A new method to dispatch split particles in Particle-In-Cell codes

TL;DR

This paper introduces a new, efficient particle splitting method for Particle-In-Cell codes with adaptive mesh refinement, improving accuracy while minimizing computational overhead.

Contribution

It develops a cost-function-based particle splitting technique that approximates distribution function preservation without high computational costs.

Findings

Method minimizes the difference between original and split particle assignment functions.

Provides tabulated weights and positions for different interpolation degrees and dimensions.

Asymptotically approaches the exact distribution function with many split particles.

Abstract

Particle-In-Cell codes are widely used for plasma physics simulations. It is often the case that particles within a computational cell need to be split to improve the statistics or, in the case of non-uniform meshes, to avoid the development of fictitious self-forces. Existing particle splitting methods are largely empirical and their accuracy in preserving the distribution function has not been evaluated in a quantitative way. Here we present a new method specifically designed for codes using adaptive mesh refinement. Although we point out that an exact, distribution function preserving method does exist, it requires a large number of split particles and its practical use is limited. We derive instead a method that minimizes the cost function representing the distance between the assignment function of the original particle and that of the sum of split particles. Depending on the interpolation degree and the dimension of the problem, we provide tabulated results for the weight and position of the split particles. This strategy represents no overhead in computing time and for a large enough number of split-particles it asymptotically tends to the exact solution.