Comparative Study of Explicit vs. Implicit Particle-in-Cell schemes for Plasma Sheath Simulations

In this work we present a comparative study of explicit vs. implicit fully-kinetic full-orbit Particle-in-Cell schemes, using: (1) the explicit Vlasov-Poisson scheme of the hPIC[1] code, and (2) the implicit Maxwell-Vlasov scheme of Chacon et al.[2]. Implicit schemes remain stable at much longer time steps than traditional, explicit schemes, but at greater computational cost. The Maxwell-Vlasov formulation avoids the use of a Poisson solver by directly evolving the electric field in time based on the particle fluxes. We report simulation results of asymmetric phase-spaces (e.g. bump-on-tail instability) and finite-size domains (non-periodic) facing an absorbing wall, where a plasma sheath is formed. [1] Khaziev, Curreli, Comput. Phys. Commun. 229, 87, 2018; [2] Chacon, Chen, Barnes, J. Comp. Phys. 233, 1–9, 2013.