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 (PIC) codes, significantly enhancing accuracy in various scenarios, especially under extreme physical conditions such as high magnetic fields and relativistic plasmas. Our approach utilizes a known exact solution for particle trajectories in a uniform electromagnetic field. The assumption of a uniform field within a time step is an approximation shared with the conventional Boris pusher. However, in several scenarios, Boris pusher may break down, leading to inaccuracies in particle trajectories and global properties, such as particle energy spectra. By employing a mid-point integration scheme, the APP achieves second-order accuracy. To handle pushing particles in non-uniform electromagnetic fields, we propose extending the pusher to higher orders using a deferred-correction scheme. We benchmark the analytic pusher against several standard single-particle and self-consistent problems, demonstrating its advantages and discussing its particular relevance and utility in addressing unresolved astrophysical challenges.