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For decades, the Vlasov-Darwin model has been recognized to be attractive forparticle-in-cell (PIC) kinetic plasma simulations in non-radiativeelectromagnetic regimes, to avoid radiative noise issues and gain computationalefficiency. However, the Darwin model results in an elliptic set of fieldequations that renders conventional explicit time integration unconditionallyunstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwinmodel in multiple dimensions, which overcomes many difficulties of traditionalsemi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwinfield equations and particle equations of motion is space-time-centered,employing particle sub-cycling and orbit-averaging. The algorithm conservestotal energy, local charge, canonical-momentum in the ignorable direction, andpreserves the Coulomb gauge exactly. An asymptotically well-posed fluidpreconditioner allows efficient use of large time steps and cell sizes, whichare determined by accuracy considerations, not stability, and can be orders ofmagnitude larger than required in a standard explicit electromagnetic PICsimulation. We demonstrate the accuracy and efficiency properties of thealgorithm with various numerical experiments in 2D-3V.

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm