Non-stationary magnetized axially symmetric equilibrium from the fluid equations of motion

TL;DR

This paper analyzes the equilibrium states of a fully ionized plasma under coaxial electric and magnetic fields, incorporating magnetization effects and examining how pressure profiles influence equilibrium feasibility.

Contribution

It introduces a modified Hall term with a 1/2 factor and incorporates magnetization forces into the plasma equilibrium equations, providing new insights into plasma behavior.

Findings

Magnetization can significantly affect plasma equilibrium conditions.

Pressure profile near the outer edge is crucial for equilibrium feasibility.

Modified Hall effect term influences charge motion in plasma.

Abstract

The equations of motion for a fully ionized hydrogenic plasma in applied coaxial electric and magnetic fields are analyzed, where the term for the Hall effect in the generalized Ohm's law equation picks up a factor of 1/2 relative to its usual expression. Magnetization of the medium is incorporated through the decomposition of the Hall term and the inclusion of the magnetization force, which is found to equal or exceed the gradient of the scalar pressure. A limit on the kinetic pressure obtains which corresponds to the usual limit of unity for a certain selection of parameters. Solutions of these equations for the free motion of the charges in the case of an infinite column with azimuthal symmetry are compared for various prescribed pressure profiles, where one finds that the profile near the outer edge plays an important role in the feasibility of the equilibrium.