Morse-Smale flows and the model of the topology of magnetic fields in plasma

A. N. Saharov ; A. A. Shilovskaya

Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 1, pp. 88-101.

Résumé

This article is a continuation of the work [14] and is devoted to the presentation of results related to the construction of models of magnetic fields in an electrically conductive medium (plasma) in terms of dynamic systems. Research in this direction has been intensively pursued over the past 20 years. Since the solution of magnetic hydrodynamics’ equations is associated with certain difficulties approximate models of magnetic fields are used. A class of vector fields' models is constructed, united by the common name model of the topology of magnetic charges. Fields from this class generate continuous dynamical systems (flows) on three-dimensional manifolds with a sufficiently simple structure. First, the non-wandering set is finite and consists of hyperbolic equilibrium states. Second, these flows allow the existence of a so-called self-indexing energy function that allows them to be complete topological classified. In addition, fields of this class may be arbitrarily closely approximated by vector fields generating structurally stable flows. Particular attention is paid to the fields in the corona of the Sun, which is associated with the actual problem of energy release estimation in solar flares.

Détail

Keywords: singular points of the field, magnetic field lines, sinks, separatrix, separators, heteroclinic curves.
Mots-clés : sources

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