Energy-Conserving Semi-Lagrangian Scheme for Multiscale Plasma Dynamics

Plasma systems exhibit complex multiscale dynamics that require full kinetic models for accurate representation. Explicit kinetic schemes are easy implemented but require time steps finely resolved to the plasma period and suffer from numerical heating, while implicit schemes ensure stability but at the expense of computationally intensive nonlinear solvers. Semi-implicit methods strike a balance between efficiency and stability, but struggle to conserve energy, leading to potential instabilities. While ECSIM introduced a pioneering energy-conserving semi-implicit PIC framework, developing efficient and unconditionally stable grid-based schemes with energy conservation remains a significant challenge.

We propose an inherently noise-free energy-conserving semi-Lagrangian (ECSL) scheme that retains the efficiency of explicit methods and the stability of implicit approaches. Numerical experiments validate its accuracy, efficiency, and energy conservation, demonstrating ECSL as a promising tool for multiscale plasma simulations.