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

Abstract

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 secondorder 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 (E × B) drift frequency.

High power impulse magnetron sputtering discharges: Instabilities and plasma self-organization

“…The magnetic topology in these experiments is more complex than in, e.g., simple drift wave experiments in cylindrical plasmas confined by co-axial homogeneous magnetic fields. 12,13 Following our conclusion that the instability rotation direction corresponds to the drift direction generated by thẽ E ÂB drift and the finding by Choueri 10 that instabilities in Hall thrusters, where plasma parameters are comparable to HIPIMS plasma parameters, are high frequency azimuthal drift waves, we can conclude that our observed waves are of the generalizedẼ ÂB drift wave type.…”

“…This is characteristic of a saturated drift mode type instability. 12,13 At other parameters, multiple frequencies and even chaotic states may be observed. This will be analyzed in detail in further investigations.…”

Drifting localization of ionization runaway: Unraveling the nature of anomalous transport in high power impulse magnetron sputtering

“…60) and in hollow cathode discharges with axial magnetic field. 61,62 The point of this long list of references is that plasma instabilities under E Â B conditions are the rule, not the exception, and one should not be surprised that HiPIMS discharges contribute to this rich field.…”

Non-uniform plasma distribution in dc magnetron sputtering: origin, shape and structuring of spokes

“…The nomenclature on plasma nonhomogeneities in E × B discharge devices is rather broad. Terms such as plasma instabilities, oscillations, waves, electrostatic fluctuations and others are commonly used to refer to plasma non-homogeneities [18][19][20][21][22][23][24][25][26]. Such inconsistency can be attributed to the complexity and 'richness' of plasma properties; however, in some cases these studies are clearly related to the spokes phenomenon.…”