Geometry of Source Neutrons Assemblies
Since at PWRs the source range neutron detectors are usually placed outside the reactor (excore). A source neutrons assemblies should be placed at least a few migration lengths from core periphery. The main reason is that source range detectors should not register primarily the source neutrons.
Source Neutrons and Subcritical Multiplication
Source neutrons play an important role in reactor safety, especially during shutdown state and reactor startup. Without source neutrons, there would be no subcritical multiplication and the neutron population in the subcritical system would gradually approach to zero. That means, each neutron generation would have fewer neutrons than the previous one because keff is less than 1.0.
With source neutrons, the population remains at levels that can be measured by the source range excore neutron detectors, so that operators can always monitor how fast the neutron population is changing (can always monitor the reactivity of subcritical reactor). Note that, if neutrons and fissionable material are present in the subcritical reactor, fission will take place (even a deep subcritical reactor will always be producing a small number of fissions).
The source neutrons enter the life cycle and experience the same environment that fission neutrons experience. It must be noted, source neutrons are produced at different energies (e.g. 24keV for Sb-Be source), usually below energies of fission neutrons.
When the reactor is made subcritical after operating at a critical state, the neutron population at first undergoes a prompt drop as a result of rapid decrease in prompt neutrons. After a short time begins to decrease exponentially with a period corresponding to decay of the longest-lived delayed neutron precursors (i.e. ~80s). With source neutrons, the neutron flux stabilizes itself at a corresponding level, which is determined by source strength, S, and by the multiplication factor, keff.
For a defined source strength of n0 neutrons per neutron generation, the neutron population (i.e. the neutron flux) is given by:
where, n0 are source neutrons (0. generation) and n0keffi are neutrons from i-th generation. As i goes to infinity, the sum of this geometric series is (for keff < 1):
As can be seen, the neutron population of a subcritical reactor with source neutrons does not drop to zero, the neutron population stabilizes itself at level n, which is equal to source multiplied by factor M.