Abstract
While the particle-in-cell (PIC) method has been the subject of years of theoretical study, the common misconception that PIC approximates the collisionless Vlasov-Maxwell system of equations, or the Vlasov-Poisson system for the electrostatic case, is widely cited. In this paper, a PIC-relevant generalization of the instability enhanced Lenard-Balescu collision operator is derived. The analysis of this collision operator demonstrates that while coulomb collisions are truncated by the electric field grid resolution, longer range collisions that arise from imperfect shielding in the presence of instabilities persist. These instability enhanced collisions are completely captured by PIC as long as there is sufficient grid resolution to resolve the wavenumber of the unstable modes of the instability. The inclusion of this behavior is akin to particle wave interactions in the Vlasov based quasilinear theory but with one important difference. Quasilinear theory requires an initial spectral energy density which cannot be supplied self-consistently from within the theory because its initial value is determined by non-Vlasov collisional effects. With the proper electric field grid resolution, the initial spectral energy density is included self-consistently, along with the generation of plasma waves originating from discrete particle motion. Predictions of the grid resolution effect are found to be in agreement with PIC simulations at varying grid resolutions.
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Published Version
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