Abstract
The backward equation for the space and energy-dependent probability generating function of the density fluctuations in a nuclear reactor, has been reduced to a more tractable form by the application of a slowing down kernel technique. Simple working expressions have been obtained for the variance, the correlation function and the power spectral density (P.S.D.) in terms of the infinite medium slowing down kernel. The method includes the effects of detectors, delayed neutrons and slowing down time. In addition, the frequency characteristics of the detection apparatus have been accounted for. It is shown that the dominant break frequency, of the fundamental mode component in the power spectral density, is markedly dependent on the slowing down lengths of the delayed neutrons, a result that can lead to appreciable corrections to the experimentally calculated neutron lifetime in certain systems. A general formalism accounting for slowing down, delayed neutrons and detector geometry is developed, and is applied to detectors of various shapes. Marked differences in the P.S.D. are noted for the different detectors in an infinite medium; however, for the finite medium, the effect of detector geometry is not so important and it is shown that, in certain circumstances, experiments can be analysed according to the simple, infinite medium-infinite detector formula.
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