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Topology bounds the magnetic energy in planar kinematic dynamos | | L. C. Garcia de Andrade
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29 Jan 2007 | | Abstract: | Curvature and helicity topological bounds for the magnetic energy of the streamlines magnetic structures of a dynamo flow are computed. The existence of the filament dynamos are determined by solving the magnetohydrodynamic equations for planar flows and the solution is used to determine these bounds. When the flow is assumed geodesic and the sign of the curvature and normal coordinate coincides we show that the Arnold theorem for the helicity bound of energy of a divergence-free vector field is satisfied for these streamlines and the constant which depends on the size of the compact domain $M C R^{2}$, where the vector field is defined is determined in terms of the dimensions of the constant cross-section filament. It is shown that when the Arnold theorem is violated by the filament no dynamo structure appears and the magnetic field decays in space. | | Source: | arXiv, astro-ph/0701806 | | Services: | Forum | Review | PDF | Favorites | |
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