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

While the gyrokinetic approximation has been extremely successful in accelerating simulations of strongly magnetized plasmas, there is growing interest in full-orbit simulation in key cases where the gyrokinetic ordering breaks down.  As such, we present an implicit time-stepping scheme for charged particles that recovers the gyrokinetic limit when stepping over the gyration scale while converging to the exact, full-orbit dynamics in the small time-step limit. The scheme preserves the exact total energy conservation enjoyed by recently-developed implicit PIC schemes. Development proceeds in two stages. First, we summarize prior work in which Crank-Nicolson is modified to capture the drift-kinetic limit by introducing an effective force to capture the magnetic drift.  Next, to handle finite Larmor radius effects, we alternate large and small time-steps to sample equispaced gyrophases.  The numerical time-scales introduced by the scheme are analyzed and resulting time-step bounds derived. Tests on single particle motion in complex field configurations are shown.  The ability to step over the gyration time-scale and recover correct dynamics is demonstrated - even in configurations featuring structure on the gyroradius scale - along with the scheme’s conservation properties.