Wave-Plasma Interactions: Non-Maxwellian Distributions and High Resolution in 2-D and 3-D

D.B. Batchelor, L.A. Berry, M.D. Carter, E. F. Jaeger, E. D'Azevedo—ORNL
C.K. Phillips, H. Okuda—PPPL, R. Dumont—(now CEA) P.T. Bonoli, J. C. Wright—MIT
D.N. Smithe—Mission Research Corporation, R.W. Harvey—CompX
D.A. D'Ippolito, J.R. Myra—Lodestar Research Corporation

Summary

Non-Maxwellian particle distribution functions are a common phenomenon is both laboratory and natural plasmas. Fusion alpha particles and the energetic neutral beams used for plasma heating both lead to such distributions. Similar distributions are observed in space plasmas, e.g., the solar corona. In this case plasma turbulence is the likely source. For sufficiently high powers, wave sources used for plasma heating and control can also drive non-Maxwellian distributions. In all cases, the perturbed functions can lead to very different plasma wave characteristics. New modes are possible, and wave absorption can increase or decrease with respect to the equivalent Maxwellian. In addition, plasma stability can either be enhanced or degraded.

The computational challenge is twofold. First we must replace the analytic plasma conductivity at the center of the wave calculation with a 2-D numerical integral in velocity. This step must be carefully optimized because it now dominates the overall calculation. This step has been accomplished and runs are producing important insights. Second, because the distribution function and waves couple nonlinearly, the models must be coupled and iterated. This effort is under way.

Depending on the resolution, ~10,000 processor-hours are needed on the NERSC Seaborg computer for a single run. 2-D modeling with non-Maxwellian plasma components provides the capability to address a wide range of new problems. They include plasma stabilization with RF-driven fast ion tails and parasitic absorption of heating and current drive power by (in ITER) alpha particles and (in present experiments). neutral beam fast ions

The results from an AORSA2D run for a National Spherical Tokamak (NSTX) discharge with neutral beam heating are shown on the next page. The plasma conductivity for the bulk electron and hydrogen components is computed with the standard analytical model, while the deuterium beam component contribution uses a distribution function calculated with the CQL3D Fokker-Plank code. The net power deposition for the two cases is roughly the same, but the radial profiles are significantly different. The non-Maxwellian case has much sharper absorption peaks at the ion cyclotron frequency harmonics (n = 10, 11, 12) than the equivalent Maxwellian. Subsequent, nonlinear evolution of the fast-ion distribution function is much more likely for this latter case.

Non-Maxwellian (P D = 56%)	Equivalent Maxwellian (P D = 63%)
High-harmonic fast wave power deposition for NXTX. On the left is the non-Maxwellian response calculated using a distribution function that was calculated with the CQL3D model. On the right is the Maxwellian response with the same average energy and density for the deuterium fast ions. [ NSTX shot 108251 (Rosenberg: invited APS talk, 2003)]

The second area of emphasis in the RF-Plasma Project is higher resolution calculations for both 2-D and 3-D. Higher resolutions have been achieved in both dimensionalities. The motivation for the 2-D effort, using the TORIC code, is to understand the role of full wave effects on the propagation of lower hybrid waves with mm-wave lengths. Previous calculations have employed geometrical optics, ray-tracing calculations. Experimental observations have suggested (as one hypothesis) that wave absorption must be stronger than ray tracing indicates. The 2-D TORIC calculations do suggest that diffraction is indeed leading to stronger, more localized lower hybrid absorption, thus suggesting that full-wave effects are important even though the wave lengths are very short. The 3-D calculations are required for understanding RF plasma heating in stellarators. Even with the largest available computers, such calculations were not possible until the problem was transformed to configuration space, allowing the explicit elimination of unknowns that were in the solution domain but inside metal structure and thus known to be zero. These calculations have been central to design of the RF system for the proposed Quasi-Poloidal Stellarator.

The project's near-term plans have two thrusts. First, we will continue the tasks needed to “close the loop” and self-consistently model wave propagation and the resulting non-Maxwellian particle distribution functions. The major computational challenge will be to iteratively couple the AORSA2D model with the distribution function package (CQL3D).

Second, we will continue our effort to understand the characteristics of lower hybrid propagation in 2-D in order to understand the impact of full wave modeling on the wave absorption, i.e., what is the role of diffraction in closing the spectral gap.

For further information on this subject contact:
Dr. Donald B. Batchelor, Principal Investigator
Oak Ridge National Laboratory
Phone: (865) 574-1288
batchelordb@ornl.gov

back to project page