Mathematics Faculty Research

Title

Global Magnetic Confinement for the 1.5D Vlasov-Maxwell System

Document Type

Article

Publication Date

Spring 3-2015

Abstract

We establish the global-in-time existence and uniqueness of classical solutions to the ``one and one-half'' dimensional relativistic Vlasov--Maxwell systems in a bounded interval, subject to an external magnetic field which is infinitely large at the spatial boundary. We prove that the large external magnetic field confines the particles to a compact set away from the boundary. This excludes the known singularities that typically occur due to particles that repeatedly bounce off the boundary. In addition to the confinement, we follow the techniques introduced by Glassey and Schaeffer, who studied the Cauchy problem without boundaries.

Publication Title

Kinetic and Related Models

Volume

8

Issue

1

First Page

153

Last Page

168