Inverse Generalized Perturbation Theory in Reactor Core Constrained Calculations

Perturbation theory has been conceived to determine the effect of an external perturbation on the reactivity or, in its general formulation, on any other observable quantity, if it can be expressed as a ratio of linear functionals of the flux. Ronen (in 1979) introduced the inverse perturbation approach to extend some measurement results from a reactor system to another one. In constrained calculations, where the value of an external parameter is searched, with the constraint to reach a target value of an observable quantity, the use of the inverse approach rises quite naturally. A common example of this kind of problem is the search of the axial position of a control bank (the constrained parameter) leading the axial offset of the power distribution (the observable) to a target value. We present here an inverse general perturbation method, which has the advantage with respect to classical procedures used to solve this kind of problem, based on the iterative Newton-Raphson method, to reduce the computation time in situations where changes on the control parameter make a high distortion on the flux distribution, as it is the case of the control banks. Some numerical examples illustrate the performances and the gain in stability of this method in the case of control of the axial offset of the power distribution. Other examples show the application of the method to the determination of the number density of several isotopes constrained to several observables in a transport code. A simple algorithm to compute the generalized importance is proposed.