THE EFFECT OF HOLES IN A REACTING MATERIAL ON THE PASSAGE OF NEUTRONS, WITH SPECIAL REFERENCE TO THE CRITICAL DIMENSIONS OF A REACTOR

In this paper we discuss the increase in the migration length of neutrons in a reactor caused by the presence of holes in the reactor. It is shown how this effect can be evaluated in terms of a simple geometric function of the shape of the holes, and it is found that, in addition to a variation as the inverse overall density of the material in the reactor, the migration length also contains a term which depends upon the size and shape of each hole. When the hydraulic radius of the hole becomes comparable to the mean free path of neutrons in the reactor material, this last term becomes dominant, and it is therefore desirable that all holes should be kept as small as possible. Holes which are totally enclosed, or which contain a uni-directional infinity (cylinders) all give results of the same order of magnitude, but anything in the nature of a two-dimensional plane gash leads to a theoretically infinite increase in the migration length, and hence to a serious escape of spare neutrons. We have considered the cases both of holes of regular shape and of the interstices between a random arrangement of regular-shaped solid bodies.