# American Institute of Mathematical Sciences

December  2020, 13(6): 1135-1161. doi: 10.3934/krm.2020040

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

 University of Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany

Received  March 2020 Revised  June 2020 Published  September 2020

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.

Citation: Jörg Weber. Confined steady states of the relativistic Vlasov–Maxwell system in an infinitely long cylinder. Kinetic & Related Models, 2020, 13 (6) : 1135-1161. doi: 10.3934/krm.2020040
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