An energy conserving and asymptotic preserving time integrator for implicit PIC schemes

Tremendous progress has been made on implicit PIC schemes in recent years. They have been shown to be more robust against the finite grid instability than their explicit counterparts. However, the classical Crank-Nicholson integrator on which implicit PIC is built fails to capture grad-B drifts when the cyclotron frequency is not resolved. Prior modifications correct for this but break the crucial energy conservation property enjoyed by implicit PIC. We present a new time integration scheme which recovers the correct guiding center motion for arbitrary time step while retaining exact energy conservation. The resulting implicit PIC scheme holds great promise for systems in which magnetization varies widely over the spatial domain and as an alternative to gyrokinetics.