An assembly which includes fissionable material may function in one of two fashions: if keff is less than 1, the assembly is known as a subcritical assembly; if keff is 1 or greater, it is a reactor. Control rods move neutron absorbing material into, and out of, the core region, changing the configuration from one mode to the other.
We are interested in evaluating the effect of the control rods on the multiplication of the core when in a subcritical mode. To achieve this, consider the core with all rods in. A neutron source is placed (and kept) in, or adjacent to, the core. As a result of fissions induced in the fuel, there is a multiplication of the source neutrons. A neutron detector located in, or adjacent to the core, will respond to the total neutron population (composed of both primary (source) and fission neutrons).
If S neutrons/s from the source impinge on the detector in the absence of fuel, then when fuel is introduced both source and fission neutrons will influence the detector. This sum can be computed by noting that at the end of one generation the neutrons produced will be Skeff; after two generations, Skeff2; etc. The keff is the effective multiplication factor for the subcritical configuration under consideration.
The steady state multiplication for the assembly is thus the ratio of the events contributed by all generations divided by those due only to the first generation:
M = {S + S keff + S keff2 +S keff3+......} / S
which becomes:
M = 1 / {1 - keff}
provided:
keff < 1
If changes are made to the assembly geometry or composition, keff changes, and the multiplication changes.
Note that the multiplication may be defined in terms of the response of the detector:
Then, the multiplication is:
M = C/Co
and
C = S / {1 - keff}
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With the core in a shutdown condition, withdrawing a blade (control or regulating) removes neutron absorbing material from the core. As a result, the reading of neutron detecting channels will change. The change is difficult to predict, as it is dependent upon many factors:
However, the change in count rate recorded at the detector is readily obtained. By moving the blade out of the core in discrete steps, the count rate (Cn) may be recorded at each of the n steps. Note that Co cannot be measured unless the core is unloaded.
Two possibilities for presenting the data exist. First, if the Cn values are plotted versus rod position, one notes that the shape will be the same as a plot of Cn/Co values, since Co is a constant. This plot will show the relative effect of rod position on change of multiplication due to motion of the rod.
On the other hand, absolute values can be found by dividing (Cn - Cn1)/Cn1 which is the same as dividing the change in multiplication from (n1) to (n) by that at (n1). This of course describes the fractional change in multiplication due to movement of the rod.
With the source in the core source holder, and an operator at the console:
Withdraw Control Blade #1 three inches per step. Take 3 one-minute counts at each interval.
Present two curves for the control blade. One curve should present the average counts versus rod position. The second curve should show the fractional change in multiplication versus rod position.
Discuss the results:
