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Theory of Branching Processes of Neutrons in a Multiplying Medium

Keiichi Saito, Yukichi Taji

Nuclear Science and Engineering / Volume 30 / Number 1 / Pages 54-64

October 1967


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Statistical aspects of neutron transport in low-power reactors are studied from the viewpoint of branching processes. The probability generating function of a neutron population originating from an ancestor neutron is expressed in the form of the factorial moment expansion, and it is shown how a factorial moment is constructed out of the lower-order moments. The formalism is based on a physical statement that neutrons occupying a certain set of the prescribed space-time points are composed of subgroups which are chain related to the closest common branching point. The statement is found to be a natural extension of Feynman’s derivation of the well-known formula for Variance-to-Mean Ratio Method of measuring reactor noise. The form of the factorial moment expansion of the one-ancestor problem is applied to counting statistics in reactors with random sources. The result turns out to be the factorial cumulant expansion of the probability generating function of count number. It is shown that all the higher factorial cumulants are successively  constructed out of the lower orders. New adjoint fields are introduced. It is pointed out that analysis of reactor noise depends on two models of introducing  extraneous neutrons into the system, i.e., the random source model and the burst-of-neutrons model.

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