Completeness of the higher order harmonics

Applications using higher order harmonics (HOH) require knowledge of the corrpleteness of the HOH for the diffusion difference equation. This paper shows that the set of HOH for the fission source is complete, but that the set for the flux using the multi-group model is not complete. This paper uses the assumption that the set of flux vectors of HOH for every group is complete. This assumption can be proven only for those groups into which no scattering neutrons enter. However, it is also shown to be true for several practical reactor models. Analysis shows that the number of HOH with non-zero eigenvalues is equal to the number of difference meshes with fissile material, and that the eigenvalues have positive real values. This assumption is valuable for HOH applications, but requires further theoretical study to verify whether it is universally applicable.