Physics
Scientific paper
Dec 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974soph...39..393m&link_type=abstract
Solar Physics, vol. 39, Dec. 1974, p. 393-404.
Physics
32
Atmospheric Models, Equilibrium Equations, Force-Free Magnetic Fields, Magnetohydrodynamic Stability, Solar Atmosphere, Upper Atmosphere, Boundary Conditions, Boundary Value Problems, Hydrodynamic Equations, Laplace Equation, Linear Equations, Magnetic Field Configurations, Potential Fields, Solar Activity, Thermal Energy, Virial Theorem
Scientific paper
Force-free magnetic fields are analyzed on the basis of first-approximation magnetohydrodynamics equations for the case where the field energy is higher than the thermal energy of the medium. Such conditions may occur in active regions in the solar upper atmosphere. As a consequence of the virial theorem it is shown that only two cases are possible for any solution of the corresponding system of nonlinear equations: either the total energy of the field is described by a divergent integral, or the field is no longer force free in some regions. Hence, a force-free current system cannot exist everywhere, and boundary value problems for fields of this type are as essential as for harmonic fields. Integral relations are derived which constitute the necessary conditions for the solution of boundary value problems. It is shown that force-free fields are stable with respect to small changes in the boundary conditions, and that hydrodynamically configurations of such fields exist.
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