Microscopic evolution of the ionizing collision frequency in Townsend avalanches

Information obtained from the analysis of the spectra of the Townsend avalanche amplification provides the basis for the study of average microscopic behaviour of the electrons. The electrical field E is uniform, and the avalanches are triggered off at the cathode by a single primary electron. Experimental conditions are such that no secondary effects or space charge can take place. The results of these experiments (methane, 50< E/p <300 V cm −1 Torr −1 ) prove that the multiplication process is a non-markovian one, and also that it rapidly attains asymptotic behaviour. When interpreted in the light of the age-dependent branching processes, the results enable one to determine some distribution functions: the distribution g (θ) of the time intervals θ between two ionizing collisions, the multiplication coefficient a (τ) characterizing the ionizing capacity of the electron as a function of its `age' τ. a (τ) describes the phenomenon more precisely than does the first Townsend coefficient. The application of this method when E/p and pd are constant ( p represents gas pressure and d gap distance) shows that these distributions comply with the similarity principle.