Mathematics – Logic
Scientific paper
Mar 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984apj...278..409t&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 278, March 1, 1984, p. 409-419.
Mathematics
Logic
33
Hamiltonian Functions, Magnetic Field Configurations, Magnetohydrodynamic Stability, Magnetostatics, Plasma Equilibrium, Stellar Magnetic Fields, Topology, Degrees Of Freedom, Hamilton-Jacobi Equation, Kolmogoroff Theory, Lines Of Force, Perturbation Theory, Phase-Space Integral, Solar Magnetic Field, Two Dimensional Flow
Scientific paper
The topological stability of MHD equilibria is investigated by exploring the formal analogy, in the ideal MHD limit, between the topology of magnetic lines of force in coordinate space and the topology of integral surfaces of one- and two-dimensional Hamiltonian systems in phase space. It is demonstrated that in an astrophysical setting, symmetric magnetostatic equilibria satisfying the ideal MHD equations are exceptional. The principal result of the study is that previous infinitesimal perturbation theory calculations can be generalized to include finite-amplitude and symmetry-breaking effects. The effect of the ergodicity of perturbed symmetric equilibria on heat dispersal in magnetically dominated plasmas is discussed.
Distler Jacques
Rosner Robert
Tsinganos K. C.
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