Study of particle transport and gas amplification mechanism in proportional counters

Gas amplification is an essential feature of the proportional counter. The Boltzmann equation and the Townsend ionization coefficient are introduced to describe the behavior of electrons and the gas amplification in proportional counters, respectively. However, it is difficult to solve the Boltzmann equation completely and to obtain the critical radius at which electron avalanche begins. Therefore, we try to employ the Continuity equation and the linear stopping power to derive the distribution of particles and the critical radius. The space charge effect was also investigated to understand its influence on the gas amplification of the proportional counter. Finally, the gas amplification was calculated based on the classical theory of electron transport. The results indicate that the theoretical value is in good agreement with the experimental data. This means that the continuity equation and the linear stopping power can be used to depict the particle transport and gas amplification mechanism in proportional counters.