Instability of a Plasma Column in a Longitudinal Magnetic Field

Abstract

The stability of a positive column in a longitudinal magnetic field is investigated by linearization of the macroscopic equations of motion and continuity for ions and electrons. The treatment is more general than similar calculations by Kadomtsev and Nedospasov and Hoh, in that diffusion and magnetic field interaction terms are included in the ion equation of motion, and also in that the equations are solved in a rigorous manner without any a priori assumptions regarding the form of the radial dependence of the perturbations of density and potential. In the one example calculated, for the helical instability, an important result is the existence of a finite perturbed potential at the wall radius. The boundary between stability and instability as a function of longitudinal electric and magnetic fields is shown graphically, along with the wavelength and frequency of the helical mode at the critical value of the magnetic field.