The SWIM “Slow” MHD Campaign: Overview, MHD Plans and Accomplishments

1. The SWIM “Slow” MHD Campaign: Overview, MHD Plans and Accomplishments D. D. Schnack, T. Jenkins, J. Callen. C. Hegna. C. Sovinec, F. Ebrahimi University of Wisconsin, Madison, WI, E. Held, J.-Y. Ji, Utah State University, Logan, UT, S. Kruger,J. Carlson, Tech-X Corp., Boulder, CO

2. What to Get Done this Week • Begin dialog between MHD, RF, and CS researchers on “Slow MHD” problem • Provide update on MHD plans and progress • Get feedback from RF/ CS folks • Agree on technical plan and timeline • Produce report for PM addressing the following issues:

3. 0. What Problem are We Trying to Solve? O(1/) • Demonstrate proof of principle of stabilization of resistive islands with some RF model? • Demonstrate coupling between RF and MHD physics codes? • Demonstrate proof of principle of stabilization of resistive islands with coupled RF/MHD models?

4. Demonstrate stabilization of pre-existing (finite amplitude) NTM island with RF? • Demonstrate seeding, growth, and eventual RF stabilization of NTM island? • Understand physics of island stabilization (inner or outer regions)? • Evaluate efficacy of various experimental RF deposition scenarios?

5. Determine how much RF power is required for ITER? • All of the above? (Do we have the resources?) • Some of the above? (Must match to resources) • None of the above? (Then, what?)

6. What are MINIMUM Requirements to Satisfy SOW? O(1) • What is the technical plan for meeting this goal? Is it reasonable? • What resources are required, and are they available? • What is the timeline for meeting this goal? Is it reasonable?

7. What is Required to do the Problem “Better” O() • Reasonable technical plan? • Resources? • Reasonable timeline?

8. What is Required to do the Problem “Right” O(2) • Reasonable technical plan? • Resources? • Reasonable timeline?

9. RF/MHD Dialog Issues - 1 • Is the MHD plan reasonable? • What information does MHD want from RF? • What information can MHD give to RF? • What is the RF physics plan? • What information does RF want from MHD? • What information can RF give to MHD? • What RF codes are involved? • Are substantial modifications to RF codes required? • Island geometry?

10. RF/MHD Dialog Issues - 2 • Are there algorithmic issues that might affect numerical stability? • Can they be mitigated? • How do we envision the RF/MHD code coupling? • Strong coupling? (RF called from MHD) • Weak coupling? (Separate code execution) • What is the most efficient means of passing data? • Are there any CS obstacles? • Can they be mitigated?

11. Technical Approach • Recognize that problem is additive • Modified Rutherford equation: • Can approach problems in parallel • Don’t need to get NTM “right” before attacking RF • Can start with RF/tearing coupling

12. Implementation Plan (MHD) • I: Add RF source module and interface to NIMROD • II: Define “simple” RF closure (force on electrons) • III: ad hoc analytic source term (force on electrons) in Ohm’s law • Tearing mode stabilization => proof of principle • IV:Evolutionary equation for RF source • V:Revisit NTM calculations • Kruger/Hegna heuristic closure? • Collisional Braginskii nonlinear electron viscous stress tensor? • V: Couple to RF codes • VI: Throughout, refine theoretical closure models and implementations

13. Physics Issues (Kinetic Equation) • How to incorporate RF effects into fluid models? • Start with kinetic equation Quasi-linear diffusion tensor Output of RF codes

14. Force on electrons Heating Physics Issues (Closures) • Take moments • RF sources modify fluid equations RF produces no particles Existing closures are also modified! RF closures

15. Information (RF <==> MHD) • Chapman-Enskog-Like theory can produce closures, i.e., Maxwellian • Moments can be computed by numerical integration in velocity space once DQL is specified • DQL(v) produced at each mesh point by RF codes

16. RF/MHD Coupling • NIMROD produces n(r,t), T(r,t), B(r,t) => RF codes • RF codes produce DQL(r,v) on rays => interpolated to NIMROD grid • NIMROD integrates in v => moments of Q => force on electrons and modified moments • NIMROD produces n(r,t+t), T(r,t+t), B(r,t+t) • t +t => t • Go to 1 RF module. Presently has model Jrf(r,t).

17. Issues • What are the most appropriate fluid moments? • What is the most efficient way to compute them? • Are there any new numerical stability issues? • Can NTM growth and saturation be demonstrated? • How often does RF need to be updated? • How should data be passed between MHD and RF codes? • Do RF codes need to be modified (islands, etc)? • Do we need to go beyond ECCD? • ???

18. MHD Results • Electron force localized in poloidal plane, toroidally symmetric • Current spreads over flux surfaces • Demonstrated in cylinder and DIII-D geometry

19. Rutherford Linear Tearing Mode Stabilization by RF in DIII-D geometry(Tom Jenkins)

20. MHD Status • Closure procedure defined • Spitzer-like problem formulated • Data required from RF modules defined • General source modules and interfaces added to NIMROD • Simple axi-symmetric source implemented • Stabilization of 2/1 resistive tearing mode demonstrated in DIII-D geometry • Conversations with RF physicists beginning

21. More About the Workshop • Informal! • Purpose is to have a dialog, not to impress with latest results! • 2-way communication • Allow plenty of time for discussion • Discussion leaders: Take notes! • Thursday morning: Produce coordinated technical plan and timeline • Will all be input for report to PM