Instability of a discharge with a closed EperpendicularH electron drift and a distributed electric field

The stability of a discharge with a closed Hall-current circuit and a distributed electric field is analyzed with respect to long-wave, low-frequency perturbations propagating in the electric drift direction (''low-frequency'' here is with respect to the ion transit time). The analysis is carried out in the linear theory. A dispersion relation derived in the first approximation of the Bubnov--Galerkin method is analyzed numerically. The instability which is found requires a threshold to be attained, which occurs when the neutral density exceeds a certain critical value. An increase in the magnetic field, in contrast, has a stabilizing effect. The instability is oscillatory and develops over wavelengths lying in a finite interval which depends on the dimensions of the device, the magnetic field, and the gas pressure. The wave phase velocity is of order √V/sub i//M, where V/sub i/ is the ionization potential and M is the ion mass. The calculated oscillation frequencies and propagation velocities for the perturbations agree satisfactorily with experimental data. The wave structure is analyzed, and the nature of the instability is determined. Perturbations with an elevated plasma density move in the electric drift direction and correspond to an ionization wave