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We present a novel Relativistic Semi-Implicit Method (RelSIM) forparticle-in-cell (PIC) simulations of astrophysical plasmas, implemented in acode framework ready for production runs. While explicit PIC methods havegained widespread recognition in the astrophysical community as a reliable toolto simulate plasma phenomena, implicit methods have been seldom explored. Thisis partly due to the lack of a reliable relativistic implicit PIC formulationthat is applicable to state-of-the-art simulations. We propose the RelSIM tofill this gap: our new method is relatively simple, being free of nonlineariterations and only requiring a global linear solve of the field equations.With a set of one- and two-dimensional tests, we demonstrate that the RelSIMproduces more accurate results with much smaller numerical errors in the totalenergy than standard explicit PIC, particularly when characteristic plasmascales (skin depth and plasma frequency) are heavily underresolved on thenumerical grid. By construction, the RelSIM also performs much better than theRelativistic Implicit-Moment Method (RelIMM), originally proposed forsemi-implicit PIC simulations in the relativistic regime. Our results arepromising to conduct large-scale (in terms of duration and domain size) PICsimulations of astrophysical plasmas, potentially reaching physical regimesinaccessible by standard explicit PIC codes.

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