A Theory of the Initial Avalanche in the Breakdown of a Discharge Counter in Helium

Abstract

On the basis of the discussion on Townsend's criterion for breakdown, definite hypotheses are arrived at as to the behavior of both the positive ions and the photons in the initial avalanche in the breakdown between coaxial cylinders in helium. Calculations of the shape of the field through which the avalanche passes show that to a good approximation the field is proportional to $\frac{1}{r}$ up to a point where the space charge effect of the positive ions in the avalanche starts to modify the field, and thereafter the field through which the avalanche travels can be considered constant. The functional form of the photon effect leads to the assumption that two types of photons are operative, which can be identified with the resonance radiation of He I and He II. Theoretically derived graphical methods for predicting breakdown voltages are given. Comparison between theoretical and experimental threshold curves leads to good agreement for all cylindrical geometries from that usually employed in Geiger-Müller counters up to the limiting case of parallel plates.