  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, particularly 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 (RelIMM), 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.
