REACTIVITY
DOE-HDBK-1019/2-93 Reactor Theory (Nuclear Parameters)
Example:
The number of neutrons in the core at time zero is 1000 and keff = 1.002. Calculate the
number of neutrons after 50 generations.
Solution:
Use Equation (3-4) to calculate the number of neutrons.
Nn No
keff
n
N50 1000 neutrons
1.002
50
1105 neutrons
Reactivity
If there are No neutrons in the preceding generation, then there are No(keff) neutrons in the
present generation. The numerical change in neutron population is (Nokeff - No). The gain or
loss in neutron population (Nokeff - No), expressed as a fraction of the present generation (Nokeff),
is shown below.
No keff No
No keff
This relationship represents the fractional change in neutron population per generation and is
referred to as reactivity (r). Cancelling out the term No from the numerator and denominator,
the reactivity is determined as shown in the equation below.
(3-5)
r
keff 1
keff
From Equation (3-5) it may be seen that r may be positive, zero, or negative, depending upon
the value of keff. The larger the absolute value of reactivity in the reactor core, the further the
reactor is from criticality. It may be convenient to think of reactivity as a measure of a reactor's
departure from criticality.
NP-03
Rev. 0
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