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

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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

- 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:

- 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?

- 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?

- 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?)

- 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?

- Reasonable technical plan?
- Resources?
- Reasonable timeline?

- Reasonable technical plan?
- Resources?
- Reasonable timeline?

- 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?

- 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?

- 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

- 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

- How to incorporate RF effects into fluid models?
- Start with kinetic equation

Quasi-linear diffusion tensor

Output of RF codes

Force on electrons

Heating

- Take moments
- RF sources modify fluid equations

RF produces no particles

Existing closures are also modified!

RF closures

- 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

- 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).

- 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?
- ???

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

Rutherford

Linear

- 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

- 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