A perturbation theory for the non-linear system of neutron transport and burnup equations

A perturbation theory for use in nuclear reactor burnup analysis is derived. An important characteristic function is defined, and the related adjoint equation is obtained simply by using the variational principle. The adjoint matrix operator is evaluated directly from its defining differential expression. Responses at the end of cycle due to changes in initial material inventory, in nuclear data, and in power demands can be calculated using the previously determined forward and adjoint solutions. The method has additional applications, notably in selecting beginning of cycle conditions so as to achieve a particular end of cycle condition.