The Townsend criterion for electrical breakdown in gases is based upon a singularity in the Townsend expression for the current as a function of voltage. The conventional derivation of this equation involves the assumption that space charges are absent. A more precise expression of this criterion, involving the effects of space charge, removes the singularity and describes a current that is finite at every finite point. Beyond a certain current, however, the derivative of the current with respect to voltage becomes negative, indicating that the system is incapable of withstanding a voltage larger than that at which the negative characteristic develops. In most cases, the breakdown voltage so established should not differ appreciably from that given by the ordinary Townsend equation.

The second Townsend coefficient is normally determined from the curvature found, as the sparking separation is approached, in plots of the logarithm of the current versus electrode separation at constant electric field. The extent of this curvature can be influenced somewhat by distortion of the electric field by space charges if the initial photocurrent from the cathode is sufficiently large.

• Received 21 April 1954

DOI:https://doi.org/10.1103/PhysRev.96.10