Modelling of a vibrating reactor boundary and calculation of the induced neutron noise

Three different models of a moving (vibrating) reactor boundary in time-dependent diffusion theory are investigated. The models are: (a) a localized absorber of variable strength at the boundary (equivalent to a perturbational treatment); (b) a time-varying extrapolation length; (c) explicit treatment of the moving boundary with a new transformation technique. The induced neutron noise was calculated in first order of the perturbation parameter both exactly and in the adiabatic approximation. All three models lead to equivalent results, confirming the applicability of perturbation techniques in treating moving perturbations (e.g. vibrating control rods). Application of the adiabatic approximation in model (c) required the extension of the Henry formalism, i.e. the use of orthogonality relations expressed as integrals over the system, to cases with non-constant system volume. The incentives for investigating a time-varying boundary arose from problems related to vibrating control rods; however, the results have some general relevance for systems with a varying volume such as gaseous core or liquid fuel reactors.