Considerations on Spark- Gap Channel Radius and Electrical Conductivity

Abstract

A simple phenomenological model is established to determine the temporal evolution of spark gap channel radius and electrical conductivity during the resistive phase period. The present determination is based on the Braginskii’s equation for the channel radius which includes the electrical conductivity of the discharge channel as a constant quantity. In the present model, however, the electrical conductivity is regarded as a time varyingquantity. Basing on this, a mathematical formulation for the channel radius as a function of time was derived, and this has made possible the derivation of an explicit expression for the conductivity as a function of time as well. Taking the temporal average of the electrical conductivity offers an alternative mathematical formulation for the instantaneous radius based on a steady conductivity value that can be determined according to some experimental parameters. It has been verified that both of the channel radius formulations mentioned above lead to similar results for the temporal evolution. The obtained results of the channel radius were used to determine the instantaneous inductance of the spark channel. The present model was used to examine the role of gas pressure and gap width on the temporal evolutions of the channel radius, conductivity, and inductance in nanosecond spark gaps.