Probabilistic modelling of the high-pressure arc cathode spot displacement dynamic

Abstract

A probabilistic modelling approach for the study of the cathode spot displacement dynamic in high-pressure arc systems is developed in an attempt to interpret the observed voltage fluctuations. The general framework of the model allows to define simple, probabilistic displacement rules, the so-called cathode spot dynamic rules, for various possible surface states (un-arced metal, arced, contaminated) and to study the resulting dynamic of the cathode spot displacements over one or several arc passages. The displacements of the type-A cathode spot (macro-spot) in a magnetically rotating arc using concentric electrodes made up of either clean or contaminated metal surfaces is considered. Experimental observations for this system revealed a 1/f∼1 signature in the frequency power spectrum (FPS) of the arc voltage for anchoring arc conditions on the cathode (e.g. clean metal surface), while it shows a `white noise' signature for conditions favouring a smooth movement (e.g. oxide-contaminated cathode surface). Through an appropriate choice of the local probabilistic displacement rules, the model is able to correctly represent the dynamic behaviours of the type-A cathode spot, including the FPS for the arc elongation (i.e. voltage) and the arc erosion trace formation. The model illustrates that the cathode spot displacements between re-strikes can be seen as a diffusion process with a diffusion constant which depends on the surface structure. A physical interpretation for the jumping probability associated with the re-strike event is given in terms of the electron emission processes across dielectric contaminants present on the cathode surface.