Reactivity Measurement in the Prompt-Jump Approximation for the Neutron Flux
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SCIENTIFIC AND TECHNICAL COMMUNICATIONS REACTIVITY MEASUREMENT IN THE PROMPT-JUMP APPROXIMATION FOR THE NEUTRON FLUX B. D. Abramov*
UDC 519.6:621.039.51
Methods of calculating the nuclear reactor reactivity from the measured time-dependence of the neutron flux are discussed. It is noted that the corresponding problems for the direct and inverse equations of point kinetics in the approximation of a prompt-jump change of neutron flux are not equivalent, which is expressed in that the reactivity values in these problems do not coincide with one another. The reasons for the nonequivalence and ways of its elimination are investigated. New equations of inverse point kinetics without this deficiency are proposed. It is shown that the proposed equations give the correct reactivity immediately after the onset of a perturbation in the reactor and not asymptotically as in the case of the conventional equations.
The equations of inverse point neutron kinetics of a reactor are widely used in the practice of neutronic measurements to calculate the reactivity on the basis of the time-dependence of the neutron flux. However, questions associated with, for example, the elimination of spatial and other reactivity effects arising because of a mismatch between the real and point models of reactor kinetics and with the optimal choice of the coefficients in the equations of point inverse kinetics as well as other issues still remain here [1–10]. In the present work, the model of inverse point kinetics in the approximation of a jumplike change of the neutron flux is refined [1, 2], the reasons for the non-equivalence of the direct and inverse problems for the equations of point kinetics in this approximation are discussed, and new equations without this drawback are proposed. It is shown that these equations lead to reactivity determined immediately after a prompt perturbation and not asymptotically as in the case of the conventional equations. Direct and inverse equations of point kinetics. We are studying the equations of point neutron kinetics of a reactor:
dn + ( )n = j c j + q; dt j
dc j dt
= j c j + j n, j = 1, ..., J,
(1)
Σ
where Λ is the lifetime of prompt neutrons; n(t) is the amplitude of the neutron flux; β = j βj is the effective delayed-neutron fraction; ρ is the reactivity; cj(t), λj, and βj are, respectively, the concentration, decay constant, and yield of the precursors of delayed neutrons belonging to the group j; q is the source of extraneous neutrons; and J is the number of groups. These equations are used to solve the direct problem (Cauchy problem) of finding the amplitude n(t) of the neutron flux for t > 0 given ρ, βj, λj, q, and the initial conditions n(0) and cj(0). Its solution for constant ρ = ρ+ < 0, q can be written in the form J
(t) =
[ (ak + bk / k )exp( k t ) bk / k ] k ,
(2)
k =0 *
Deceased.
State Science Center of the Russian Federation – Leipunskii Institute for Physics and Power Engineering (IPPE), Obninsk, Russia. Translated from Atomnaya Énergiya, Vol. 128, No
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