Study of non-equilibrium electron avalanches, application to proportional counters

The process of gas multiplication in uniform and non-uniform electric fields is analyzed on the basis of a numerical solution of the Boltzmann equation, Monte Carlo simulations and experimental gas gain measurements. We give a brief Boltzman equation description of gas multiplication that points out the different behaviour of the ionization coefficient in uniform and non-uniform electric fields. We introduce the concept of quasi equilibrium as an extension of the equilibrium formulation to non-uniform electric fields. Monte Carlo results for the reduced ionization coefficient and reduced gas gain for methane and propane in cylindrical geometry are presented illustrating their simultaneous dependence on the reduced voltage K and the reduced electric field S. Gas gain measurements for a propane-tissue-equivalent gas mixture are presented, which demonstrate this dependence.