Critical Calculations of the Slab Reactors

The problem of critical dimensions of an infinite-slab multi-layer multiplying system can be solved by a general procedure due to K. M. Case. The angular neutron distribution and the critical core size can then be found by solving the Fredholmtype integral equation with an additional critical condition. Numerical calculations have been done for the case of a multiplying slab surrounded by an infinite reflector, assuming one-energy group and isotropic scattering of neutrons, the mean number of secondary neutrons per collision in a medium-c being a variable parameter. Various approximations of the exact solution have been compared and the asymptotic theory has been found applicable in a wide range of c values in both media. 272