##
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)