The Reactivity Effect of a Regular Array of Empty Cylindrical Channels in a Critical System

A critical system consisting of a regular infinite array of cylindrical channels of any cross section in a homogeneous multiplying medium is divided into equivalent cells of finite height. For such a cell two-group diffusion theory is applied with additional terms for the loss and gain of neutrons by the channels. The resulting integral-differential equations are solved with sufficient accuracy by the perturbation method, giving the reactivity loss due to the channels. With the method proposed the neutron leakage at the ends of the channels is included and deviations from the original unperturbed flux of the reactor without channels are taken into account. The results are compared with calculations based on the usual assumption of unperturbed flux, using the Behrens formula to compute the diffusion lengths. It is shown that reactivity calculations are also possible for arrays of finite extent, assuming separability of the flux in an axial and a radial part.