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Time evolution of a Vlasov-Poisson plasma with magnetic confinement

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

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