Abstract:
The aim of this work is to derive quadrature formulas for nuclear reactor kinetic equations in the form of Volterra integral equations of
the second kind and reactimeter equations in the form of integral convolution, the kernel of which is a decay function of delayed neutron
precursors (DNP) in the non-group form. The expediency of the transition to integral equations is caused by the unification of the direct
(calculation of power dynamics) and the reverse (calculation of current reactivity) tasks of reactor kinetics. As a result, the solution is
reduced to the calculation of the delayed neutrons integral (DNI). This eliminates the source of computational-experimental discrepancies in
estimations of reactivity, which is due to the difference in computational algorithms of direct and inverse problems. The paper describes a
general scheme for converting different transport equation approximations to describe the contribution of delayed neutrons by means of an
integral convolution without using dynamic equations of the DNP concentration. This conversion reduces the model dimension, simplifies the
software implementation, eliminates the stiffness problem of differential kinetic equations and provides the stability of calculations. The model
dimension is preserved in the case of several fissile nuclides. The integral form of the equations makes it possible to use the experimental
decay function in quadrature formulas, which can be identified in the operating conditions of a nuclear reactor and stored pointwise in a
nongroup form without decomposition into the sum of exponentials. This eliminates the need to solve the non-linear problem of identifying
group parameters of delayed neutrons and increases the adequacy of modeling. A series of quadrature formulas for the calculation of the
DNI are obtained and the corresponding algorithms of a digital reactimeter and numerical simulation of the reactor kinetics are described.
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