A perturbation method to examine the steady-state charge transport in the recombination and saturation regimes of ionization chambers

We developed a perturbation method to predict the behaviour of ionization chambers functioning in current mode when the space charges are neglected. This method allowed us to go for the first time beyond the Thomson problem by taking into account, in the output current calculation, the spatial variations of the primary charge density induced by the incident ionizing particles. The results obtained are presented under the form of series for which we studied the convergence radius and quality in a simple case. Additionally, we solved the Thomson problem when the space charges are neglected and established for the first time the explicit relationship linking the input voltage to the output current. Finally, we calculated the voltage that delimits the transition between the recombination regime and the saturation plateau.