An exact solution of the moving boundary problem for the relativistic plasma expansion in a dipole magnetic field

Abstract

Abstract. An exact analytic solution is obtained for a uniformly expanding, neutral, highly conducting plasma sphere in an ambient dipole magnetic field with an arbitrary orientation of the dipole moment in the space. Based on this solution the electrodynamical aspects related to the emission and transformation of energy have been considered. In order to highlight the effect of the orientation of the dipole moment in the space we compare our results obtained for parallel orientation with those for transversal orientation. The results obtained can be used to treat qualitatively experimental and simulation data, and several phenomena of astrophysical and laboratory significance.

Resistive magnetohydrodynamic model for cylindrical plasma expansion in a magnetic field

“…Using a simple model for the electrical conductivity we have also studied the energy balance during the plasma expansion as well as the spatio-temporal distribution of the magnetic field with an arbitrary orientation of the initial field. In contrast to the previous treatments with highly conducting plasmas [13][14][15][16][17][18], our model calculations demonstrate some new features arising due to the finite conductivity of the expanding plasma.…”

“…Previously significant attention has been paid [4,5,[14][15][16][17][18] to the question of what fraction of energy is emitted and lost in the form of electromagnetic pulse propagating outward of the expanding plasma. In this section we consider the energy balance during the plasma cylinder expansion in the presence of the homogeneous magnetic field.…”

“…In Refs. [13][14][15][16][17][18] plasma has been considered as a highly conducting medium with zero magnetic field inside. From the point of view of electrodynamics, it is similar to the expansion of a superconductor in a magnetic field.…”

“…Of the vast literature on the theory of plasma expanding into a vacuum or into a background plasma, Refs. [11][12][13][14][15][16][17][18][19][20][21][22] (see also references therein) illustrate various aspects and approaches. In Refs.…”

“…[15] in a one-dimensional (1D) geometry for a plasma layer. In our recent papers, we obtained an exact analytic solution for the uniform relativistic expansion of a highly conducting plasma sphere [16,17] or cylinder [18] in the presence of a dipole or homogeneous magnetic field, respectively.…”