The Parker Magnetostatic Theorem

Details The Parker Magnetostatic Theorem The Parker Magnetostatic Theorem

2010-02-23

arxiv.org/abs/1002.4399v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

13 pages, no figure

Scientific paper

We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibirum condition. The theorem then follows from the deduction that a continuous nonequilibrum field with a topology not in that subset must find a force-free state containing tangential discontinuities.

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