Low-frequency flute instabilities of a hollow cathode arc discharge: Theory and experiment

The characteristics of two low-frequency electrostatic flute instabilities of a low-pressure hollow cathode arc discharge are reported. Mode I has azimuthal mode number m = 1, and occurs when the radial electric field is negative (directed inward) while mode II has m = −1 and occurs when the field is positive. The radial electric field is controlled by varying the potential of a secondary anode cylinder located close to the outer discharge radius. A linear perturbation analysis, based on the two-fluid equations, is given for a low-β, collisionless, cylindrical plasma column, immersed in a uniform axial magnetic field, having a Gaussian density profile and an arbitrary radial electric field profile. Reasonable correlation between theory and experiment is demonstrated for both modes, by comparing the calculated and measured frequencies, mode numbers, and also the eigenfunctions of the density and potential fluctuations. The instabilities are basically centrifugal flute modes, driven by E × B drift in the presence of a density gradient and modified by the velocity shear due to nonuniform E × B rotation.