Most of the volume of the universe is in the plasma state. Plasmas are inherently complex and difficult to model and simulate: typical astrophysical, space, and laboratory plasmas present a broad range of time and space scales that span many orders of magnitude. Much of plasma physics is well described by classical equations of motion for the plasma dynamics (fluid or kinetic) coupled to Maxwell’s equations for the self-consistent electromagnetic fields. In general the equations of motion are nonlinear, and plasmas tend to be rife with instabilities and turbulence, which necessitates the use of numerical methods to address rather stiff problems. Much progress has been made in the last fifty years in the simulation of plasmas, particularly in the development of models and algorithms that address the multiple time and space scale challenges [1].
Recent research conducted by the UCLA-LLNL collaboration led by Russ Caflisch have improved algorithms for the simulation of kinetic phenomena in plasmas with special emphasis on Coulomb collisions. Kinetic simulation of plasmas generally requires more computational resources than do fluid simulations, e.g., a fluid simulation might be in three configuration-space dimensions while the kinetic simulation might require six phase-space dimensions. Moreover, in particle simulations of plasmas the accurate computation of Coulomb collisions is an additional expense and is often a significant bottleneck. In our research we have achieved significant computational gains by employing hybrid methods (formulations in which the plasma is decomposed into fluid and kinetic parts, minimizing the kinetic fraction), higher-order time integration schemes for stochastic differential equations (including some clever new methods for representing and sampling Levy areas), and the use of multi-level time-integration schemes. Our development of new algorithms has been rigorously motivated and derived, realized in simulation examples, and reported in recent publications.
[1] J. U. Brackbill and B. I. Cohen, eds., Multiple Time Scales, Computational Techniques, Vol. 3 (Academic Press, Orlando, 1985).
*In collaboration with R. Caflisch, A. Dimits, M. Rosin, and L. Ricketson. This work was performed under the auspices of the U.S. Department of Energy under contract DE-AC52-07NA27344 at the Lawrence Livermore National Laboratory. LLNL-ABS- 649973
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