport
  asymmetry, configuration, and classical drifts
  should be studied.

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Modeling of dust particle dynamics and transport
in NSTX tokamak
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Dust Transport (DUSTT) code
The code simulates the 3D transport of dust
particles (intrinsic and injected dusts) in
plasmas. It calculates the impurity profiles
associated with dust evaporation and related
radiation emissivity for dust diagnostics. The
code is designed to be coupled to edge-plasma
transport code UEDGE (T. Rognlien, LLNL) in order
to study self-consistently the effects of dusts
on plasma parameters, plasma contamination by
impurities, and erosion/deposition in tokamaks
and linear devices. On the final stage of
development, the code should incorporate the
detailed models for dust generation, acceleration
in magnetized plasma sheath, transport in edge
plasma, collisions with walls and
micro-turbulences, surface charging, and ablation
(and other effects which may be important but we
do not know about them yet). We encourage people
to contribute.
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Underlying physics equation
DUSTT solves a set of coupled differential
equations for temporal evolution of radius-vector
r, velocity v, temperature Td, and size Rd of
dust particle. Assume that particle is
spherical md 4/3 ?Rd3 ?d Equations of
motion dr/dt v Cd,wall?r
Cd,turb?r md dv/dt Fd,plasma Cd,wall?v
Cd,turb?v Forces applied to dust particle from
plasma Fd,plasma ??Rd2mivtirNni(Vplas-v) -
4?Rd2 eZdEplas mdg etc Dust particle charge
is calculated from equilibrium e2Zd/Rd?Te
Plasma flow velocity Vplas and electric field
Eplas vectors and Te, ni are obtained from
UEDGE. Operators Cd,wall and Cd,turb describe
the change in trajectory due to collisions with
wall and plasma micro-turbulence.
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Evaporation model for dust in plasma
The radius Rd of spherical particle decreases in
time as ?d dRd/dt - ms?s The specific fluxes
?s of particles with mass ms out from dust are
due to physical and chemical sputtering and
radiation enhanced sublimation caused by ions and
neutrals as well as due to thermal
sublimation. Under assumption that temperature
profile inside the dust particle is flat, the
surface temperature Td evolves in time as
dCdmdTd/dt 4?Rd2 Qplas - ?d?sb(Td4 -Tw4) -
Gs?s The heat flux Qplas absorbed by particle
is due to (i) kinetic energy transfer from plasma
ions and electrons and from neutrals, (ii)
release of plasma potential energy, and (iii)
absorption of plasma radiation.
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Numerical model
The DUSTT code operates on 2D curvilinear
non-uniform mesh based on MHD equilibrium and
generated by UEDGE. Equations of dust particle
motion are solved based on toroidal symmetry of
tokamak. Plasma parameters are assumed be
constant within a mesh cell. We use simple
explicit solver for a system of differential
equations. The Monte Carlo method is used to
treat the dust collisions with material surfaces
and with plasma micro-turbulences. The Monte
Carlo method is also employed to perform
averaging over an ensemble of test dust
particles. The initial dust parameters (birth
point, velocity vector, mass, radius, and etc)
are scored using model distribution functions.
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Dust particles are very mobile in NSTX
NSTX 109033, L-mode, detached inner divertor
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Dust particles preferentially move in the
direction of plasma flow. The flow directions
predicted by DUSTT on inner and outer legs are
opposite in agreement with experiment. The
trajectory is elongated in toroidal direction.
Originating from inner strike point
Originating from outer strike point
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Velocity of dust particle is determined by the
resulting force
Toroidal velocity component V? is dominant. Due
to curvature, V? can give raise to Vr,Vz. The
sign and magnitude of V? are very sensitive to
plasma recycling and flows. In hot plasma
regions, a micron size particle can be
accelerated up to few hundred m/s. The steps are
due to collisions with walls
1µm
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Dust heats up to sublimation temperatures when it
passes through hot plasma regions
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Dust particles lost the mass mainly due to
sublimation and collisions with walls
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Light particles accelerate to high speed but
their lifetime is short. Heavy particles move
slowly but on a longer distance
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Reflection probability of dust particle from
tiles is vital parameter in dust transport
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Due to curvature the dust particle can gain
significant radial velocity at the inner midplane
as well as extra wall collisions at the outer
midplane
Inner mid-plane
Outer mid-plane
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We plan to validate the DUSTT code against
experiments in various tokamaks, in particular,
the experiment on multi-view imaging of intrinsic
and injected dust particles with fast cameras in
NSTX.
With newly developed DUSTT code, we studied the
dust particle dynamics using realistic plasma
profiles obtained by UEDGE for NSTX tokamak. The
results showed that dust particles are very
mobile. The dusts can be accelerated to 10m/s
(10µm) up to 1 km/s (0.1 µm) and some can travel
to a distance about a meter. Our code reproduced
an important features of recent tokamak plasma
experiments near divertor plate the dusts
preferentially move in the direction of plasma
flow the preferential directions of dust are
opposite on inner and outer plates. In hot
plasma regions dusts heat up above 3000K. The
dominant mechanisms for dust mass loss are
thermal sublimation and collisions with walls.