Mesh refinement for particle-in-cell plasma simulations: Applications to and benefits for heavy ion fusion

Abstract

The numerical simulation of the driving beams in a heavy ion fusion power plant is a challenging task, and simulation of the power plant as a whole, or even of the driver, is not yet possible. Despite the rapid progress in computer power, past and anticipated, one must consider the use of the most advanced numerical techniques, if we are to reach our goal expeditiously. One of the difficulties of these simulations resides in the disparity of scales, in time and in space, which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. We discuss the challenges posed by the implementation of this technique into plasma simulations (due to the presence of particles and electromagnetic waves). We present the prospects for and projected benefits of its application to heavy ion fusion, in particular to the simulation of the ion source and the final beam propagation in the chamber. A collaboration project is under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to couple the adaptive mesh refinement library CHOMBO developed by the ANAG group to the particle-in-cell accelerator code WARP developed by the Heavy Ion Fusion–Virtual National Laboratory. We describe our progress and present our initial findings.

A node-centered local refinement algorithm for Poisson's equation in complex geometries

“…A prototype axisymmetric (r, z) AMR Poisson solver has been implemented in Warp and used to carry out time-dependent simulations of the injector. These simulations have shown the benefit and the effectiveness of the mesh refinement technique in converging to the right physical solution using less grid resolution [13] [12].…”

Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams

“…Using prototypes, we have performed studies of various issues. We summarize here our findings and refer the reader to [2] for a more detailed presentation.…”

“…Using a numerical technique introduced in [11] (a numerical three-dimensional extension of the analytical method used by Lampel and Tiefenback in one dimension), it is possible to derive from WARP the voltage profile corresponding to the emission of a very sharply rising current emitted from a source in a three-dimensional geometry. Such a profile was derived for the STS500 diode experiment [10] and is plotted in Fig.7 together with the current predicted using three-dimensional WARP simulations (with axisymmetric representation of the field) with and without mesh refinement.…”

Implementations of mesh refinement schemes for Particle-In-Cell plasma simulations

“…This may potentially alter the particle motion to a degree which cannot be neglected. This effect was studied in detail for a one particle test in (5). It was determined that, when using the "1-pass" solver, a sufficient number of guard cells can be defined on the border of the patch that effectively mitigates most of the effect of the spurious force, since its amplitude grows with the inverse of the distance to the patch border.…”