Charge collection efficiency in ionization chambers operating in the recombination and saturation regimes

We solve the electric charge transport equations in the recombination and saturation regimes using an iterative perturbation method. We then calculate the charge collection efficiencies of ionization chambers. The formulae obtained are presented in the form of series for which we calculate the first coefficients. Our approach allows to account for the spatial as well as the temporal variations of the primary charge density N(r,t) in the calculations. Finally, we apply our method to study different density patterns, N, including the textbook case N=N0δ(t) and the charge clusters and columns.