Investigation of oscillations and anomalous transport in a hydrogen hollow cathode discharge by a spatially three-dimensional two-fluid model

A spatially three-dimensional two-fluid model for electrons and ions has been developed in order to describe the plasma state of a magnetized hollow cathode arc burning in hydrogen at low pressure. In this direct current (DC) supplied discharge strong self-excited periodical oscillations have been observed previously, where a helically shaped plasma column rotates eccentrically around the magnetic field axis. The theoretical description of this plasma is based on the system of two-fluid equations formulated by Braginskii. After some estimations and approximations derived from the experimental results and by limiting the discussion to stationary and low-frequency phenomena, the system of equations can be reduced and a second-order differential equation of elliptic type for the plasma potential is derived. Using the measured spatial distributions of time resolved electron density and temperature as input data, this differential equation is solved numerically and the spatial distributions of the electric field, drift velocities, current densities and other quantities can be calculated. The results of our calculations show that an eccentrically rotating minimum of the plasma potential exists, while the arc current is concentrated in an annular region of maximum electron temperature. The magnitude of the radial particle transport coefficient is found to be in the order of the Bohm diffusion coefficient, which is about one order of magnitude larger than the classical diffusion coefficient. The measured oscillation frequencies can be explained by the drift frequency.