# Presentation: 146997

## 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

## 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 M~1 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.

## Simulation of large parallel plasma flows in the SOL of NSTX tokamak

## 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

- Parallel plasma flows cause the “1st order” effect on edge plasma parameters by filling up the inner divertor by particles and energy
- 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.
- The physics mechanisms of flow generation and acceleration/de-acceleration should be understood , e.g. for the flow control purposes.
- These flows carry and re-deposit the material, tritium, and can push dust into core or at wall as a bullet.

- .

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

-   Classical plasma drifts
-   Cross-field transport asymmetry
-   Magnetic configuration

## 2D diffusive-and-convective model for cross-field plasma transport suggests the in/out asymmetry

**Γ****┴****(********,θ)= –D****┴****(********,θ) ∂n/∂r  +  n V****┴****conv**** ****(********,θ)**

- Poloidal profiles of **D****┴****(********,θ)** , **χ****┴****(********,θ)** , **V****┴****conv (********,θ)** 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.

- The edge physics code **adjusts**
-  **D****┴****(********,θ)** , **χ****┴****(********,θ)** , **V****┴****conv (********,θ)** profiles
- to match a set of experimental data.

- Anomalous cross-field plasma flux:

## Asymmetries in LSN magnetic configuration of NSTX

**Shot  #109033**

- 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.

## UEDGE model

- multi-species (D+C)
- Anomalous cross-field transport
- Ballooning-like asymmetry is prescribed to cross-field diffusivities (D, , , )
- 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.
- Ion charge states have different sign and amplitude of Vconv.
- Diffusive transport dominates on confined magnetic flux surfaces, whereas convection dominates in the SOL
- 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
-             as=TC(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

## 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
- HFS/LFS asymmetry factor of TC is     as=1/20
- Real flux asymmetry at the separatrix is LFS/|HFS|=33, LFS=1350A, HFS=40A.

## To match experimental data, anomalous transport coefficients D, , and Vconv should vary also radially in the ψN-space

- D is a weakly increasing with ψ . It is typically around 0.6m2/s at ψ=1.
- χ  is strongly decreasing function by factor 5. In L-mode, typically χ=15-20 m2/s at ψ=0.7.
- Vconv strongly increases with ψ (in L-mode, from zero at ψ=0.7 to 10-40m/s at ψ=1 and further to 100-200m/s at the wall.

## 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

## The plasma flow up to M=0.8 is predicted by UEDGE at the inner mid-plane of NSTX 

- Here magnetic flux surfaces are mapped to the outboard mid-plane.
- The inner SOL is ~2.5X broader.

- 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 M||=V||/sqrt[(te+ti)/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 doesn’t depend on boundary conditions at the divertor plates.

## Parallel plasma flow in the SOL at the inner mid-plane carries significant particle flux

- Here magnetic flux surfaces are mapped to the outboard mid-plane. The inner SOL is ~2.5X broader.

- 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||.

## At the outboard mid-plane, the parallel flow is directed to inboard but is relatively quiescent <V||>~2.5km/s, <M||>~0.03

## 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

**Outer mid-plane**

**Inner midplane**

**Top**

- =1.78 cm

- =0.5 cm

**Inner divertor**

**Outer divertor**

## 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.

**Recycling at the outboard chamber wall**

**Leakage from inner divertor**

**Gas puff and associated**
**recycling**

## Flow direction pattern in the case of large flows typically contains stationary “zonal” flows. 

**Clockwise**

**Counter**
**clockwise**

**Counter**
**clockwise**

- Attached inner divertor

- Detached inner divertor

**Clockwise**

## 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**

**Inner**
**midplane**

**Outer**
**midplane**

## 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**

## Magnetic configuration affects the far SOL flow. V|| and M|| closely follow the Btotal variation

**C-Mod**

**NSTX**

## 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)

## “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.

## Modeling of dust particle dynamics and transport in NSTX tokamak

## 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.

## 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 Rd**3** d
- Equations of motion:
-      d**r**/dt  = **v  **         + Cd,wall**r**  + Cd,turb**r**
- md d**v**/dt = **F**d,plasma  + Cd,wall**v** + Cd,turb**v **
- Forces applied to dust particle from plasma:
**F**d,plasma = Rd**2**mivtirNni(**V**plas-**v**) - 4Rd**2** eZd**E**plas + md**g** + etc
- Dust particle charge is calculated from equilibrium:
- e**2**Zd/Rd=Te
- Plasma flow velocity **V**plas and electric field **E**plas 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.

## 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:
- d[CdmdTd]/dt = 4Rd**2** {Qplas - dsb(Td**4** -Tw**4**) - 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.

## 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.

## Dust particles are very mobile in NSTX 

**NSTX #109033, L-mode, detached inner divertor**

## 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**

## Velocity of dust particle is determined by the resulting force 

- Toroidal velocity component Vθ is dominant.
- Due to curvature, Vθ can give raise to Vr,Vz.
- The sign and magnitude of Vθ 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

**1****μ****m**

## Dust heats up to sublimation temperatures when it passes through hot plasma regions

## Dust particles lost the mass mainly due to sublimation and collisions with walls 

## Light particles accelerate to high speed but their lifetime is short. Heavy particles move slowly but on a longer distance

## Reflection probability of dust particle from tiles is vital parameter in dust transport

## 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**

## 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.