Selfsimilar Evolution of Magnetized Plasmas. I. Quasistatic Solution
Abstract
The concept of linear expansion, suggested in our 1989 and 1990 papers, describes the selfsimilar evolution of a magnetic structure. Linear expansion can be represented by a single function ξ(t), which connects the evolving physical parameters of the plasma with their initial values in explicit forms. A general selfsimilar dynamic equation, therefore, is derived. As the first step toward more general consideration, the quasistatic solution is investigated in this paper. It is shown that a γ = 4/3 polytrope may evolve through consecutive equilibria if its magnetic field expands selfsimilarly. The change of the energy everywhere inside the plasma equals the work done by the internal plasma pressure and magnetic field for the expansion. For the special case of an expanding forcefree magnetic field, the selfsimilar expansion is a clean expansion. No free magnetic energy is left anywhere inside the magnetic structure. The approximation in quasistatic modeling of a pressure confined magnetized plasmoid is analyzed. It requires that the characteristic Alfven traveling time τ_A_ of the plasmoid is negligible as it is compared to the relative change rate of the external pressure. If the finite relaxing time is taken into account, excess magnetic potential energy may accumulate.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1992
 DOI:
 10.1086/171446
 Bibcode:
 1992ApJ...392..465Y
 Keywords:

 Interplanetary Magnetic Fields;
 Plasma Jets;
 Solar Corona;
 Solar Flares;
 Hydrodynamic Equations;
 Magnetic Clouds;
 Magnetohydrodynamics;
 Radio Sources (Astronomy);
 Solar Atmosphere;
 Astrophysics;
 GALAXIES: JETS;
 MAGNETOHYDRODYNAMICS: MHD;
 PLASMAS;
 SUN: CORONA