Point Reactor Kinetic Equations for a Non-Stationary One-Group Bare Reactor with Delayed Neutrons
In this case, the reactor is not critical and the effective multiplication factor is different from unity, and it is written as
is the macroscopic fuel absorption cross section ~La is the absorption cross section B2 is the geometrical buckling
The equations governing the precursors' concentrations will be a modification of Equation 9.9, accounting for the time dependence as
The average energies of the delayed neutrons range are from (about) 0.25 to 0.62 MeV. The balance equation for the thermal neutrons in terms of the flux with a source term is
Substituting Equation 9.12 into Equation 9.1 yields
It is reasonable to suppose that the spatial variation of the concentration of the delayed neutron precursors is proportional to that of the neutron flux and that this mode persists even though the magnitude of the flux changes with time. Thus, let us assume
and the boundary condition at the extrapolated radius of the reactor is F(Rextrapolated) = 0. Hence, Equation 9.13 becomes
These reactor kinetic equations are coupled linear first-order ordinary differential equations.
Duderstadt, J. J. and Hamilton, L. J. 1976. Nuclear Reactor Analysis. John Wiley & Sons, New York. Ghoshal, S. N. 2010. Nuclear Physics. S. Chand & Co. Ltd, New Delhi, India.
Glasstone, S. and Sesonke, A. 2004. Nuclear Reactor Engineering, 4th edn., Vol. 1. CBS Publishers and Distributors Private Limited, New Delhi, India.
Hetrick, D. L. 1971. Dynamics of Nuclear Reactors. University of Chicago Press, USA.
Lamarsh, J. R. 1983. Introduction to Nuclear Engineering. Addison-Wesley Publishing Company, U.K. Nayak, S. and Chakraverty, S. 2016. Numerical solution of stochastic point kinetic neutron diffusion equation with fuzzy parameters. Nuclear Technology 193(3):444-456.
Sharma, Y. R., Nanda, R. N. and Das, A. K. 2008. A Textbook of Modern Chemistry. Kalyani Publisher, New Delhi, India.
Stacey, W. M. 2007. Nuclear Reactor Physics. Wiley-VCH, Weinhein, Germany.