Sur un nouveau traitement multigroupe de la diffusion des neutrons dans les milieux reproducteurs Application a la correction des perturbations subies par les flux thermiques et rapides au voisinage d'un reflecteur, d'une source de neutrons ou d'un reseau different

Abstract

Part 1—If the equilibrium between thermal and fast neutrons propagated in a reproducing medium is perturbed by a neighbouring medium (a reflector, a fast neutron source, a system with a different lattice, etc.) the spatial distribution of each of the groups is also perturbed: it no longer obeys the elementary diffusion equation: $\text{ϵ}{}^{\mathrm{\varphi }}\text{+}\text{K − 1}\text{M}{}^2\text{ϵ = 0}$

On the other hand, the linear combination $\text{T =}\text{σ}\text{i}\text{1}\text{3}\text{λ}{}_{\mathrm{i}}\text{ε}{}_{\mathrm{i}}$ covering all the neutron groups, no matter how many, is very little affected by these perturbations: this combination satisfies an equation (No. 22) which differs from the above diffusion equation by the addition of corrective terms, modifying the Laplacian, which are proportional to the perturbations of the spectral distribution. Discussion shows that the effect of these corrective terms is negligible in practice for natural uranium lattices (Fig. 3); it is also small for enriched piles.

A physical interpretation of these results is based on the following statement: the gradient of T is equal to the total neutron current.

The introduction of this quantity naturally simplifies certain problems in permitting the use of one group theory (if necessary with slight corrections) to give a better precision than the classical two group theory.

In particular the systematic errors in the measurements of the Laplacian due to the conditions at the extremities of the medium under study, are avoided.

Part 2—The practical application of the properties of the function T assumes an experimental knowledge of the function. It is defined for a large number of groups, whereas the actual measurements are often limited to the activities of detectors in the thermal and resonance energy ranges: T can in fact be deduced from them if one knows the diffusion law which applies during slowing down. The calculation is carried through for two particular cases of perturbation,—a neighbouring source of fissions, and a neighbouring reflector.

The results may be expressed in a two group formula (equation 46 for example) by means of the weighing coefficients, functions of the space co-ordinates—which must be applied to the quantities q_n and q_r which are proportional to the two measured activities. It is more convenient to employ the ratio h of these activities (or, what amounts to the same thing, the “cadmium ratio”) since this does not presuppose an absolute calibration of the detectors.

T is then expressed (41) by the measure of the thermal flux (q_n) modified by a correction term proportional to the perturbation.

The elementary formulae of the one group theory may be conveniently applied to the result of this correction in the order to calculate the this correction in the order to calculate the Laplacian.