Double adjoint method for determining the contribution of composition to reactivity at different times

The double adjoint method uses the adjoint reactivity and transmutation problems to describe how the system composition is related to the system reactivity at different points in time. Values of the contribution to the reactivity are determined using the adjoint reactivity problem, and these are then used as the source function for the adjoint transmutation problem. The method is applied to the problem of determining the contribution of the beginning of cycle composition to the end of cycle reactivity. It is tested in both fast and thermal systems by comparing the behaviour of the multiplication factor at the end of cycle in calculations with perturbed initial compositions to that predicted by the double adjoint method. The results from the fast system are good, while those from the thermal system are less favourable. This is believed to be due to the method neglecting the coupling between the composition and the flux, which plays a more significant role in thermal systems than fast ones. The importance of correcting for the effects of the fuel compound is also established. The values found are used in calculations to determine the appropriate fuel reloading of the systems tested, with the aim of duplicating the behaviour of the multiplication factor of the original system. Again the fast system gives good results, while the thermal system is less accurate. The double adjoint method is also used for a definition of breeding ratio, and some of the features of this definition are illustrated by examining the effects of different feed materials and reprocessing schemes. The method is shown to be a useful tool for the comparison of the reactivity behaviour of different fuel compositions, particularly its inclusion of the effects of the feed and fuel compound materials. The breeding ratio definition can be applied to non-equilibrium cycles, a significant advantage over many existing definitions.

► The double adjoint method is described.
► System reloading is determined so the multiplication factor behaviour is repeated.
► Both fast and thermal systems behave as desired.
► Allowance must be made for indirect effects in thermal systems.
► An alternative definition of breeding ratio is derived.