Development of a 3D Spectral Boltzmann Solver for Plasma Modeling

A numerical framework for studying plasma flows in electric propulsion systems is developed. The novelty of this kinetic-theory-based method is the spectral treatment of the Boltzmann collision operator using Fourier-Galerkin scheme coupled with the computational efficiency of the streaming of the lattice Boltzmann method. This spectral treatment (i) avoids the low Mach number restriction of the lattice Boltzmann method or gas-kinetic method and (ii) makes the present scheme valid over a wider range of Knudsen numbers. The sum of two three-dimensional Maxwell distributions were used for verification of the method. Spectral order accurate computations of plasma flows in electric propulsion systems are achievable with this approach. Nomenclature A = magnetic potential a = particle acceleration B = magnetic induction B = kernel in collision integral D = electric displacement field E = electric field f = particle velocity distribution function f̂ = Fourier coefficients fN = truncated Fourier series approximating f φ = electric potential g = relative particle velocity H = magnetic field J = net current density L = loss term in collision operator m = mass N = number of spectral modes Q = collision operator q = charge ρe = net charge density v = particle velocity Aerospace Engineering Department, Texas A & M University, College Station, Texas, 77843 3141 1 The 31 International Electric Propulsion Conference, University of Michigan, USA September 20–24, 2009