Computer Science – Numerical Analysis
Scientific paper
Jul 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...429..876h&link_type=abstract
The Astrophysical Journal, vol. 429, no. 2, pt. 1, p. 876-889
Computer Science
Numerical Analysis
14
Continuity, Discontinuity, Ejecta, Magnetostatic Fields, Mathematical Models, Physical Properties, Solar Atmosphere, Solar Corona, Stability, Analytic Functions, Boundary Value Problems, Equilibrium, Linearization, Magnetohydrodynamics, Numerical Analysis, Solutions
Scientific paper
A model is presented for the static equilibrium of a magnetized, polytropic atmosphere stratified by uniform gravity and invariant in a Cartesian direction. The profiles of plasma pressure and magnetic shear as functions of the magnetic stream function, which render the governing equation linear, lead to unphysical features if these profiles are applied to the infinite half-space bounded below by a plane. These undesirable features are shown to be removed when these special profiles are localized to a region bounded by a magnetic flux surface, outside of which is an atmosphere in plane-parallel hydrostatic equilibrium with a potential magnetic field. Two families of solutions are constructed by direct solution of the Cauchy boundary value problem for the Laplace equation, one with continuous and the other with discontinuous pressures across this magnetic boundary. Illustrative solutions are analyzed, with applications to long-lived density enhancements and depletions in the solar corona. In particular, the hydromagnetic stability of pressure discontinuities is studied as an example of a general result due to Hu (1988). It is pointed out that the stability of the sharp interface between the prominence cavity and the high-density coronal helmet may be understood in terms of competing effects arising from density stratification and magnetic curvature. The model presented lays the mathematical groundwork for the other papers of the series.
Chye Low Boon
Hundhausen J. R.
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