Validation of the Townsend criterion for ignition of volume gas discharges

Abstract

An eigenvalue problem governing ignition of volume discharges is formulated in the drift approximation with account of photoionization and the presence of multiple ion species with various reactions. The Townsend ignition (self-sustainment) criterion is deduced by partial integration of this eigenvalue problem neglecting the photoionization, and, in the case of electronegative gases, also the detachment. The Townsend criterion is applied to three examples of discharge ignition in high-pressure air, two of them referring to negative coronas in concentric-cylinder and point-to-plane configurations and one to a configuration with weakly nonuniform electric field. The comparison of the results obtained from different forms of the Townsend criterion with those given by the accurate numerical solution of the full eigenvalue problem shows that the neglect of the diffusion of the charged particles produces an error in the ignition voltage of the order of or less. The effect of photoionization for these configurations is also weak as expected. The lower and upper estimates of the effect of negative ions over the ignition voltage are obtained from different forms of the Townsend criterion. A form of the Townsend criterion, which employs an effective attachment coefficient in air and takes into account, in an approximate way, also the detachment, gives a virtually exact value of the inception voltage in all the cases considered. Practical recommendations are given on when one can use the Townsend self-sustainment criterion, and when one should resort to a numerical solution of the general eigenvalue problem governing discharge inception.