Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas
Manuel Kirchen, Remi Lehé, Sören Jalas, Olga V. Shapoval, Jean-Luc Vay, Andreas R. Maier
Abstract
Discretizing Maxwell's equations in Galilean (comoving) coordinates allows the derivation of a pseudospectral solver that eliminates the numerical Cherenkov instability for electromagnetic particle-in-cell simulations of relativistic plasmas flowing at a uniform velocity. Here we generalize this solver by incorporating spatial derivatives of arbitrary order, thereby enabling efficient parallelization by domain decomposition. This allows scaling of the algorithm to many distributed compute units. We derive the numerical dispersion relation of the algorithm and present a comprehensive theoretical stability analysis. The method is applied to simulations of plasma acceleration in a Lorentz-boosted frame of reference.