Microscopic evolution of the ionizing collision frequency in Townsend avalanches

Abstract

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.

Monte Carlo simulation of electron avalanches and avalanche size distributions in methane

“…We chose this particular gas in order to compare the results of the simulation with the measurements reported in Vidal et al [14] The details of the experiment in which avalanche size distributions were measured will be briefly described in this section. We chose this particular gas in order to compare the results of the simulation with the measurements reported in Vidal et al [14] The details of the experiment in which avalanche size distributions were measured will be briefly described in this section.…”

“…In our study, we will compare our modelling results with the experimental data from the study of Vidal et al [14], so we give a brief description of the experiment. The measurements were carried out in methane (99.995% purity) at constant pressure and a reduced electric field at different inter-electrode distances.…”

“…[7,8] In order to explain this deviation, numerous statistical models were proposed. [14][15][16][17][18][19][20][21][22][23] A kinetic model for the evolution of electron population, accompanied by measurements of electron avalanches at a constant electric field and pressure and at different gap lengths, in methane was presented in ref. [13] Besides the statistical models, other models for the description of avalanche development have been proposed.…”

“…[7][8][9][10][11][12][13] A detailed analysis of these models can be found in ref. [14] It was shown that the shape of the reduced avalanche size distribution (n × P(n∕n), where n is the mean avalanche size) is independent of the inter-electrode distance, that the electron multiplication process is non-Markovian, and that the distributions comply with the similarity principle. [14][15][16][17][18][19][20][21][22][23] A kinetic model for the evolution of electron population, accompanied by measurements of electron avalanches at a constant electric field and pressure and at different gap lengths, in methane was presented in ref.…”

“…[14] Furthermore, the independence of the distribution shape of the mean size at a constant reduced electric field was analysed and statistically proven. The model is used to calculate the number of electrons in an avalanche (avalanche size), to simulate the avalanche size distribution, and to discuss the influence of different conditions on its shape.…”