Reactor Theory (Reactor Operations)
DOE-HDBK-1019/2-93
SUBCRITICAL MULTIPLICATION
Instead of plotting M directly, its inverse (1/M) is plotted on a graph of 1/M versus rod height.
M
1
1 keff
1
M
1 keff
As control rods are withdrawn and keff approaches one and M approaches infinity, 1/M
approaches zero. For a critical reactor, 1/M is equal to zero. A true 1/M plot requires
knowledge of the neutron source strength. Because the actual source strength is usually
unknown, a reference count rate is substituted, and the calculation of the factor 1/M is through
the use of Equation (4-5).
(4-5)
1
M
CRo
CR
where:
1/M
=
inverse multiplication factor
CRo
=
reference count rate
CR
=
current count rate
In practice, the reference count rate used is the count rate prior to the beginning of the reactivity
change. The startup procedures for many reactors include instructions to insert positive
reactivity in incremental steps with delays between the reactivity insertions to allow time for
subcritical multiplication to increase the steady-state neutron population to a new, higher level
and allow more accurate plotting of 1/M. The neutron population will typically reach its new
steady-state value within 1-2 minutes, but the closer the reactor is to criticality, the longer the
time will be to stabilize the neutron population.
Example:
Given the following rod withdrawal data, construct a 1/M plot and estimate the rod
position when criticality would occur. The initial count rate on the nuclear
instrumentation prior to rod withdrawal is 50 cps.
Rod Withdrawal
(inches)
Count Rate
(cps)
2
55
4
67
6
86
8
120
10
192
12
500
Rev. 0
NP-04
Page 7
