A seminar given by
Dr. John M. Finn,
Tibbar Plasma Technologies (USA)
Meshfree analysis and stability in particle-based kinetic plasma simulations
Abstract: We reconsider a meshfree approach to plasma kinetic theory, specialized to 1D electrostatic plasmas. This method uses kernel density estimation for the charge density and a related Green’s function method, from Gauss’s law, for the electric field. The kernel K(x−y) represents the the charge distribution within each macroparticle, both for computing the electric field E(x) and for using E(x) to compute the force on each macroparticle. This method has good conservation properties, conserving momentum and energy exactly. Similarly, the continuity equation is satisfied exactly, and this Vlasov-Gauss system is exactly equivalent to the Vlasov-Ampere and the Vlasov-Poisson systems. The use of the same kernel above leads to a symmetric / positive definite kernel, the correlation of the original kernel with itself, and allows an analog of the kernel trick in Machine Learning: a single positive definite kernel can be substituted for this correlation. We show how the positive definiteness of the kernel guarantees numerical stability. This analysis uncovers a connection between kernels used for density estimation and positive definite (reproducing) kernels. This analysis is useful for constructing meshfree codes and for analyzing PIC codes, which have a grid. For the latter, I will discuss how the numerical stability in the meshfree formulation can break down or be preserved with a grid, depending on the discretization.
Bio: Dr. Finn is a recognized expert in plasma physics as applied to magnetic fusion devices as well as solar and astrophysical plasmas and nonneutral plasmas. He worked at Los Alamos National Laboratory for 23 years, and at the University of Maryland and the Naval Research Laboratory before that. He has worked in the magnetohydrodynamic (MHD) stability and nonlinear behavior of toroidal devices such as tokamaks, reversed field pinches and spheromaks and in the basic theory of magnetic reconnection in laboratory, solar and astrophysical plasmas.
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