Spark Breakdown Threshold in Non-Uniform Fields

Abstract

We develop a criterion for spark breakdown in non-uniform field geometries with positive polarity and small electrode separations so that breakdown evolves without the formation of a leader. We arrive at the spark-breakdown criterion by framing it in terms of gain and instability conditions, whose relative importance are established from an analysis of the experimental breakdown characteristics and correlations with streamer behavior in short gaps. Results are presented in the context of two generic geometries having coaxial and point-plane electrodes. For nearly uniform field situations, we re-confirm that the breakdown criterion obtained by the usual extension of either the Townsend or Meek criteria satisfactorily predicts the experimental results. On the other hand, for increasing non-uniformity, the results for the corona and spark branches of the breakdown characteristics are shown inconsistent with a breakdown criterion solely based on either the Townsend or streamer mechanisms. In particular, the avalanche gain factor, the primary component of the Townsend and streamer criteria does not determine the spark breakdown criterion. Streamers can cross the gap for a significantly wide range of applied voltages without triggering a spark. We find that it is the instability condition, derived from a relation between the minimum Laplacian field in the gap and the local streamer body field (which we relate to the streamer sustaining field), that is sufficient for determining the spark threshold thereby yielding a breakdown criterion. We examine the physics of the discharge occurring in the several parts of the nonuniform field gap to elucidate the underpinning of the threshold criterion. These include streamer stability and branching in the stressed electrode region, cathode fall setup near the planar-type electrode, and importantly, the renewed ionization of the discharge resulting from neutral expansion of the gas discharge driven by currents, which are critically dependent on the minimum field level in the gap. We also discuss experiments which were carried out to examine instabilities associated with the streamer breakdown of uniform gaps with triggering.