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.
Highlights
The occurrence of the numerical Cherenkov instability (NCI) [1,2,3,4] can severely limit the applicability of the particlein-cell (PIC) method [5,6] for simulations of relativistic beams or plasmas
A more general solution is given by the class of pseudospectral time-domain (PSTD) solvers [12,13], which represent the spatial derivatives in the frequency domain
For a beam or plasma comoving with the Galilean coordinates, the arbitrary-order GalileanPSATD solver remains free of numerical Cherenkov radiation (NCR) and eliminates the NCI
Summary
The occurrence of the numerical Cherenkov instability (NCI) [1,2,3,4] can severely limit the applicability of the particlein-cell (PIC) method [5,6] for simulations of relativistic beams or plasmas. At the cost of reducing the accuracy of the spatial derivatives to that of an FDTD solver, the evolution of the fields on the grid becomes more local. For a beam or plasma comoving with the Galilean coordinates, the arbitrary-order GalileanPSATD solver remains free of NCR and eliminates the NCI. We thereby remove the limitation of the original solver to efficiently scale to many compute units and lay the foundation for intrinsically stable and massively parallel PIC simulations of relativistically streaming plasmas. IV we apply the parallelized solver to multi-GPU Lorentz-boosted frame simulations of laserplasma acceleration using the quasi-3D PIC code FBPIC [16]
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