Åse-Marit Janse - Spontaneous Current Sheets: Radically different in 3D fields vs in 2D fields!

Under conditions of very high electrical conductivity, such as in the fully ionized, million-degree solar corona, the magnetic field is essentially frozen into the plasma and, therefore, the magnetic field topology cannot change. The topology is described by where each thin flux tube enters and leaves the volume, and the twist and linkages of the magnetic flux tubes. The freezing of magnetic flux prevents the mixing of local fluid volumes that trap different flux systems. This can induce thin sheets of intense electric-current density to flow tangentially on the magnetic flux surfaces. The nonlinear thinning of these current sheets can reach the point where resistive dissipation becomes significant, producing heating and changes in field topology, as described by the Parker theory. If small-scale current sheet production pervades the corona, the dissipated energy is a means to heat the quiescent corona. Macroscopic size current sheets have been suggested to be the origin of solar flares.

Together with B. C. Low (HAO, NCAR), Åse has studied current-sheet formation in a special class of magnetic fields: Topologically untwisted magnetic fields. (Basically a field is untwisted if: (i) each of its flux tubes is internally untwisted, that is, there is no net twist along its entire length from a tube footpoint to the other footpoint, and, (ii) these flux tubes do not twist among themselves.) Our model starts with a topologically untwisted field inside a cylinder of perfectly conducting fluid. The field is anchored by its magnetic footpoints fixed at the cylinder ends, so that its topology is invariant to a continuous change in the length of the cylinder. Whereas this field of a fixed topology may have a continuous equilibrium state, as a potential field, for a particular length of the cylinder, no continuous equilibrium state is available to the field when the cylinder is given other lengths. In the latter case, magnetic discontinuities or current sheets must form, whose dissipation can then change the field topology to one compatible with a continuous state.

While magnetic neutral points or separatrix flux surfaces are necessary for current sheet formation in two-dimensional fields, in fully three-dimensional fields current sheets form readily even in the complete absence of neutral points and separatrix surfaces, and, these sheets can form densely throughout the field in response to changes in the magnetic volume.

ASP Spotlight October 2008
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