Nikolay Oshkanov
Ural Federal University, Russian Federation.

Background: In the classical kinetics theory of a nuclear reactor, inserting the slightest reactivity-jump leads to an unlimited exponential increase in the reactor power.  The purpose this study is the establishment of the nature of such a phenomenon.

Methods: Theoretical research is based on the physics of the chain fission reaction as a sequence of cycles, each cycle of which is initiated by neutrons of the previous cycle. The study method consists in determining the change in the output neutron density of the cycle sequence under the reactivity-jump action.  
Results: It is established that the delayed neutron lifetime does not exceed the cycle duration in which they are born.  This is fundamentally different from the classical statement that this time is large (several tens of thousands of cycles).  The kinetics equations of the sequence of chain reaction cycles are derived.  The solution of these equations for the reactivity jump of a less effective fraction of delayed neutrons shows a limitation of the neutron density by a stable level, and not an unlimited growth. It is established that this limitation is due to a previously unknown feedback on the rate of change in the density of delayed neutron precursors.

 Conclusions: An analysis of the solution of the derived kinetic equations and the fact that the lifetime of delayed neutrons does not exceed the lifetime of the cycle in which they are generated allows us to conclude that there is a previously unknown feedback with respect to the rate of change in the density of precursors of delayed neutrons. This feedback leads to self-regulation of the reactor power when inserting a positive reactivity of a less effective fraction of delayed neutrons.  The results of the study indicate the need to revise the classical theory of the kinetics of a nuclear reactor.
Keywords: reactor kinetics, lifetime of delayed neutrons, self-regulation of reactor power.