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. The calculated values for ionization chambers filled with CO2 were also in good agreement with the experimental data of Moriuchi et al.