THE OFFICE OF NONPROLIFERATION

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Kansas Annual NSF EPSCoR Statewide
ConferenceWichita, KS January 12-13, 2012

• Simulation of pellet ablation in DIII-D
• Tianshi Lu
• Patrick Rinker
• Department of Mathematics
• Wichita State University
• In collaboration with
• Roman Samulyak, Stony Brook University
• Paul Parks, General Atomics

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Model for pellet ablation in tokamak

• Tokamak (ITER) Fueling
• Fuel pellet ablation
• Striation instabilities
• Killer pellet / gas ball for plasma disruption
  mitigation

Courtesy of Ravi Samtaney, PPPL

• MHD system at low ReM
• Explicit discretization
• EOS for partially ionized gas
• Free surface flow
• System size cm, grid size 0.1 mm

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Schematic of pellet ablation in a magnetic field
Schematic of processes in the ablation cloud
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MHD at low magnetic Reynolds numbers
Heat deposition of hot electron
Equation of state for partially ionized gas
Elliptic equation
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Axisymmetric MHD with low ReM approximation
Centripetal force
Nonlinear mixed Dirichlet-Neumann boundary
condition
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Transient radial current approximation
f(r,z) depends explicitly on the line-by-line
cloud opacity u?.
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Simulation results of pellet ablation

• Spherical model
• Excellent agreement with NGS model
• Axisymmetric pure hydro model
• Geometric effect found to be minor (Reduction by
  18 rather than 50)
• Plasma shielding without rotation
• Subsonic ablation flow everywhere in the channel
• Ablation rate depending on the ramp-up time
• Cloud charging and rotation
• Supersonic rotation causes wider channel and
  faster ablation
• Ablation rate independent of the ramp-up time

Spherical model
Axis. hydro model
Plasma shielding
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Plasma shielding without rotation
Mach number distribution
Double transonic flow evolves to subsonic flow
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Plasma shielding without rotation
Formation of the ablation channel and ablation
rate strongly depends on plasma pedestal
properties and pellet velocity.
-.-.- tw 5 ms, ne 1.6 ? 1013 cm-3 ___ tw
10 ms, ne 1014 cm-3 ----- tw 10 ms, ne 1.6
? 1013 cm-3
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Cloud charging and rotation
Supersonic rotation of the ablation channel
Density redistribution in the ablation channel
Steady-state pressure distribution in the widened
ablation channel
Isosurfaces of the rotational Mach number in the
pellet ablation flow
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Fixed pellet effect of ramp up time

• Gsteady of a rotating cloud is independent of
  tramp
• G(tramp) lt Gsteady
• G(tramp) increases with tramp
• Fast pellet
• Short ramp-up distance

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Shrinking pellet tumbling pellet model

• Due to anisotropic heating, the pellet would
  evolve to a pancake shape.
• In reality, the pellet is tumbling as it enters
  the tokamak, so its shape remains approximately
  spherical.
• In the simulation, the pellet shrinking velocity
  is averaged over the surface to maintain the
  spherical shape.

Pancake pellet
Tumbling spherical pellet
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Shrinking pellet DIII-D temperature profile
DIII-D Temperature and Density Profile
G from simulation agrees with 0.8 GNGS
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Conclusions and future work

• Conclusions
• Supersonic rotation causes wider channel and
  faster ablation
• Good agreement with NGS model for DIII-D profile
• Smaller Ablation rate during fast ramp-up
• Future work
• Inclusion of grad-B drift in the simulation
• Non-transient radial current for smaller B field
  finite spin up
• Mechanism of striation