A Generalized Formulation of Point Nuclear Reactor Kinetics Equations

The most general current formulations of the point reactor kinetics equations permit the flux shape function to be time dependent. This permissibility has led to the development of a class of space-time analyses referred to as adiabatic or quasistatic. The use of time-independent importance weighting, however, can lead to difficulties, as is shown in an example. In this paper, point kinetics equations are derived from a variational principle in such a way as to permit time-dependent importance shape functions. “Extra” terms due to the explicit time dependence of the shape functions appear, and normalization conditions are obtained by which these terms can be eliminated. Additional differences from conventional form appear if one chooses to use different importance shape functions for flux and precursor equations, but these differences can be neglected for many cases of practical interest.