(untitled) (Communications in Computational Physics, 2024)
An implicit, asymptotic-preserving and energy-charge-conserving (APECC) Particle-In-Cell (PIC) method is proposed to solve the Vlasov-Maxwell (VM) equations in the quasi-neutral regime. Charge conservation is enforced by particle orbital averaging and fixed sub-time steps. The truncation error depending on the number of sub-time steps is further analyzed. The temporal discretization is chosen by the Crank-Nicolson method to conserve the discrete energy exactly. The key step in the asymptotic-preserving iteration for the nonlinear system is based on a decomposition of the current density deduced from the Vlasov equation in the source of the Maxwell model. Moreover, we show that the convergence is independent of the quasi-neutral parameter. Extensive numerical experiments show that the proposed method can achieve asymptotic preservation and energy-charge conservation.