The Energy Conserving Particle-in-Cell Method

TL;DR

This paper introduces an energy conserving Particle-in-Cell method that uses implicit differencing and a Jacobian-free Newton Krylov solver, effectively eliminating finite grid instability and conserving total energy in plasma simulations.

Contribution

The paper presents a novel energy conserving PIC method employing implicit time differencing and JFNK solver, improving stability and energy conservation in plasma simulations.

Findings

Eliminates finite grid instability in simulations.

Accurately models two-stream and Weibel instabilities.

Computational time scales linearly with particle number.

Abstract

A new Particle-in-Cell (PIC) method, that conserves energy exactly, is presented. The particle equations of motion and the Maxwell's equations are differenced implicitly in time by the midpoint rule and solved concurrently by a Jacobian-free Newton Krylov (JFNK) solver. Several tests show that the finite grid instability is eliminated in energy conserving PIC simulations, and the method correctly describes the two-stream and Weibel instabilities, conserving exactly the total energy. The computational time of the energy conserving PIC method increases linearly with the number of particles, and it is rather insensitive to the number of grid points and time step. The kinetic enslavement technique can be effectively used to reduce the problem matrix size and the number of JFNK solver iterations.