The Growth of Pre-breakdown Currents in a Uniform Electric Field Gap†

The pre-breakdown current across a uniform electric field gap has been calculated in the presence of ionization by electron impact and secondary electron processes. The solution improves upon the Townsend equation (1915) by allowing for the loss of secondary electron current out of the discharge gap. By using the published results of other workers, it has been shown that pre-breakdown currents, measured in the presence of losses, have fitted both the proposed solution and the Townsend equation but for different values of the electron ionization coefficient and the secondary electron coefficient (denoted by α and γ, and α T and γ T respectively). For all gases αT ≥ α and γ T ≤ γ and the inequality existed for all E/p values when photon secondary processes were active. The largest disagreement (α T / α = 1 → 1 and γ / T = 20 → 1) was calculated for argon for E/ < v cm−1 torr−1.