1. NIMROD Simulations of a DIII-D Plasma Disruption S. Kruger, D. Schnack (SAIC) April 27, 2004 Sherwood Fusion Theory Meeting, Missoula, MT

2. DIII-D SHOT #87009 Observes a Plasma Disruption During Neutral Beam Heating At High Plasma Beta Callen et.al, Phys. Plasmas 6, 2963 (1999)

3. Free-Boundary Simulations Models “Halo” Plasma as Cold, Low Density Plasma Typical DIII-D Parameters: T core ~10 keV T sep ~1-10 eV n core ~5x10 19 m -3 n sep ~ 10 18 m -3 Spitzer resistivity:  ~T -3/2 –Suppresses currents on open field lines –Large gradients 3 dimensionally Requires accurate calculation of anisotropic thermal conduction to distinguish between open and closed field lines

4. Goal of Simulation is to Model Power Distribution On Limiter during Disruption Plasma-wall interactions are complex and beyond the scope of this simulation Boundary conditions are applied at the vacuum vessel, NOT the limiter. –Vacuum vessel is conductor –Limiter is an insulator This is accurate for magnetic field: –B n =constant at conducting wall –B n can evolve at graphite limiter No boundary conditions are applied at limiter for velocity or temperatures. –This allows fluxes of mass and heat through limiter –Normal heat flux is computed at limiter boundary

5. Free-Boundary Simulations Based on EFIT Reconstruction Pressure raised 8.7% above best fit EFIT Above ideal MHD marginal stability limit Simulation includes: –n = 0, 1, 2 –Anisotropic heat conduction (with no T dependence)  par  perp   Ideal modes grow with finite resistivity (S = 10 5 )

6. First Macroscopic Feature is 2/1 Helical Temperature Perturbation Due to Magnetic Island Island result of 1/1 and 3/1 ideal perturbation causing forced reconnection

7. Magnetic Field Rapidly Goes Stochastic with Field Lines Filling Large Volume of Plasma Region near divertor goes stochastic first Islands interact and cause stochasticity Rapid loss of thermal energy results. Heat flux on divertor rises

8. Maximum Heat Flux in Calculation Shows Poloidal And Toroidal Localization Heat localized to divertor regions and outboard midplane Toroidal localization presents engineering challenges - divertors typically designed for steady-state symmetric heat fluxes Qualitatively agrees with many observed disruptions on DIII-D

9. Investigate Topology At Time of Maximum Heat Flux Regions of hottest heat flux are connected topologically Single field line passes through region of large perpendicular heat flux. Rapid equilibration carries it to divertor Complete topology complicated due to differences of open field lines and closed field lines

10. Initial Simulations Above Ideal Marginal Stability Point Look Promising Qualitative agreement with experiment: ~200 microsecond time scale, heat lost preferentially at divertor. Plasma current increases due to rapid reconnection events changing internal inductance Wall interactions are not a dominant force in obtaining qualitative agreement for these types of disruptions.

11. Future Directions Direct comparison of code against experimental diagnostics Increased accuracy of MHD model –Temperature-dependent thermal diffusivities –More aggressive parameters –Resistive wall B.C. and external circuit modeling Extension of fluid models –Two-fluid modeling –Electron heat flux using integral closures –Energetic particles Simulations of different devices to understand how magnetic configuration affects the wall power loading

12. Conclusions NIMROD’s Advanced Computational Techniques Allows Simulations Never Before Possible Heating through  limit shows super-exponential growth, in agreement with experiment and theory in fixed boundary cases. Simulation of disruption event shows qualitative agreement with experiment. Loss of internal energy is due to rapid stochastization of the field, and not a violent shift of the plasma into the wall. Heat flux is localized poloidally and toroidally as plasma localizes the perpendicular heat flux, and the parallel heat flux transports it to the wall.