Topologically Driven Magnetic Dissipation

Klaus Galsgaard, Dept of Appl Math, University of St Andrews

Abstract: Dissipation of magnetic energy is most likely the main heating mechanism in a a number of non-thermal astrophysical environments; e.g., the solar corona and the corona above accretion disks.  A qualitative and quantitative understanding of the dissipation process is therefore of great interest.

In general, a magnetically dominated plasma driven by braiding motions on boundaries at which magnetic field lines are anchored is forced to dissipate the work being done upon it, no matter how small the electrical resistivity may be.  The problem lies in understanding at what level the balance between boundary work and volume dissipation is obtained.

Recent numerical experiments have clarified the mechanisms through which balance is achieved. The results largely confirm Parker's (1972) idea of ``topological dissipation''; dissipation occurs through the formation of a hierarchy of electrical current sheets. Current sheets form when the "local winding number" reaches values of the order of unity, as a result of the topological interlocking of individual strands of magnetic field.

The average level of dissipation is well described by a scaling law that is independent of the electrical resistivity.

Further reading:  Topologically Forced Reconnection, Nordlund & Galsgaard (1997)