RelSIM: A Relativistic Semi-implicit Method for Particle-in-cell Simulations

Abstract

We present a novel Relativistic Semi-Implicit Method (RelSIM) for particle-in-cell (PIC) simulations of astrophysical plasmas, implemented in a code framework ready for production runs. While explicit PIC methods have gained widespread recognition in the astrophysical community as a reliable tool to simulate plasma phenomena, implicit methods have been seldom explored. This is partly due to the lack of a reliable relativistic implicit PIC formulation that is applicable to state-of-the-art simulations. We propose the RelSIM to fill this gap: our new method is relatively simple, being free of nonlinear iterations and only requiring a global linear solve of the field equations. With a set of one- and two-dimensional tests, we demonstrate that the RelSIM produces more accurate results with much smaller numerical errors in the total energy than standard explicit PIC, in particular when characteristic plasma scales (skin depth and plasma frequency) are heavily underresolved on the numerical grid. By construction, the RelSIM also performs much better than the relativistic implicit-moment method, originally proposed for semi-implicit PIC simulations in the relativistic regime. Our results are promising to conduct large-scale (in terms of duration and domain size) PIC simulations of astrophysical plasmas, potentially reaching physical regimes inaccessible by standard explicit PIC codes.

An Exactly Energy-conserving Electromagnetic Particle-in-cell Method in Curvilinear Coordinates

“…These works present large-scale simulations utilizing explicit codes, usually implemented with one specific (four-dimensional) metric corresponding to the particular physical case in question. With the method presented in this work (modified by adding a time component of the metric and relativistic effects; see, e.g., Bacchini et al 2019;Bacchini 2023), we can simultaneously avoid the aforementioned downsides of explicit codes (i.e., numerical instability and lack of energy conservation) and generalize such simulations to any arbitrary metric tensor that might be of interest, opening the possibility for more physical cases to be studied.…”