Newtonian Development of the Dynamical Properties of Ionized Gases of Low Density

TLDR

The authors derive macroscopic dynamical equations for a low‑density ionized gas in a magnetic field by averaging over anisotropic ion and electron motions. The equations recover standard hydromagnetic behavior, show that anisotropic particle motions only modify the ponderomotive force coefficient, agree with previous isotropic and Boltzmann results, and predict that magnetic field lines are frozen into the plasma, with residual drift motions persisting near equilibrium and the equations remaining valid even at neutral surfaces.

Abstract

The macroscopic dynamical equations of a tenuous ionized gas in a magnetic field are developed by averaging over the individual ion and electron motions, which do not necessarily possess an isotropic distribution. It is shown that the principal motion of the gas is related to the magnetic field by the usual hydromagnetic equations, as developed for conducting liquids and dense gases; the anisotropy of the individual particle motions shows up primarily as a coefficient multiplying the pondermotive force exerted by the magnetic field on the plasma. The results reduce properly to the earlier work of Schl\"uter, Cowling, and Spitzer for isotropic pressure, and are in agreement with the recent developments from the Boltzmann equation. It is pointed out that the magnetic lines of force are permanently connected and move in the frame of reference of the electric drift. It is shown that near static equilibrium, when the principal motions vanish, there remain small macroscopic drift motions of the gas in the field inhomogeneities.It is also shown that the field equations, obtained by assuming that the radius of gyration of the thermal motions is small compared to the scale of the field, are valid even near neutral surfaces, on which the field density vanishes.