An efficient, fully implicit electrostatic full-PIC algorithm for strongly magnetized plasmas

We introduce a new fully implicit, strictly charge- and energy-conserving, asymptotic-preserving electrostatic particle-in-cell algorithm for strongly magnetized plasmas. The algorithm extends earlier electrostatic fully implicit particle-in-cell (PIC) implementations\footnote{Chen, Chac\'on, and Barnes, \textit{JCP,} \textbf{230} p.7018 (2011)} with a new asymptotic-preserving particle-push scheme\footnote{Ricketson and Chacon, \textit{JCP,} \textbf{418} 109639 (2020) } that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all the averaged particle drifts, while recovering the standard CN scheme for small timesteps. The scheme allows for a seamless, efficient treatment of particles in coexisting magnetized and unmagnetized regions, conserves energy and charge exactly, and is compatible with arbitrary boundary conditions, all the while without spoiling implicit solver performance. We demonstrate by numerical experiment with several strongly magnetized problems (e.g., diocotron instability, modified two-stream instability, drift instability, etc.) that orders of magnitude wall-clock time speedups vs the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution quality. We will also discuss possible extensions to the electromagnetic context.