Excitation of Higher Space Modes in Reactor Transfer Function Measurement (Part I)

An explicit time-dependent two-group flux, expressed by a series of space modes, is established when a forced oscillation is applied to a reactor. The self-consistent time-dependency method developed here minimizes necessary mathematical transformations and enables one to clearly visualize the physical reasons why the higher space modes are only excited at high frequencies. The conditions necessary for a particular higher space mode to be appreciably excited and detected are discussed in detail. The results show that the major factor is due to the increase of the input frequency as compared with the decay constants of several higher space modes at high frequencies. This method was applied to the NORA reactor for which the space-dependent transfer functions have been measured. Results of the calculations closely agree with the published experimental results as well as with theoretical gain and phase shift curves obtained by the conventional modal expansion-Laplace transform method. The relative amplitude of each higher space mode with respect to the fundamental mode shows the rate of convergence of the modal expansion method.