Mathematisches Kolloquium

Zusammenfassung: Magnetic reconnection is a process in plasma that involves the breaking and recombination of magnetic field lines that can result in significant amounts of magnetic energy being converted into kinetic energy. This process occurs in the Earth's magnetosphere both on the dayside and in the magnetotail, and leads to magnetic storms that can damage orbiting satellites. Magnetic reconnection events are also believed to be important in solar flares. In both of these applications the magnetic reconnection is essentially collisionless. Although sufficient for capturing flow features such as the basic structure of the magnetosphere, single fluid systems such as ideal MHD (magnetohydrodynamics) do not correctly model magnetic reconnection. In fact, ideal MHD is only able to produce a slow form of reconnection (Sweet-Parker) that is insufficient to explain observations. In order to account for the correct physics, various forms of multi-fluid effects must be included. In this talk we first review the problem of magnetic reconnection. We then discuss various mathematical models for collisionless plasma, focusing in particular on two-fluid models. Next we describe our efforts to develop a class of discontinuous Galerkin methods for solving a few of these models. Some results on applying these methods to the GEM (geospace environment modeling) magnetic reconnection challenge problem are presented. Finally, we discuss some open questions that we hope to tackle in future work.