Capturing finite Larmor radius effects with an implicit, asymptotic preserving full-orbit integrator for particle-in-cell schemes

While gyrokinetics is extremely useful for simulations of strongly magnetized plasmas, there is growing interest in full-orbit simulations when the gyrokinetic ordering breaks down. We present an implicit time-stepping scheme for charged particles that recovers the drift- and gyrokinetic limits when stepping over the gyroperiod while converging to the resolved orbit with small time-steps. The scheme preserves the exact total energy conservation enjoyed by recently developed implicit PIC schemes [1]. Development proceeds in three stages. Firstly, we review prior work that modified Crank-Nicolson to capture the drift-kinetic limit by introducing an effective magnetic-drift force [2]. Next, to handle finite Larmor radius effects, we evaluate the electric field at equispaced points on an approximate gyro-orbit, keeping total energy conservation by an analogous modification of the current deposition. Full-orbit convergence is maintained by adaptive selection of the number and location of these points, depending on time-step size and local field structure. Finally, we introduce a strategy of alternating large and small time-steps that dramatically relaxes the time-step constraints on the scheme, along with a corresponding adaptive stepping strategy. Tests on single-particle motion in complex field configurations demonstrate the ability to step over the gyration time-scale and recover correct dynamics -- even with field structure at the gyroradius scale -- along with strict conservation properties.

[1] Chen et al., JCP 230 (2011)
[2] Ricketson et al., JCP 418 (2020)