Numerical dispersion free in longitudinal axis for particle-in-cell simulation

Abstract

We introduce a new scheme for a field solver for particle-in-cell simulations; it uses P- and S-polarized variables in the modified Maxwell equations to eliminate numerical dispersion along the longitudinal axis. By obtaining numerical stability of the dispersion relation, the scheme has two major advantages of simulating the exact laser group velocity and the exact electron beam propagation. Those advantages are important for simulations of laser wakefield acceleration in a low-density plasma, and of the propagation of an electron beam that has low emittance. The scheme is implemented in multi-dimensional Cartesian and cylindrical coordinates following Fourier decomposition of the azimuthal direction. Results of both calculations compare well with results of three-dimensional simulations.