Anode Spot Instability I. The Homogeneous Short Gap Instability

If the current in a "vacuum arc" surpasses a certain critical value a conspicuous and destructive phenomenon occurs at the anode, the ANODE CONSTRICTION INSTABILITY or ANODE SPOT FORMATION [1 - 10]. This paper will give a quantitative analysis of this phenomenon within the limits of a model which can be characterized by lateral homogenity, collision dominance and small electrode separation. Matching the various model regions results in a differential equation for the anodic spot area which exhibits an anode constriction instability of the "explosive type". A marginal instability criterion is derived and evaluated for various materials. This yields extensive information about the dependence of the constriction instability on the parameters of the experimental set up. The findings are compared with the experimental results and show satisfactory agreement within the limitations of experiments and theory.