Reflector savings in calculation of the critical mass

The critical mass which is known as the smallest amount of fissile material required in any system of geometry for a sustainable fission chain reaction can be approximately calculated by using the steady-state one-group neutron diffusion equation. In the solution of the diffusion equation, it is important if the core is just bare or surrounded by a reflector material. In such analytical calculations, it is seen that the mass and size of the bare system decreases dramatically if there is reflector material. This thesis considers the application of Monte Carlo Method to hypothetical bare and reflected systems in spherical, cylindrical and rectangular coordinates, and compares its results with those of analytical solutions of neutron diffusion equation for bare and reflected systems in three basic geometries, respectively. We show that our numerical calculations for the size of the systems in these geometries by Monte Carlo Method are in very good agreement with those of the analytical solutions. Our method is very simple, understandable and applicable in any computer program language, and the results are in consistent with those of analytical ones.