Confined steady states of the relativistic Vlasov–Maxwell system in an infinitely long cylinder

Jörg Weber

doi:10.3934/krm.2020040

Article Contents

2020, Volume 13, Issue 6: 1135-1161. Doi: 10.3934/krm.2020040

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Confined steady states of the relativistic Vlasov–Maxwell system in an infinitely long cylinder

Jörg Weber

University of Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany

Received: February 29, 2020

Revised: May 31, 2020

Early access: September 2020

Published: November 2020

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Abstract

The time evolution of a collisionless plasma is modeled by the relativistic Vlasov–Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. In this work, the setting is two and one-half dimensional, that is, the distribution functions of the particles species are independent of the third space dimension. We consider the case that the plasma is located in an infinitely long cylinder and is influenced by an external magnetic field. We prove existence of stationary solutions and give conditions on the external magnetic field under which the plasma is confined inside the cylinder, i.e., it stays away from the boundary of the cylinder.

Keywords:

Relativistic Vlasov–Maxwell system,
magnetic confinement,
nonlinear partial differential equations,
stationary solutions.

Mathematics Subject Classification: 35Q61, 35Q83, 82D10.

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