Implicit and Explicit Higher Order Perturbation Methods for Nuclear Reactor Analysis

A critical study of higher order perturbation methods for reactor analysis is made. These methods are classified as explicit, semi-implicit, and implicit, according to their ability to allow perturbative expressions to any order of approximation explicitly in terms of the perturbation. This latter condition is desirable in analytical studies or optimization searches for reactor systems. Emphasis is placed on the problem of real flux normalization. Practical first- and second-order explicit formulations are finally given relevant to perturbations of the flux density. A typical example is described that indicates the potentiality of the so-called “standard method.”