Abramov B.D.
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia
We consider methods for calculating the reactivity of a nuclear reactor from the measured dependence of the neutron flux in the reactor on time, based on the use of the inverse point kinetics equations, which relate the values of reactivity and neutron flux in the reactor.
The main attention is paid to the correction of the equations of inverse point kinetics in the prompt-jump approximation (or in the theory of singular perturbations for equations with a small parameter with the highest derivative).
The nonequivalence of the corresponding problems for the direct and inverse point kinetics equa-tions in the prompt-jump approximation is noted, which consists in the fact that, contrary to expecta-tions, the reactivity values appearing in these problems do not generally coincide with each other. The reasons for this non-equivalence are investigated and ways to eliminate it are considered.
New inverse point kinetics equations are proposed in the prompt-jump approximation, devoid of the indicated disadvantage of the traditional equations.
These equations are tested by substituting in them analytical solutions of the corresponding (direct) Cauchy problems for point kinetics equations using the apparatus of the theory of systems of ordinary differential equations, adapted to the problem in question.
It is shown that the use of the equations proposed in the work leads to the correct determination of reactivity immediately after the instantaneous introduction of a disturbance into the reactor, and not in asymptotics, as is usually the case when applying traditional equations.
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