When establishing a critical geometry, confirmation of the calculation of the critical size is experimentally verified. During the experiment it is important to approach the critical geometry in a controlled, predictable manner. The following analysis sets forth the basis for proceeding: the reactor is gradually built up in size by adding fuel and moderator in discrete increments until the critical dimensions are attained. During assembly, 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 the detector reads S neutrons/s from the source alone, then at any (subcritical) stage of the core assembly it will indicate both source and fission neutrons. This sum can be computed by noting that at the end of one generation the neutrons produced will be S keff ; after two generations, S keff2; etc. The keff is the effective multiplication factor for the subcritical assembly at that stage.
The steady-state multiplication for the assembly is then:
M = {S + S keff + S keff2 + S keff3+......}/S
Which becomes: M = 1 / {1 - keff}
Provided: keff < 1
As the size of the assembly increases, leakage decreases, and keff approaches 1, driving M to infinity.
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Since infinity is difficult to locate on a plot, the reciprocal of the multiplication is used. By making observations of the count at two steps (fuel loading 1 and 2) of the core loading, the two values of 1/M can be plotted as a function of fuel mass (or number of fuel elements). Extrapolation of the trend to zero predicts the required fuel loading. Following the addition of more fuel (less than predicted for criticality) the above treatment of points 2 and 3 will yield a new prediction of the amount of fuel required to reach a critical configuration. The process is then repeated until criticality is actually achieved.
The reactor staff will have the core partially unloaded prior to the lab. Using the reactor control panel neutron count information, take an initial neutron count with all control blades fully withdrawn. If possible, use neutron count information from two different detectors. The reactor staff will follow the applicable procedure for fuel loading. An arbitrary initial amount of fuel (much less than expected to reach critical) will be added to the core to provide a second neutron count with which to extrapolate a predicted critical mass. Using your predicted critical mass, load additional fuel up to 1/2 of the predicted mass. Repeat this process until criticality is achieved.
