Time evolution of a Vlasov-Poisson plasma with magnetic confinement

Silvia Caprino; Guido Cavallaro; Carlo Marchioro

doi:10.3934/krm.2012.5.729

Article Contents

2012, Volume 5, Issue 4: 729-742. Doi: 10.3934/krm.2012.5.729

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Time evolution of a Vlasov-Poisson plasma with magnetic confinement

1.
Dipartimento di Matematica, Università di Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma
2.
Dipartimento di Matematica "Guido Castelnuovo", Università La Sapienza P.le A. Moro 5, 00185 Roma

Received: May 31, 2012

Revised: May 31, 2012

Published: November 2012

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Abstract

We study the time evolution of a Vlasov-Poisson plasma moving in an infinite cylinder, in which it is confined by an unbounded external magnetic field. This field depends only on the distance from the border of the cylinder, is tangent to the border and singular on it. We prove the existence and uniqueness of the solution, and also its confinement inside the cylinder for all times, i.e. the external field behaves like a magnetic mirror. Possible generalizations are discussed.

Keywords:

Vlasov-Poisson equation,
magnetic confinement.

Mathematics Subject Classification: Primary: 82D10, 35Q99, 76X05; Secondary: 35L60.

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