2022/11/18 by Zhuoning Li, Zhenli Xu, Li, Zhuoning +3 · 1 citation
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Magnetic confinement fusion research #Numerical Analysis (math.NA) #Particle accelerators and beam dynamics #Plasma Diagnostics and Applications #Plasma Physics (physics.plasm-ph)
paper · pdf · doi:10.48550/arxiv.2211.10070
openalex publication_date 2022/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an efficient and accurate energy-conserving implicit particle-in-cell~(PIC) algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness for simulating complex plasma systems with multiple physical scales. This method consists of several indispensable elements: (\romannumeral1) the reformulation of the original Vlasov-Poisson system into an equivalent Vlasov-Ampère system with divergence-/curl-free constraints; (\romannumeral2) a novel structure-preserving Fourier spatial discretization, which exactly preserves these constraints at the discrete level; (\romannumeral3) a preconditioned Anderson-acceleration algorithm for the solution of the highly nonlinear system; and (\romannumeral4) a linearized and uniform approximation of the implicit Crank-Nicolson scheme for various Debye lengths, based on the generalized Ohm's law, which serves as an asymptotic-preserving preconditioner for the proposed method. Numerical experiments are conducted, and comparisons are made among the proposed energy-conserving scheme, the classical leapfrog scheme, and a Strang operator-splitting scheme to demonstrate the superiority of the proposed method, especially for plasma systems crossing physical scales.