A High-Precision Multi-Step Particle-in-Cell Method with Explicit Prediction and Implicit Correction

We propose a novel Particle-In-Cell (PIC) method that utilizes prior multi-step particle information through an explicit prediction-implicit correction approach, named the multi-step PIC (MSPIC) method. The key advantages include: (i) high accuracy by leveraging existing data, (ii) an implicit correction step that significantly broadens the stability range of the time step while maintaining accuracy, and (iii) the complexity of the field solver is analogous to that of explicit PIC, enabling straightforward extensions to electromagnetic and relativistic scenarios. Among multiple Adams multi-step methods using four-step prediction and three-step correction, we employ the boundary locus method to identify the scheme with maximum negative real axis stability region. Theoretical analysis and benchmark experiments confirm the MSPIC algorithm's stability, high precision, and energy conservation based on accuracy. The resulting solution maintains good robustness over a larger step size span on PIC/Monte Carlo. The MSPIC method has also been successfully coupled with external circuit and transmission line models, and been used to simulate capacitively coupled plasmas successfully.