Numerical solutions of differential equations of an ionization chamber: plane-parallel and spherical geometry.

A system of reduced differential equations generally valid for plane-parallel, cylindrical and spherical ionization chambers, which is appropriate for numerical solution, has been derived. The system has been solved numerically for plane-parallel and spherical ionization chambers filled with air. The comparison of the calculated results of Armstrong and Tate, for plane-parallel ionization chambers, and Sprinkle and Tate, for spherical ionization chambers, with the present calculations has shown a good agreement.

Numerical solutions of differential equations of a cylindrical ionization chamber.

The differential equations of the cylindrical ionization chamber filled with air have been solved numerically for different ratios of the outer and inner electrode for both polarities of the voltage supply. The obtained distributions of the electric field strength inside the chamber confirm the analysis of Thomson and Thomson and the calculations made by Mie. The calculated collection efficiencies are in good agreement with the results of the calculation of Sprinkle and Tate, and with the experimental data of Moriuchi et al.