Global magnetic confinement for the 1.5D Vlasov-Maxwell system

TL;DR

This paper proves the global existence and uniqueness of classical solutions for a bounded 1.5D relativistic Vlasov-Maxwell system with an external magnetic field that confines particles, preventing boundary singularities.

Contribution

It extends the analysis of the Vlasov-Maxwell system to bounded domains with boundary conditions, demonstrating confinement effects of an external magnetic field.

Findings

Particles are confined away from the boundary due to the magnetic field.

Existence and uniqueness of solutions are established globally in time.

Boundary singularities are avoided through magnetic confinement.

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.