Perturbation Methods for Reactor Diffusion Equations

The multigroup diffusion equations are solved formally by expanding the flux in each group in a series of eigenfunctions of the scalar Helmholtz equation. The resulting secular determinant is complicated, but a perturbation solution may be developed for the coupled multigroup equations. In the case of one energy group, the perturbation method chosen reduces to a formula simpler to use and more rapidly convergent than the Rayleigh-Schroedinger formulas. An operator convenient for expressing the boundary conditions at an interface in multiregion reactors is defined. The foregoing techniques are applied to the Fermi age equation for a reflected reactor. Numerical examples are given to illustrate the rates of convergence in typical reactor design problems.