Quebec Mathematical Sciences Colloquium

from March 23, 2007 16:00 to February 23, 2007 18:00 (Montreal/Miami time) On location

Extreme heating of the sun's atmosphere and the topology of magnetic field lines

Colloquium presented by Ed Stredulinsky (University of Wisconsin-Richland)

The temperature of the sun's atmosphere is about three magnitudes higher than that of the surface of the sun. A classical explanation of this remarkable phenomenon involves the notion that intense electrical currents are produced when tangled magnetic field lines try to move to lower energy configurations. A simple model problem is used to demonstrate how imposition of topological constraints can produce singularities in a solution to an energy minimization problem which would not arise in the absence of such constraints. More precisely a topological decomposition of W^{1,2} Sobolev functions in two dimensions is used to establish existence of magnetic fields in cylindrical symmetry with prescribed field line topology. This is applied to a classical example related to existence of current sheets in the solar corona to illustrate a method of establishing existence of discontinuities in magnetic fields.


UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., room SH-3420