SUBCRITICAL MULTIPLICATION
DOE-HDBK-1019/2-93
Reactor Theory (Reactor Operations)
Because the reactor is subcritical, neutrons introduced in the reactor will have a decreasing effect
on each subsequent generation. The addition of source neutrons to the reactor containing
fissionable material has the effect of maintaining a much higher stable neutron level due to the
fissions occurring than the neutron level that would result from the source neutrons alone. The
effects of adding source neutrons at a rate of 100 neutrons per generation to a reactor with a keff
of 0.6 are shown below.
Generation
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
11th
12th
100
60
36
22
13
8
5
3
2
1
0
0
100
60
36
22
13
8
5
3
2
1
0
100
60
36
22
13
8
5
3
2
1
100
60
36
22
13
8
5
3
2
100
60
36
22
13
8
5
3
100
60
36
22
13
8
5
100
60
36
22
13
8
100
60
36
22
13
100
60
36
22
100
60
36
100
60
100
Total n
100
160
196
218
231
239
244
247
249
250
250
...
A neutron source strength of 100 neutrons per generation will result in 250 neutrons per
generation being produced from a combination of sources and fission in a shutdown reactor with
a keff of 0.6. If the value of keff were higher, the source neutrons would produce a greater
number of fission neutrons and their effects would be felt for a larger number of subsequent
generations after their addition to the reactor.
The effect of fissions in the fuel increasing the effective source strength of a reactor with a keff
of less than one is subcritical multiplication. For a given value of keff there exists a subcritical
multiplication factor (M) that relates the source level to the steady-state neutron level of the
core. If the value of keff is known, the amount that the neutron source strength will be multiplied
(M) can easily be determined by Equation (4-1).
(4-1)
M
1
1 keff
NP-04
Rev. 0
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