Progress on an energy-conserving, asymptotic-preserving orbit integrator for implicit PIC simulations of arbitrarily magnetized plasmas

We build on previous work [1], which developed an implicit, asymptotic preserving (AP) time-integrator for charged particle motion that (a) correctly recovers guiding center motion when stepping over the gyro-period, (b) converges to full-orbit motion in the small time-step limit, and (c) conserves energy exactly.~ We extend the scheme to additionally capture the finite Larmor radius effects that appear in many applications.~ This is done by alternating large and small time-steps in a coordinated fashion.~ New restrictions on time-step size are derived, which leads to an adaptive time-stepping strategy.~ Results from simple test problems verify the AP behavior and strict conservation properties.~ Finally, we report on progress in implementing the new method in an implicit PIC scheme [2].~ ~ [1] L.F. Ricketson, and L. Chac\'{o}n. Journal of Computational Physics (2020): 109639. [2] G. Chen, L. Chac\'{o}n, and D.C. Barnes. Journal of Computational Physics 230.18 (2011): 7018-7036.