Fully implicit, energy-conserving electromagnetic particle-in-cell simulations in multiple dimensions

We discuss a new, implicit 2D-3V particle-in-cell (PIC) algorithm for non-radiative, electromagnetic kinetic plasma simulations, based on the Vlasov-Darwin model.\footnote{Nielson and Lewis, \textit{Methods Comput. Phys.} \textbf{16} p.367 (1976)} The Vlasov-Darwin model avoids radiative noise issues, but is elliptic and renders explicit time integration unconditionally unstable.\footnote{Nielson, Lewis (1976)} Absolutely stable, fully implicit, charge and energy conserving PIC algorithms for both electrostatic and electromagnetic regimes have been recently developed in 1D.\footnote{Chen, Chac\'on, and Barnes, \textit{JCP} \textbf{230} p.7018 (2011)}\textsuperscript{,}\footnote{Chen and Chac\'on, \textit{CPC} \textbf{185} p.2391 (2014)} In this study, we build on these recent successes to develop a multi-D, fully implicit PIC algorithm for the Vlasov-Darwin model.\footnote{Chen and Chacon, \textit{CPC}, submitted (2015)} The algorithm conserves global energy, local charge, and particle canonical-momentum exactly. The nonlinear iteration is effectively accelerated with a fluid preconditioner, allowing the efficient use of large timesteps compared to the explicit CFL. We demonstrate the potential of the approach with various numerical examples in 2D-3V.