Advancing Multi-Scale Physics Modeling in Strongly Magnetized Relativistic Plasmas: A Sub-Cycling Approach of Analytic Particle Pusher

Modeling multi-scale physics in astrophysical and laboratory plasmas with strong magnetic fields for particle acceleration poses challenges for conventional explicit relativistic Particle-in-Cell (PIC) simulations that employ the leapfrog scheme. The leapfrog scheme utilizes a fixed time step for both fields and particles, which works well when the time step determined by the field solver (CFL condition) is the smallest time-scale of the simulation. However, in the presence of a strong magnetic field, a gyro-motion timescale may be even smaller than the CFL-determined time step. To address this issue, we propose a particle sub-cycling approach [1] by employing a known analytical solution of particle motion in arbitrary constant electromagnetic fields [2] to construct approximate solutions with non-uniform fields. By incorporating the analytic particle pusher with sub-cycling, our method enables significant improvements in achievable scales within the kinetic model for systems with strong magnetic fields, surpassing the limitations of standard approaches. We demonstrate the effectiveness of the proposed particle pusher in test particle problems and the PIC algorithm through standard benchmark tests such as Landau damping and 2-stream instabilities. Additionally, we compare the performance of the new algorithm with standard PIC simulations on problems spanning a range of magnetization strengths from relatively weak to strong regimes. Overall, our study presents a novel approach to address the challenges of multi-scale physics modeling in plasmas with strong magnetic fields, offering improved capability and accuracy.

[1] COHEN, BRUCE I. "Orbit averaging and subcycling in particle simulation of plasmas." Multiple Time Scales. Academic Press, 1985. 311-333.



[2] Landau, L. D., and E. M. Lifshitz. The Classical Theory of Fields: Volume 2. Butterworth-Heinemann, 1994.