Authors & Affiliations
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:
Examines the effect of the spectral gap q (also known as dominant ratio) on the spatial stability of the field of neutrons in nuclear reactor.
It is noted that the magnitude of the spectral gap q, which characterizes the amplitude of perturbation of neutrons in the reactor, is the universal criterion for the spatial instability of neutron field.
However, to characterize in detail the effect of a particular perturbation on the field of neutrons using only one parameter q is not possible. In such cases it is necessary either to use the direct numerical solution of the perturbed problems, or to use the apparatus of perturbation theory, which requires, in turn, compute, at least a few eigenvalues and the corresponding eigenfunctions (harmonics) of the conditional critical equations, that is very difficult. The use of perturbation theory of the first order is often uninformative and may serve as a source of error in the evaluation of the response of neutron field on the perturbation.
In addition to the influence of the spectral gap q on the spatial stability of the neutron fields it is interesting to know its effect on stability of conditionally critical model of reactor. To assess this influence in the work proposed a new approach based on the use of coefficients γ=δρ/δρ(0) and k=(δρ-δρ(0))/δρ(0), calculated on the basis of direct numerical solution of the perturbed and unperturbed problems, where δρ the exact reactivity effect, whereas δρ(0) the effect in the first approximation of perturbation theory.
This approach allows us to estimate the influence of all harmonics on the reactivity and thus on the stability of the conditional critical model of reactor. It is based on the traditional codes of the neutron-physical calculations and does not require calculating higher eigenvalues and eigenfunctions (harmonics) of the conditional critical equations.
Of interest, finally, evaluation of the comparative sensitivity to perturbations of neutron fields in fast and thermal reactors, which are also presented in the work.
The results are illustrated on the examples of the one-speed problems in plane and cylindrical geometries in the diffusion approximation. These examples are demonstrated, in particular, that the field of neutrons in a large flattened fast reactor is more stability to perturbations than in a thermal reactor of the same size and shape.
spectral gap, the stability of the neutron fields in the reactor, the stability of conditional critical modes of the reactor