A coupled guiding center-Boris particle pusher for magnetized plasmas in compact-object magnetospheres

We present a novel numerical scheme for simulating the motion of relativistic charged particles in magnetospheres of compact objects, typically filled with highly magnetized collisionless plasmas. The new algorithm is based on a dynamic switch between the full system of equations of motion and a guiding center approximation. The switch between the two formulations is based on the magnetization of the plasma particles, such that the dynamics are accurately captured by the guiding center motion even when the gyro-frequency is under-resolved by the time step. For particles with a large gyro-radius, due to acceleration in, e.g., reconnecting current sheets, the algorithm adaptively switches to solve the full equations of motion instead. The new scheme is directly compatible with standard Particle-in-Cell codes, and is readily applicable in curved spacetimes via a dedicated covariant formulation. We test the performance of the coupled algorithm by evolving charged particles in electromagnetic configurations of reconnecting current sheets in magnetized plasma, obtained from special- and general-relativistic Particle-in-Cell simulations. The new coupled pusher is capable of producing highly accurate particle trajectories even when the time step is many orders of magnitude larger than the gyro-period, substantially reducing the restrictions of the temporal resolution.