Colloque des sciences mathématiques du Québec

de 23 mars 2007 16 h 00 à 23 février 2007 18 h 00 (heure de Montréal/Miami) Sur place

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

Colloque par 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.

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