# 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

where

is the macroscopic fuel absorption cross section *~L _{a}* is the absorption cross section

*B*is the geometrical buckling

^{2}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

where

and the boundary condition at the extrapolated radius of the reactor is *F(R _{extrapolated})* = 0. Hence, Equation 9.13 becomes

and

These reactor kinetic equations are coupled linear first-order ordinary differential equations.

# Bibliography

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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.

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