Stability of the Positive Column in a Time-Dependent Magnetic Field

The stability of a weakly ionized plasma column in a longitudinal magnetic field containing a small time varying component is investigated, using a macroscopic approach previously developed by the authors for a static field. The time dependence of the field is taken to be linear, and its influence on the column given by the presence of the induced azimuthal electric field. A dispersion relation is derived from the linearized equations of continuity and momentum conservation for the ions and electrons, from which a family of stability boundary curves in the Ez vs B plane are found for the case of a helical perturbation in helium. The condition of energy balance of the column including the azimuthal electric field is combined with the dispersion relation to yield a family of stability boundary curves in the Eθ vs B plane with gas pressure times column radius as a parameter. These curves indicate regions of stability which are absent in the case of a static magnetic field.