High fidelity simulations of the multi-species Vlasov-Maxwell system with the Numerical Flow Iteration

Abstract The validity of fluid plasma models breaks down for non-thermal or weakly collisional plasmas which are often present, e.g., in the solar wind. In collisionless regimes one has to resort to modeling through the first-principles Vlasov-Maxwell system, but its six-dimensional phase-space dynamics, strong tendency for filamentation, and multi-scale structure make direct numerical simulations extremely demanding. Particle-in-Cell (PIC) methods remain the standard for fully kinetic plasma studies, yet their memory cost, intrinsic noise, and stability requirements render large-scale simulations extremely demanding, especially when multiple particle species are included and when electron scales need accurate resolution. In this paper, we introduce an alternative Vlasov-Maxwell method based on an iterative-in-time approximation of characteristics. The approach reconstructs the phase-space dynamics from the time history of the electromagnetic fields and the initial distribution functions, enabling noise-free, extremely high effective resolution far below the phase-space grid scale without storing or advecting high-dimensional data. Earlier work demonstrated this capability for the multi-species electrostatic Vlasov system. Here, we discuss an extension of the method to the full Vlasov-Maxwell equations using a Hamiltonian splitting to advance the solution in a structure-preserving way while retaining the reduced memory footprint.