Reactor Theory (Reactor Operations)
DOE-HDBK-1019/2-93
SUBCRITICAL MULTIPLICATION
The equation for N1 can be divided by the equation for N2.
N1
N2
S
1
1 k1
S
1
1 k2
N1
N2
1 k2
1 k1
Because the source strength appears in both the numerator and denominator, it cancels out of
the equation. Therefore, the neutron level at any time can be determined based on the neutron
level present at any other time provided the values of keff or reactivity for both times are known.
The neutron level in a shutdown reactor is typically monitored using instruments that measure
the neutron leakage out of the reactor. The neutron leakage is proportional to the neutron level
in the reactor. Typical units for displaying the instrument reading are counts per second (cps).
Because the instrument count rate is proportional to the neutron level, the above equation can
be restated as shown in Equation (4-4).
(4-4)
CR1
CR2
1 k2
1 k1
where:
CR1
= count rate at time 1
CR2
= count rate at time 2
k1
= keff at time 1
k2
= keff at time 2
Equation (4-4) is very useful during the shutdown operation of a reactor. Before adding positive
reactivity to a reactor, it is possible to predict the effect the reactivity addition will have on the
neutron level.
Example:
A reactor that has a reactivity of -1000 pcm has a count rate of 42 counts per second
(cps) on the neutron monitoring instrumentation. Calculate what the neutron level should
be after a positive reactivity insertion of 500 pcm from the withdrawal of control rods.
Rev. 0
NP-04
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