Numerical Calculations of Wave-Plasma Interactions
in Multi-dimensional Systems -- Overview

D.B. Batchelor, L.A. Berry, M.D. Carter, E. F. Jaeger, E. D’Azevedo – ORNL
C.K. Phillips, A. Pletzer – PPPL, 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

Our overarching goal is to understand wave behavior in complex inhomogeneous systems. The details of the systems we study are specific to fusion plasmas, although similar wave phenomena confront virtually every field of physics and engineering. For the first time, these issues can be quantitatively analyzed in realistic 2D and even 3D situations necessitating the use of sophisticated terascale numerical modeling.

The magnetic fusion energy research program aims to produce energy by the same process that the sun does. In fact the fuel must be heated to temperature hundreds of millions of degrees in order to react, even hotter than the sun. At these astronomical temperatures, the fuel atoms are torn apart into their constituent electrons and nuclei, forming a state of matter called plasma.

One of the techniques to get the fuel this hot is to use intense electromagnetic waves, much as a microwave oven is used in the home. Waves are also used for other important purposes such as to drive electric currents affecting the plasma magnetic configuration, to force mass flow of the plasma, affecting its stability, and for other plasma control tasks. It is quite important therefore to have a good theoretical understanding of the wave behavior and to be able to calculate it accurately. The goal of the project is to develop the computational capability to understand the physical behavior of waves in fusion plasmas and to model these wave phenomena sufficiently accurately so that their effect on other plasma processes such as stability and transport of particles and energy can be understood.

Because the particles are so hot, they move at speeds almost the speed of light and can travel a distance comparable to a wavelength in the time of a few oscillations of the wave. This motion makes it difficult to calculate how the plasma particles will respond to the waves and how much heating or electric current they will produce. Another challenge is that at a given frequency, several kinds plasma waves can exist with very different wavelengths and polarizations. A wave launched into the plasma can in a short distance completely change its character to another type of wave, a process called mode conversion. To study these effects the computer model must have very high resolution to see the small-scale structures that develop, which means that very large computers are needed to solve for the very large number of unknowns in the equations. Also, the computers must be extremely fast in order to obtain the solutions in a reasonable time. The maximum resources of the largest available supercomputers are being used for this purpose.

Until now researchers wishing to calculate the effects of waves in plasma have been forced by computational feasibility to make a difficult choice between restricting consideration to a single dimension or simplifying the physics model. The first choice, treating the plasma geometry as one-dimensional, is akin to tunnel vision. The wave is computed along a single line through the plasma, but one does not get a picture of what is occurring in the whole plasma cross-section. The second choice eliminates from consideration many of the wave processes of most importance in today’s fusion experiments that require high frequencies and can have very short wavelengths in some regions of the device.

In a partnership between plasma physicists and computer scientists, our project has increased the resolution and speed of our plasma wave solvers to the point that it is possible for the first time to study the mode conversion process in the complicated geometry and the full scale of real fusion devices. We have developed new wave solvers in 2D and 3D called All-Orders Spectral Algorithm (AORSA) solvers based on a more general formulation of the physics called an integral equation. It is now possible to compute plasma waves across an entire plasma cross-section with no restriction on wavelength or frequency. In this approach the limit on attainable resolution comes not from the theory itself, but only from the size and speed of the available computer.

We are also working in a number of areas to improve the fidelity of the physics models used in the computations. In any material, the distribution of different velocities of its particles tends, over time, toward a maximally random distribution called a thermal, or Maxwellian, distribution. Wave codes for plasmas typically approximate the distribution of particles as being thermal. However, the action of the waves, or the presence of fusion reactions, or energetic particles injected into the plasma for heating purposes, can cause the velocity distribution to deviate from thermal, and can have an important influence on the propagation and absorption of the waves. Indeed waves that resonate with plasma ions are often seen to produce populations of very high energy particles which in turn stabilize the motion of the bulk plasma. We have developed a capability to allow for general velocity distributions. We hope to ultimately have a closed, self-consistent model.

Funding from the SciDAC project has enabled us to assemble a team from multiple institutions to work on a unified set of goals in a way that was not possible before SciDAC. Progress is maximized by developing single components applicable to all of the wave solvers in the project. We are making progress on all fronts. We have made advances in basic, analytic wave theory that is required for the more powerful codes. For example, we have generalized the theory of nonlinear wave-driven plasma flow to two dimensions. Working with computer scientists funded to work directly with our project through a Scientific Application Pilot Project (SAPP), we have adopted and optimized advanced algorithms to speed up our codes, in some cases by several orders of magnitude. This has made it feasible to study new regimes of wave physics which previously could only be treated in one dimension or with approximate techniques, and to carry out multiple code runs at high resolution for scientific case studies where before it was only possible to perform a single run at minimal resolution. Working with applied mathematicians, we are developing new mathematical representations for the wave fields that are more data efficient than the traditional spectral techniques presently employed and offer promise to substantially reduce the size of the computational load to solve plasma wave problems. And we are making scientific progress on problems of importance to the fusion program by applying the codes we have developed and improved.

The remainder of the project will emphasize incorporating the improved physics models into the 2D and 3D wave codes, implementing the improved field representations we have developed, closing the loop on self consistency of the velocity distribution, benchmarking the codes, and applying them to important fusion physics issues.

The greatest infrastructure need of our project is timely access to supercomputer cycles. Our 2D codes require from 128 to 512 processors and run from 5 to 6 hr on Power4 nodes. To make reasonable progress, overnight turnaround is needed. For 3D runs, at least 1600 processors with full 1Gbyte memory are required and typically 8 hr or more. For these very large, 3D runs turnaround time on the order of a week is acceptable. Our computer allocation is only one third of last year’s, and our inability at present to obtain good turnaround is having a serious impact on our progress.

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

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