The Role of Space Charge in the Study of the Townsend Ionization Coefficients and the Mechanism of Static Spark Breakdown

The mechanism of spark breakdown has been investigated largely by the study of the deviations of the pre-spark current from the simple electron ionization law $i=i_0{e}^{\alpha d}$. The deviations indicate a greater current than this for large $d$. The customary explanation has been that ionization by positive ions occurs or that additional electrons are liberated from the cathode by photoelectric processes or by ion bombardment. We have studied the possibility of increased current being caused, not by a new process, but by a distortion of the field of the spark gap by space charge, giving an apparent increase in the exponential coefficient, $\alpha$. The coefficient $\alpha$ is a function of the field strength in the gap, but the function consists of three distinct parts. When the field strength is in its lowest range of values, $\alpha$ increases exponentially with field strength; in the middle range, $\alpha$ increases as the square of the field strength; in the third region $\alpha$ increases more slowly than the first power of the field strength. It is shown by solution of Poisson's equation that space charges can occur, that they will cause an increase in $\alpha$ in the first two regions but not in the third, that the deviation of $\alpha$ from a constant value in a particular case due to field distortion occurs very sharply as $d$ increases, particularly so in the first region, and that a sparking condition occurs if the original, applied field strength is not so high that local distorted fields extend into the third region. The effect of space charge is only difficultly separable from the other (Townsend) ionization phenomena which may occur, when the field strength is up in the second region, but it is probably the primary cause of spark breakdown in the first region. The Townsend processes are undoubtedly completely valid in the third region.