A Discontinuous Phase-Space Finite Element Discretization of the Linear Boltzmann-Vlasov Equation for Charged Particle Transport

Abstract

We examine the modeling of charged-particle transport when both collision processes with background media and electromagnetic effects are important using the Boltzmann-Vlasov equation. We derive and transform the Boltzmann-Vlasov equation into a form very similar to the standard linear Boltzmann equation with additional operators. We apply the discontinuous finite element methods for discretization in the spatial, energy, and angular variables. An implementation of these methods demonstrates correct transport behavior for fixed electric and magnetic fields. We also demonstrate coupling to Maxwell's equations with a simple electromagnetic solver to generate self-consistent fields.

Keywords:

• Boltzmann
• Vlasov
• charged particle
• electromagnetic fields

Additional information

Funding

Work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin company, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.