A fully implicit, conservative, multi-scale algorithm for the multi-species Vlasov-Ampère system

We discuss the addition of a fully kinetic electron capability into the 1D-2V Vlasov-Fokker-Planck code iFP.¹ The proposed algorithm utilizes an approach similar to that in Taitano & Chacón,² but offers several advancements over this earlier 1D-1V study. Our approach utilizes a time- and space-adaptive velocity mesh, which dynamically expands/contracts individual species’ meshes as they heat/cool, and shifts to center on their bulk velocity. Additionally, we achieve full conservation of mass, momentum, and energy for an arbitrary temporal integration scheme. To demonstrate the effectiveness of the approach, we present simulation results for several canonical collisionless kinetic problems. These include the two-stream instability, and the ion acoustic shockwave, where the inverse plasma frequency is a very stiff timescale. The results demonstrate the promise of this scheme for application to complex multiscale kinetic plasma systems, such as inertial confinement fusion capsule implosions.

¹W. T. Taitano, et al., J. Comp. Phys., 365, 173-205 (2018)

²W. T. Taitano, L. Chacón, J. Comp. Phys. 284, 718-736 (2015)