An Eigenvalue Method for the Calculation of Nuclear Burnup

An iterative approach to the reactor burnup problem is developed on the basis of analytical solutions for the variable-coefficient burnup equations. The time dependence of the depletion matrices, A(t), is approximated by a polynomial representation. The number of basic time points for which spatial-diffusion calculations during burnup are required is determined only by the order of approximation necessary to give a reasonably good fit for the time dependence of A(t). Usually a low-order approximation is sufficient, so the number of diffusion calculations is reduced to a minimum. The method is applicable both to survey-type calculations and to detailed reactor-burnup studies. A comparison of some results obtained with the method described in this paper and with standard calculational methods is given for a typical example. The results show the rapid convergence and accuracy of the proposed procedure.