Elimination of Numerical Cherenkov Instability in flowing-plasma Particle-In-Cell simulations by using Galilean coordinates

Abstract

Particle-In-Cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including e.g. laser-wakefield acceleration, when viewed in a Lorentz-boosted frame), but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination of the NCI is verified empirically and confirmed by a theoretical analysis of the instability. Moreover, it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.

18 pages, 6 figures

References in corpus (5)

• Particle acceleration in relativistic collisionless shocks: Fermi process at last?
• Magnetic field evolution in relativistic unmagnetized collisionless shocks
• Implementation of a hybrid particle code with a PIC description in r-z and a gridless description in $\varphi$ into OSIRIS
• Stable discrete representation of relativistically drifting plasmas
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