Statistical fluctuations in reactors (1960)

The theory of space dependent fluctuations is developed, taking into account the effect of delayed neutrons. The 'diffusion equation' or Fokker-Planck equation is worked out in the case of age and two group theory, but the first one because of in physical significance is used in this report. The theory is applied to the study of the spectral density of fluctuations and fluctuations of counting rate and current flowing through the charge resistor of an ionisation chamber, the effect of the entrance capacity is discussed. The space dependent theory shows that the fluctuations in the core and reflector of a near critical pile obey to the same law. The spectral densities in the core and reflector are similar, there is no sensible attenuation of high frequency fluctuations in the reflector. Compared to the space independent theory, this theory give better agreement with experience, one can use the simple space independent theory but in checking with experiment it is necessary to introduce numerical factors given by the space dependent theory. (author)