1. Kansas Annual NSF EPSCoR Statewide Conference Wichita, KSJanuary 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 MHD system at low Re M Explicit discretization EOS for partially ionized gas Free surface flow System size ~ cm, grid size ~ 0.1 mm Courtesy of Ravi Samtaney, PPPL Tokamak (ITER) Fueling Fuel pellet ablation Striation instabilities Killer pellet / gas ball for plasma disruption mitigation

3. Schematic of pellet ablation in a magnetic field Schematic of processes in the ablation cloud CloudPlasma Sheath boundary  (z) Sheath Fluxes

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

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

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

7. 1.Spherical model Excellent agreement with NGS model 2.Axisymmetric pure hydro model Geometric effect found to be minor (Reduction by 18% rather than 50%) 3.Plasma shielding without rotation Subsonic ablation flow everywhere in the channel Ablation rate depending on the ramp-up time 4.Cloud charging and rotation Supersonic rotation causes wider channel and faster ablation Ablation rate independent of the ramp-up time Simulation results of pellet ablation Spherical modelAxis. hydro modelPlasma shielding

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

9. -.-.-t w = 5  s, n e = 1.6  10 13 cm -3 ___t w = 10  s, n e = 10 14 cm -3 -----t w = 10  s, n e = 1.6  10 13 cm -3 Formation of the ablation channel and ablation rate strongly depends on plasma pedestal properties and pellet velocity. Plasma shielding without rotation

10. Supersonic rotation of the ablation channel Cloud charging and rotation Isosurfaces of the rotational Mach number in the pellet ablation flow Density redistribution in the ablation channel Steady-state pressure distribution in the widened ablation channel

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

12. Shrinking pellet: tumbling pellet model “Pancake” pellet 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. Tumbling spherical pellet

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

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