Townsend coefficients for electron scattering over dielectric surfaces

A method for describing the probability of initiating flashover discharges across dielectric surfaces is presented in which a transport coefficient for electron multiplication similar to the Townsend coefficient used for gas discharges is defined. The coefficient is a function of the scaling parameter (charge released from the cathode)/(cathode-anode separation) and is also a measure of the growth of the sheath on the dielectric surface resulting from electron scattering. Results are discussed as to when the source of seed electrons does not necessarily depend upon field emission at the cathode-vacuum-dielectric triple point. For these conditions, there is a different functional dependence of flashover probability on voltage and geometry than when field emission provides the seed electrons. As a result, criteria previously used to predict flashover discharges may not apply.