Perturbation multigroup theory

D + 6D, and S + SJL. In one group theory, the flux and adjoint flux are identical, but the derivation that follows differentiates between them because it eases the generalization to multigroup theory. However, it is assumed that the perturbations are small enough so that difference between the perturbed and unperturbed flux can be ignored, and so the prime notations will be dropped. 

Comparing calculated and experimentally determined reactivity worth enables verification of the accuracy qf nuclear data and the adequacy of computational methods used. For a meaningful comparison of theory and experiment, it is essential that the perturbation theory expressions used for the calculations apply to exactly the same parameter as that deduced fi-om the experiments, and that these expressions are evaluated accurately. This paper reviews three aspects of accurate determination of reactivity (1) the definition of reactivity, (2) high-order perturbation theory expressions for reactivity, and (3) the accuracy of computational techniques based on the multigroup approximation. 

A second way to obtain the difference between the two eigenvalues is to use multigroup perturbation theory, which, for a small change in capture and fission cross sections only, states that the change in eigenvalue is given by... 

In the present work, it will be assumed that 5v is to be calculated either from the solution of the two sets of multigroup equations of the form (33) with the effective fission and capture cross sections defined by (27) and (28) or by one such set of multigroup equations and the first-order perturbation theory of (34). We require the same effective cross sections for either procedure. Various appropriate approximations are employed in the application of these formulas. 

Almost all of the practical calculations of the Doppler effect in fast reactors are carried out by the conventional method, which consists of tracing through the expressions for the effective cross sections, as developed in this paper for the different fuel isotopes and energy ranges. Then, one can either run two multigroup diffusion calculations with the effective cross sections at different temperatures and obtain the reactivity changes associated with the Doppler effect as the difference of the two criticality factors, or else one can do only one multigroup calculation and find the Doppler coefficient by the use of perturbation theory. Both ways are, of course, equivalent from a mathematical point of view. 

E. D. PENDLEBURY, A Mechanized Application of Perturbation Theory in Multigroup Neutron Transport Calculations, AWRE 0 32/64, Aldermaston, Berks. (July 1964). 

Perturbation theory can be extended to a two-group or multigroup model. This is necessary if the perturbation involves change in epithermal or fast neutron reaction rates (fuel element variation, for example). These problems are difficult and solutions are not described here. Some information is presented below on the effect of natural uranium columns, air columns and water columns. 

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