Series: Nuclear and Reactor Constants

since 1971

Русский (РФ)

ISSN 2414-1038 (online)

DOI: 10.55176/2414-1038-2019-1-250-262

Authors & Affiliations

Zemskov Е.А., Melnikov К.G., Tormyshev I.V.
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia

Zemskov Е.А. – Leading Researcher, Cand. Sci. (Phys.-Math.), A.I. Leypunsky Institute for Physics and Power Engineering. Contacts: 1, pl. Bondarenko, Obninsk, Kaluga region, Russia, 249033. Tel.: +7(484) 399-50-81; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..
Melnikov К.G. – Researcher, A.I. Leypunsky Institute for Physics and Power Engineering.
Tormyshev I.V. – Leading Engineer, A.I. Leypunsky Institute for Physics and Power Engineering.


The majority of neutron-physical problems of nuclear power plants design can be solved on the basis of various approximations to the Boltzmann transport equation in terms of the averaged characteristics of the reactor: the effective multiplication factor, neutron flux, average neutron lifetime, etc.
However, the neutron chain reaction itself is always stochastic. There are situations in which the stochastic nature of the chain reaction cannot be ignored. This is the so-called “blind” start-up problem with a weak external neutron source, the work of physical assemblies of “zero” power, the analysis of the reactivity noise of such assemblies, etc.
Despite the well-developed theoretical basis for the stochastic description of the behavior of neutrons in a nuclear reactor, there are still not enough calculation algorithms and programs for stochastic kinetics analysis.
The paper presents two computational algorithms for point reactor model, which are developed on the basis of the theory of Markov branching random processes. The first one is based on the balance equation for the probabilities of death and birth of prompt and delayed neutrons in a reactor, the second one is based on calculating the first and second moments of neutron number distributions and using the assumption that these distributions can be approximated by gamma distributions with sufficient accuracy. On the basis of these algorithms, programs have been created that allow one to calculate various scenarios for introducing reactivity and an external source into the system.
The calculation of pulsed experiments on prompt and delayed neutrons to determine the waiting time of the threshold neutron pulse at the Godiva II installation showed a qualitative agreement of the results for both the two computational algorithms and the experimental data.

stochastic neutron kinetics, prompt and delayed neutrons, probability density, generating function, gamma distribution

Article Text (PDF, in Russian)


UDC 621.039.512

Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2019, issue 1, 1:20