Simplex-in-Cell Technique for Collisionless Plasma Simulations

TL;DR

This paper introduces a simplex-in-cell (SIC) technique for collisionless plasma simulations, representing phase space with manifolds to improve accuracy and efficiency over traditional particle-in-cell methods.

Contribution

The paper extends the SIC method to plasma physics, demonstrating its implementation and advantages in simulating collisionless plasmas with fewer particles and higher accuracy.

Findings

Higher accuracy in plasma simulations

Faster convergence with fewer particles

Validated with standard plasma tests

Abstract

We extend the simplex-in-cell (SIC) technique recently introduced in the context of collisionless dark matter fluids (Abel et al. 2012; Hahn et al. 2012) to the case of collisionless plasmas. The six-dimensional phase space distribution function $f(\mathbf x,\mathbf v)$ is represented by an ensemble of three-dimensional manifolds, which we refer to as sheets. The electric potential field is obtained by solving the Poisson equation on a uniform mesh, where the charge density is evaluated by a spatial projection of the phase space sheets. The SIC representation of phase space density facilitates robust, high accuracy numerical evolution of the Vlasov-Poisson system using significantly fewer tracer particles than comparable particle-in-cell (PIC) approaches by reducing the numerical shot-noise associated with the latter. We introduce the SIC formulation and describe its implementation in a new code, which we validate using standard test problems including plasma oscillations, Landau damping, and two stream instabilities in one dimension. Merits of the new scheme are shown to include higher accuracy and faster convergence rates in the number of particles. We finally motivate and outline the efficient application of SIC to higher dimensional problems.