An Analytical Estimate of the Error in Conventional Point-Kinetics Reactivity Due to Spatial Effects

This is a theoretical investigation of the accuracy of conventional point kinetics in a multiregion reactor without feedback. The fundamental assumption of point kinetics is the splitting of the neutron density into a product of a known constant shape function and an unknown amplitude function. The model cannot acount for the distortion of the shape of the neutron distribution due to space-dependent perturbations and this results in an error in reactivity. It is to this error that bounds are derived. This is done by using the method of weighted residuals to reduce the original eigenvalue problem to that of a real asymmetric matrix. Theorems from matrix algebra are then used to find disks in the complex plane where the eigenvalues are contained. The radii of the disks depend on the perturbation in a simple manner. Examples of space-dependent step and ramp insertion of reactivity in slab reactors demonstrate the usefulness of the bound.