Criticality problems neutron sources

Cylindrical reactor with source. An attempt is made here to describe the kinetics of a homogeneous cylindrical reactor with a point source of fast neutrons located at an arbitrary interior point on the axis of the reactor. The theory developed is quite general, at least to the extent that five delayed neutron groups are taken into consideration and appropriate ages are assigned to the source neutrons, the prompt fission neutrons, and each of five groups of delayed fission neutrons. Application of the theory is made to the problem of the determination of the power level in a so-called zero power critical assembly. 

Some 30 test problems, covering a wide range of critical systems, were run to check the accuracy of the code and to examine effects on convergence rate of initial source distribution, neutrons per generation, and ther-malization parameter variations. 

Then a small fuel addition is made and the population remeasured. From the change in population, the critical mass can be predicted according to the theory developed in the next section. More fuel additions are made, and after each addition the critical mass can be predicted with increased accuracy. The caution of the approach, which is reflected in the size and number of the fuel additions, depends on the particular problem and conditions. As the critical mass is very closely approached, the neutron population increases tremendously over the source level and becomes difficult to measure. However, by this time the critical mass can be accurately predicted, and this is the purpose of the experiment. 

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