Lagrangian Velocity-Spectral Particle Method for Low-Noise Plasma and Neutral-Gas Kinetics with Conservative Distribution Exchange

A Lagrangian velocity-spectral particle (LVSP) method is developed for plasma and neutral-gas kinetics that combines low sampling noise with conservative exchange of distribution information. Moving spatial point particles carry continuous velocity distributions, replacing random velocity samples and eliminating the need for a uniform velocity grid over the entire spatial domain. The central idea is to combine characteristic transport with exchange of distribution information relative to particle motion: each particle moves with its own mean velocity and retains a spatial point representation, while a background grid organizes the relative fluxes and a conservative allocation determines how each particle's distribution changes. Transport and BGK collisions are treated within the same particle time stages, using exponential relaxation weights for collision gain. The framework unifies charged and neutral particles, and in the single-velocity and local-equilibrium limits it reduces to conventional particle-in-cell and fluid material-point descriptions, respectively. Numerical tests demonstrate low-noise resolution of weak electrostatic signals, conservative relaxation, open-boundary transport, and accurate multidimensional kinetic evolution.