Author: Evstati G. Evstatiev
Requested Type: Poster
Submitted: 2018-02-28 17:23:24
Co-authors: J. M. Finn, B. A. Shadwick, N. Hengartner
West Virginia University Institute of Technology
512 S Kanawha St
Beckley, WV 25801
Even with delta-f methods, there is still a need for reduction of noise in particle simulations, especially to do global modeling. We study particle noise in the variational particle method of Evstatiev and Shadwick. An important aspect of Ref. is energy conservation, which implies that there is no grid heating. The first step involves a 1D electrostatic code with immobile ions. We have analyzed the covariance matrix for density fluctuations, depending on the particle shape used for density estimation. A noteworthy feature is the presence of negative correlations in all cells, due to the fact that particles never enter or exit the domain, due to periodic boundary conditions. This effect is responsible for a "Brownian Bridge" effect on the electric field computed using the Poisson equation. This is to be distinguished from a statistical Poisson process, in which one specifies the expected number of particles (and particles per cell) rather than the exact number of particles.
Our method of optimizing the effect of particle noise involves bias-variance optimization (BVO). The tradeoff here is that a particle size that is too large leads to too much density smoothing and a biased estimate; a particle size too small leads to each particle contributing to too few cells, leading to too high a noise level.
A conclusion of this study is that there is no need to have particle size tightly bound to grid size and to particle smoothness. We have verified the analytic conclusions discussed above: the density correlations for various particle shapes, the negative correlations, and the BVO. This was performed both with randomly placed particles as well as particles in a 1D electrostatic simulation.
 "Variational formulation of particle algorithms for kinetic plasma simulations", E. G. Evstatiev and B. A. Shadwick, J. Comp. Phys., 2013.