Simulating a Plasma Sheath With the Kinetic Finite Mass Method

Christopher Young, Stanford University

First results of a plasma sheath simulation using the Kinetic Finite Mass (KFM) Method are presented. The KFM Method, derived from the Finite Mass Method of [1], is a gridless Lagrangian simulation technique that partitions the system mass into “packets” or “superparticles” that evolve over time. The packets have finite extent in 1-D phase space, continuous Gaussian internal mass distributions, and a defining set of Gauss-Hermite quadrature points that move under the action of forces. Much like in a Particle-In-Cell (PIC) approach, the electric field is calculated by solving Poisson’s equation over a temporary grid (introduced only when updating quadrature point positions and velocities). A Gaussian Mixture Model is employed periodically to reset the Gaussian character of the particles after distortion from the electric forces.

The current study is a simple discharge between two absorbing walls at zero potential where ion and electron particles are tracked separately. When mass reaches the wall, an equal amount of charge from both species is removed and reintroduced elsewhere in the domain, conserving total mass in the system and incorporating a simple model for ionization. Results are compared with conventional PIC simulations to good agreement. This work provides a demonstration of the powerful KFM method in preparation for simulating more complex plasma phenomena.

[1]C. Gauger et al. SIAM J. Numer. Anal. 26, 1744 (2005)

Abstract Author(s): Christopher V. Young and David J. Larson