SUBCRITICAL MULTIPLICATIONDOE-HDBK-1019/2-93Reactor Theory (Reactor Operations)Because the reactor is subcritical, neutrons introduced in the reactor will have a decreasing effecton each subsequent generation. The addition of source neutrons to the reactor containingfissionable material has the effect of maintaining a much higher stable neutron level due to thefissions occurring than the neutron level that would result from the source neutrons alone. Theeffects of adding source neutrons at a rate of 100 neutrons per generation to a reactor with a k_{eff}of 0.6 are shown below.Generation1st2nd3rd4th5th6th7th8th9th10th11th12th10060362213853210010060362213853210100603622138532110060362213853210060362213853100603622138510060362213810060362213100603622100603610060100Total n100160196218231239244247249250250...A neutron source strength of 100 neutrons per generation will result in 250 neutrons pergeneration being produced from a combination of sources and fission in a shutdown reactor witha k_{eff}of 0.6. If the value of k_{eff}were higher, the source neutrons would produce a greaternumber of fission neutrons and their effects would be felt for a larger number of subsequentgenerations after their addition to the reactor.The effect of fissions in the fuel increasing the effective source strength of a reactor with a k_{eff}of less than one is subcritical multiplication. For a given value of k_{eff} there exists a subcriticalmultiplication factor(M) that relates the source level to the steady-state neutron level of thecore. If the value of k_{eff} is known, the amount that the neutron source strength will be multiplied(M) can easily be determined by Equation (4-1).(4-1)M 11 k_{eff}NP-04Rev. 0Page 2

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