Numerical charge conservation in Particle-In-Cell codes

Abstract

A difficulty in electromagnetic PIC simulations of plasmas modeled by the Vlasov–Maxwell system is that the continuity equation may not be satisfied and that then the Maxwell system isn’t any more well-posed. Indeed, in PIC codes, fields and densities are defined at spatial grid points while charged particles can take arbitrary positions. Therefore, the current mapped from particles to the mesh may not satisfy the continuity equation at the discrete level. In this paper, we are interested in charge conserving current deposition algorithms. We study the efficiency of two methods ensuring that the continuity equation is satisfied at the discrete level: an extension of the Villasenor–Buneman method and the Esirkepov method.