Improvement on the physical description of the boundary conditions between the hollow cathode region and the A-K gap in a transient hollow cathode discharge

An Important connection between the main gap and the hollow cathode region (HCR) in a pulsed hollow cathode discharge is in the positive ions created in the main gap which subsequently enter the HCR through the cathode aperture. These energetic ions control the ionization growth rate inside the HCR through both secondary electron production and in the formation of a positive space charge immediately behind the cathode aperture. The result is the creation of a highly localized plasma on axis inside the HCR from which the injection of a large electron flux leads to the final breakdown. A 2-D fluid code reported previously modelled the ionization growth within the HCR using swarm parameters based on a local field approximation and the growth of this on axis plasma source was predicted. The model adopted to treat the ion flux was based on continuity with the electron flux leaving the HCR. This assumption Ignores the ionization events within the main gap. In this paper. we report on a new model which tackles the physics of collisions in the main gap using a 1-D description in order to return a proper ion flux for the 2-D calculation in the HCR. The methodology is computationally efficient and corrects the discrepancy observed in the relationship of breakdown delay and operating pressure.