Abstract and subjects
We extend the asymptotic preserving and energy conserving time integrator for charged-particle motion developed in Ricketson and Chacón (2020) [36] to include finite Larmor-radius (FLR) effects in the presence of electric-field length-scales comparable to the particle gyro-radius (the gyro-kinetic limit). We introduce two modifications to the earlier scheme. The first is the explicit gyro-averaging of the electric field at the half time-step, along with an analogous modification to the current deposition, which we show preserves total energy conservation in implicit PIC schemes. The number of gyrophase samples is chosen adaptively, ensuring proper averaging for large timesteps and the recovery of full-orbit dynamics in the small time-step limit. The second modification is an alternating large and small time-step strategy that ensures the particle trajectory samples gyrophases evenly. We show that this strategy relaxes the time-step restrictions on the scheme, allowing even larger speed-ups than previously achievable. We demonstrate the new method with several single-particle motion tests in a variety of electromagnetic field configurations featuring gyro-scale variation in the electric field. The results demonstrate the advertised ability to capture FLR effects accurately even when significantly stepping over the gyration time-scale.
•An asymptotic-preserving, implicit time integrator for charged particles in arbitrary electromagnetic fields is presented.•Method captures finite Larmor radius (FLR) effects, making it the first asymptotic-preserving scheme to do so.•Method preserves desired properties of correct gyroradius, first-order guiding center drifts, and energy conservation.•A new alternating time-step technique relaxes time-step constraints, allowing larger speed-ups than previously achievable.•Numerical results show dramatic accuracy improvement over prior schemes.