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A New Formulation to the Point Kinetics Equations Considering the Time Variation of the Neutron Currents

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The system of point kinetics equations
describes the time behaviour of a nuclear reactor, assuming that, during the
transient, the spatial form of the flux of neutrons varies very little. This
system has been largely used in the analysis of transients, where the numerical
solutions of the equations are limited by the stiffness problem that results
from the different time scales of the instantaneous and delayed neutrons. Its
derivation can be done directly from the neutron transport equation, from the
neutron diffusion equation or through a heuristics procedure. All of them lead
to the same functional form of the system of differential equations for point
kinetics, but with different coefficients. However, the solution of the neutron
transport equation is of little practical use as it requires the change of the
existent core design systems, as used to calculate the design of the cores of
nuclear reactors for different operating cycles. Several approximations can be
made for the said derivation. One of them consists of disregarding the time
derivative for neutron density in comparison with the remaining terms of the
equation resulting from the P1 approximation of the transport equation. In this
paper, we consider that the time derivative for neutron current density is not
negligible in the P1 equation. Thus being, we obtained a new system of
equations of point kinetics that we named as modified. The innovation of the
method presented in the manuscript consists in adopting arising from the P1
equations, without neglecting the derivative of the current neutrons, to derive
the modified point kinetics equations instead of adopting the Fick’s law which
results in the classic point kinetics equations. The results of the comparison
between the point kinetics equations, modified and classical, indicate that the
time derivative for the neutron current density should not be disregarded in
several of transient analysis situations.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Nunes, A. , Martinez, A. , Silva, F. and Palma, D. (2015) A New Formulation to the Point Kinetics Equations Considering the Time Variation of the Neutron Currents.

*World Journal of Nuclear Science and Technology*,**5**, 57-71. doi: 10.4236/wjnst.2015.51006.

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