A sufficient condition for flattening of the thermal neutron flux and some related problems (in onedimensional geometries)

Abstract

The main results of this paper, in which the problem of determination of the fuel concentration distribution $M$ inducing a prescribed thermal neutron flux $\Phi$ in the homogenized critical reactor core with given outer reflector boundary is investigated (in the two-groups diffusion approximation), are stated in the theorems 1 and 2. In theorem 1 sufficient conditions are given for the existence of a oneparametrical family of thermal neutron fluxes induced by the Goertzel's type fuel concentration distribution. This theorem enables us to seek for the flux of this oneparametrical family which gives the maximal total output of the reactor. In Theorem 2 the results of Theorem 1 are generalized for the case of such fuel concentration distributions which are not of the Goertzel's type.