Series: Nuclear and Reactor Constants

since 1971

Русский (РФ)

ISSN 2414-1038 (online)

Authors & Affiliations

Abramov B.D.
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia

Abramov B.D. – Leading Researcher, Cand. Sci. (Phys.-Math.), Associate Professor, A.I. Leypunsky Institute for Physics and Power Engineering. Contacts: 1, pl. Bondarenko, Obninsk, Kaluga region, Russia, 249033. Tel.: +7(484) 399-53-73; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..


The paper is devoted to the issues of development and modification of methods of evaluation of reactivity effects in nuclear reactors using perturbation theory. It has been demonstrated for the first time that traditional relationships of small perturbation theory used for evaluation of reactivity effects caused by perturbation of neutron-nucleus interaction cross sections should be improved. This improvement would include accounting for the new reactivity effect arising from possible rapid changes (discontinuities) of diffusion coefficients on the interfaces of reactor cells (zones) in the course of disturbance.
There have not any references to this effect in the publications available. However, the similar reactivity effect related to the emergence of discontinuities of neutron diffusion equation coefficients on the interfaces of cells caused by thermal strains was described in the paper “The “virtual” density theory on neutronics: a generic method for geometry distortion reactivity coefficients” by M. Reed, K. Smith, and B. Forget. In this paper, an effort was made to improve the well-known method by S.B. Shikhov et al., as regards accounting for the more common type strains accompanied by changes in size, form and relative positions of the reactor cells during thermal perturbation. The propositions presented in the above paper were modified by B. Abramov and K. Raskatch.
The present paper shows that the traditional formulas of perturbation theory in the diffusion approximation for reactivity effects calculating need to be refined. Corresponding specifications are given. They are caused by the imbalance of "leakage" of neutrons between subdomains of the reactor (zones, cells, etc.) in the process of perturbation. This imbalance is generated by jumps (discontinuities) of the relative increments of the diffusion coefficients at the interfaces of the subdomains.

theory and methods for calculating nuclear reactors, perturbation theory, reactivity effects, diffusion approximation

Article Text (PDF, in Russian)


UDC 519.6:621.039.51

Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2017, issue 3, 3:3