Particle-in-cell Simulations in Extreme Environments: An Analytic Particle Pusher approach

We present a novel implementation of an analytic particle pusher (APP) for particle-in-cell codes, which markedly improves accuracy in general scenarios, with a particular focus on extreme physical conditions such as high magnetic fields and relativistic plasmas. Our approach leverages a known exact solution for the particle trajectories in a uniform electromagnetic field. Notably, the assumption of a uniform field within a time step is an approximation shared with the conventional Boris pusher. In several scenarios, Boris pusher breaks down and can yield inaccuracies not only in particle trajectories but also in global properties, such as the particle energy spectra. By using a mid-point integration scheme, the APP 2nd- order accurate. We benchmark the analytic pusher by several standard single-particle and self-consistent problems. We demonstrate the advantage of our particle pusher method and discuss its particular relevance and utility in addressing unresolved astrophysical challenges.