Expansion of a Resistive Spherical Plasma in a Magnetic Field

Abstract

The expansion of a resistive plasma into an external magnetic field has been treated in the limit in which the magnetic field does not perturb the plasma motion. The use of a class of exact solutions for the purely radial motion of the plasma in the absence of a field permits the reduction of the electromagnetic problem to consideration of a diffusion equation for the magnetic stream function. Explicit solutions are derived for a resistive spherical plasma expanding into a uniform applied magnetic field. Representative numerical results related to laser-produced plasma experiments of Haught and Polk are presented.

Laser-produced plasma expansion in a uniform magnetic field

“…Because the interaction between plasma clouds and a magnetic field is one of the most fundamental problems in plasma physics, many experimental and theoretical studies have been dedicated to it. Plasma expansion in a magnetic field has been theoretically investigated (Bernstein & Fader 1968;Poukey 1969;Raizer 1974). In Raizer (1974), a detailed physical picture of interaction between a collisionless plasma flow and a magnetic field, as well as of plasma energy transformation, is given.…”

Resistive magnetohydrodynamic model for cylindrical plasma expansion in a magnetic field

“…[19][20][21][22] (see also references therein) for spherical [19], planar (1D) [20,21] and cylindrical [22] expansions employing ideal magnetohydrodynamic (MHD) equations. However, it should be noted that the ideal MHD may not be justified in some experimental situations where the typical parameters are such that the plasma resistivity is not negligible [1,3,11,12]. In this case the coupling of the magnetic field with the plasma motion, determined by the magnetic Reynolds number, should result in a distortion and diffusion of the field across the expanding plasma [11,12].…”

“…Similar problem has been treated previously in Refs. [11,12] but for a spherical plasma expansion. Of the vast literature on the theory of plasma expanding into a vacuum or into a background plasma, Refs.…”

“…However, it should be noted that the ideal MHD may not be justified in some experimental situations where the typical parameters are such that the plasma resistivity is not negligible [1,3,11,12]. In this case the coupling of the magnetic field with the plasma motion, determined by the magnetic Reynolds number, should result in a distortion and diffusion of the field across the expanding plasma [11,12]. We present here calculations of the electromagnetic field configuration in the stages preceding significant deceleration of the plasma and in the regime in which the magnetic field does not perturb the purely radial motion of the cylindrical plasma.…”

“…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.…”