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*

***Energetic particle sources such as alpha particles or fast ions from
neutral beams lead to non-Maxwellian particle distributions in
laboratory plasmas. Such distributions are also driven by wave-plasma
interactions, either from natural turbulence or from externally-driven
sources in both fusion and natural plasmas. These distributions can
change plasma stability and transport properties in addition to the
propagation and absorption characteristics of the waves that may have
created the initial distortion. Thus modeling wave propagation in
non-Maxwellian plasmas is a key element in understanding the
interactions of waves in plasmas. It is a major computational challenge
because such distribution functions add an additional layer of
computation to the already difficult problem. In parallel, the need for
modeling of short wavelength phenomena driven by lower hybrid waves in
2-D and fast waves in 3-D has pushed the need to solve ever larger
systems.***

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%)

![](media/image1.wmf){width="6.208333333333333in"
height="2.5833333333333335in"}*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>