Page 34 - Dynamics and Control of Nuclear Reactors

3.5 Perturbation form of the point kinetics equations 25

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dP=P0ðÞ ð ρ βÞ X 00 0
¼ P=P0ðÞ + λ i C i (3.22)
dt Λ
i¼1
dC 0 00 β P
i i 0 00
¼ λ i C i (3.23)
dt Λ P 0ðÞ
where
000
ð
C i ¼ FΣ f VC i =P0ðÞÞ C i
So, the form in each case is the same, different only in the quantity used to represent
neutron density, neutron flux, power or relative power and the inconsequential def-
inition of the precursor term. In subsequent appearances, the precursor term will sim-
ply be labeled, C i , even though, as we have just demonstrated, the physical definition
is different in each formulation.
If only one delayed neutron group is used for more approximate simulations, the
equations are as shown below (using the relative power or fractional power formu-
lation for this illustration).

d P ð ρ βÞ P
¼ + λC (3.24a)
dt P 0 ðÞ Λ P 0 ðÞ
dC β P
¼ λC (3.24b)
dt Λ P 0 ðÞ

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X
β ¼ β i (3.25a)
i¼1
1
1,l i is the mean lifetime of delayed neutron precursor group i: (3.25b)
6
λ ¼ 0
X
i
B β l iC
i¼1
B C
B C
B β C
@ A
λ is the one delayed neutron precursor decay constant.

3.5 Perturbation form of the point kinetics equations
It is sometimes useful to formulate the point kinetics equations in terms of deviations
from steady state. Such a formulation facilitates development of linear models for
reactors with reactivity feedback and the development of reactor transfer functions.
Development of the perturbation form of the point kinetics equations (version
with power, P, as the neutronic variable) begins with the following definitions: