Abstract
The effectiveness of the wide application of the theory of branching random processes to the description of neutron behavior is due to the adequacy of the model and the real microscopic processes occurring in the reactor. However, the classical theory of branching process cannot describe effects which are important for reactors working at power, such as the influence of control and feedbacks. Recently, a class of branching processes with a variable regime was introduced and investigated. The application of the results of these works to simulation of the behavior of the neutron population in reactors with control and feedbacks makes it possible to determine precisely and to describe the phenomena which are important for reactor operation and which deterministic methods and the classical theory of branching processes do not reveal and cannot describe. Three regimes of the critical behavior of reactors are found: they depend on the sign of the controlling actions and the feedbacks. It is found that various parameters influence the operating regime of reactors. Explicit expressions are given for the generating functions of the random power of a reactor in regimes admitting stationary solutions. For the nonstationary regimes, asymptotic expressions are written for the average value and the variance of the power.
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Boiko, R.V., Ryazanov, V.V. Stochastic Model of a Nuclear Power Reactor. Atomic Energy 93, 625–634 (2002). https://doi.org/10.1023/A:1021088513565
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DOI: https://doi.org/10.1023/A:1021088513565