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.

中文翻译：

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无限长圆柱体中相对论性Vlasov-Maxwell系统的局限稳态

无碰撞等离子体的时间演化是通过相对论的Vlasov-Maxwell系统建模的，该系统将Vlasov方程（传输方程）与电动力学的Maxwell方程耦合在一起。在这项工作中，设置为二维和二分之一维，也就是说，粒子种类的分布函数与第三空间维无关。我们考虑等离子体位于无限长的圆柱体中并受外部磁场影响的情况。我们证明了平稳解的存在，并给出了将外部磁场限制在圆柱体内的条件，即等离子远离圆柱的边界。