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

1. 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

2. 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

3. Sheath Fluxes Sheath boundary Cloud Plasma f(z) Schematic of pellet ablation in a magnetic field Schematic of processes in the ablation cloud

4. MHD at low magnetic Reynolds numbers Heat deposition of hot electron Equation of state for partially ionized gas Elliptic equation

5. Axisymmetric MHD with low ReM approximation Centripetal force Nonlinear mixed Dirichlet-Neumann boundary condition

6. Transient radial current approximation f(r,z) depends explicitly on the line-by-line cloud opacity u.

7. 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

8. Plasma shielding without rotation Mach number distribution Double transonic flow evolves to subsonic flow

9. 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

10. 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

11. Fixed pellet: effect of ramp up time • Gsteady of a rotating cloud is independent of tramp • G(tramp) < Gsteady • G(tramp) increases with tramp • Fast pellet • Short ramp-up distance

12. 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

13. Shrinking pellet: DIII-D temperature profile DIII-D Temperature and Density Profile G from simulation agrees with 0.8 GNGS

14. 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