二维轴对称相对论Vlasov-Maxwell系统的磁约束
Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus
摘要：
虽然近年来核聚变过程受到了极大的关注，但支持系统稳定性的数学分析量似乎相对不足。本文从动力学方程出发，对等离子体的磁约束进行了数学分析。当边界附近施加巨大（但时间有限）的外部磁势时，我们证明了二维环中Vlasov-Maxwell系统的全局适定性。我们假定解是轴对称的。作者希望，这项工作是一个更普遍的三维托卡马克结构的工作的一步。这项工作的亮点是对外部磁势阱的物理假设，它在有限的时间间隔内保持有限，并从这一点，我们证明了等离子体永远不会接触边界。此外，我们提供了一个充分条件上的外部磁势的大小，以保证等离子体被限制在所需的厚度，这是略大于初始支持的环。我们的方法使用Vlasov-Maxwell系统的柱坐标形式。
英文摘要：
Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to be relatively insufficient. This paper deals with the mathematical analysis of the magnetic confinement of the plasma via kinetic equations. We prove the global wellposedness of the Vlasov-Maxwell system in a two-dimensional annulus when a huge (but finite-in-time) external magnetic potential is imposed near the boundary. We assume that the solution is axisymmetric. The authors hope that this work is a step towards a more generalized work on the three-dimensional Tokamak structure. The highlight of this work is the physical assumptions on the external magnetic potential well which remains finite within a finite time interval and from that, we prove that the plasma never touches the boundary. In addition, we provide a sufficient condition on the magnitude of the external magnetic potential to guarantee that the plasma is confined in an annulus of the desired thickness which is slightly larger than the initial support. Our method uses the cylindrical coordinate forms of the Vlasov-Maxwell system.
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