Perturbation Theory of Control Elements. I

An exact expression for the reactivity effect of a control element placed in a reactor is derived within the limitation of validity of multigroup diffusion theory. The evaluation of the expression requires a knowledge of the flux distributions in the reactor with and without the element (s) inserted. Since the reactivity effect is stated in terms of the flux distribution in the perturbed and unperturbed reactors, one can calculate the effect of a control element if a good estimate for the form of the perturbed flux is made. A first-order perturbation calculation for thermally black control elements is presented. The perturbation calculation assumes that the fast flux is unaffected by the presence of the control element. The results are valid for a reactor in which the neutron age is large compared to the square of the thermal diffusion length and for a control element which is small compared to both the size of the reactor and the square root of the age.