Sinusoidal Analysis of a Low-Power Nuclear Reactor by the Wentzel-Kramers-Brillouin Approach

A solution of the zero-power kinetic equations for sinusoidal excess reactivity insertions, previously obtained by the author by Wentzel-Kramers-Brillouin approach (WKB), is further discussed. Explicit equations for the reactor period, reactivity bias, and stabilized reactor response, within the range of applicability of the method, are derived. Harmonic contents of the logarithm of flux for both pure and properly biased sinusoidal reactivity variations are analyzed. Fourier components of flux yielding the new steady-state mean power, the fundamental and the second harmonic are given. Results of the treatment are extended to the describing function of a low-power nuclear reactor and the major error involved in the earlier literature is indicated. The procedure, although developed under the assumption of one average group of delayed neutrons, is expected to yield very satisfactory results even if generalized to multigroup treatment.