Low Discrepancy Particle Simulation of Collisionless Flows

Matthew McNenly, University of Michigan

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Particle-In-Cell (PIC) simulations of collisionless flows with local background source terms are often used in plasma modeling. The plasma simulations use computational particles to approximate the kinetic behavior and depletion due to ionization of the molecules. Computational particles are selected for depletion in each cell using the Monte Carlo Collision (MCC) model based on the background cell plasma concentration and ionization rates. Pseudo-random Number Generators (PRNG) are typically used when approximating the wall and boundary interactions and ionization statistics. The drawback to the Monte Carlo approach stems from its dependence on the PRNG which results in a probabilistic error bound of O(N ) where N is the number of samples. Neiderreiter and Sloan have applied deterministic, Low Discrepancy (LD) sequences and lattices to integrate multi-dimensional functions that outperform the Monte Carlo approach. Quasi-random sequences such as the Halton sequence have a deterministic error bound of O(N -1*(logN)s), where s is the dimension of the problem, while regularization of the integrand can yield even higher convergence for the lattice methods. The goal of this paper is to create a framework such that these LD methods can be applied to the collisionless particle transport and ionization due to background source terms. In an effort to simplify the problem while maintaining the same mathematical character of the PIC-MCC simulation, this investigation will focus on 1-D, monatomic, single species, particle simulations with constant, time-varying, and spatially-varying depletion source terms in the cells.

Abstract Author(s): Matthew J. McNenly, Iain D. Boyd