An implicit, conservative, asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas

We present a new full-orbit electrostatic particle-in-cell algorithm able to use large timesteps compared to particle gyro-period in arbitrary magnetic fields [1]. The algorithm extends earlier electrostatic fully implicit PIC implementations [2] with a new asymptotic-preserving (AP) particle-push scheme [3] (recently endowed with a very fast Picard nonlinear solver [4]) that allows timesteps much larger than particle gyroperiods. The AP integrator preserves all the averaged particle drifts in the large-timestep limit, while recovering resolved particle orbits with small timesteps. The scheme allows for a seamless, efficient treatment of particles with arbitrary magnetization, conserves energy and charge exactly, and does not spoil implicit solver performance. We demonstrate by numerical experiment with several strongly magnetized problems (diocotron instability, modified two-stream instability, and drift-wave instability) that two orders of magnitude wall-clock-time speedups are possible vs. the standard fully implicit electrostatic PIC algorithm without sacrificing solution quality and while preserving strict charge and energy conservation.