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Abstiact-An analysis of the space and energy dependence of neutron fluctuations is presented, and applied to the results of reactor fluctuation experiments. Two experiments, measurements of Power Spectral Density and Variance to Mean, are singled out for special attention. These are of special interest, since previously published experimental results seem to be interpretable by space and energyindependent theories of neutron fluctuations. Both infinite and finite-geometry reactor models are treated, and calculations are presented to illustrate the effects of detector size, shape and location, and delayed neutrons. In any event, agreement with actual experimental results is achieved only when the effect of fast diffusion is included through a two-energy group model. It is seen that when the migration length is sufficiently large by comparison with a typical reactor dimension, the results of the space-energy independent theory appear as a first approximation. Thus it is argued that experiments on larger reactors would yield results not in agreement with the space-energy independent theory. * A.E.C. pre-doctoral fellow. * The role of delayed neutrons in noise analysis experiments has received such extensive attention, that we have referenced only three papers, each representing a different approach. t Of course a given experiment measures only an approximate value for 4(t).

Kinetic equations for neutrons and some of the other kinds of particles important to neutron balance in reactors and reactor-like systems are derived from a quantum Liouville equation. In particular, equations for some of the relevant singlet and doublet densities in phase space are deduced for the purpose of studying neutron density fluctuations. The equations describing neutron densities, ignoring delayed neutron precursors, are then singled out for special attention. These equations are reduced to 'one-speed' or mono-energetic analogues, and are then approximated by equations for the zeroth and first angular moments of these densities. During the process, points of connexion with the descriptions of neutron density fluctuations by various other authors are made. Formal solutions of the equations in phase space are displayed, along with an explicit solution of the reduced equations. Properties of these solutions are discussed, with particular interest paid to the implications for the 'critical limit.'

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