The Reduction of the Time-Dependent Equations for Nuclear Reactors to a Set of Ordinary Differential Equations

The average or over-all behavior of a reactor is expressed through a weighting function that corresponds to the detectors used to observe the behavior. The special properties are considered of three particular weighting functions; static, dynamic, and perturbation. The functions are compared on two grounds: first for the rigor in the reduction to the well-known equations describing reactor kinetics in the ordinary differential form, and second for the degree to which they permit approximations to the density without prejudicing the agreement between calculation and observation. The investigation considers particularly the effect of fuel mobility and the complications of the nonseparable, nonlinear problems, with a generahty that is independent of any particular physical model.