An implicit conservative electromagnetic hybrid algorithm with kinetic (particle) ions and fluid electrons*

The hybrid model with kinetic ions and fluid electrons is a promising approach to model multi-scale problems in space and laboratory plasmas. However, current explicit schemes suffer from a number of issues related to the stable propagation of whistler waves, and finite-grid instabilities for cold ion beams [1] due to non-conservation of discrete momentum or energy. Implicit methods have been recently explored [2] to step over fast timescales, but these schemes are not conservative. Here, we present a novel particle-based non-linear hybrid algorithm that features discrete conservation of mass, momentum and energy [3]. The scheme combines a cell-centered spatial discretization with implicit-midpoint time advance and adaptive integration of the ion orbits. A fluid moment-based preconditioner is used to accelerate convergence when stepping over fast normal modes. We demonstrate the unique conservation and stability properties of the scheme.

[1] P. W. Rambo, J. Comput. Phys., 118, 152-158 (1995).

[2] B. Sturdevant, et. al., J. Comput. Phys., 316, 519 (2016).

[3] A. Stanier, et. al., arxiv e-print:1803.07158