REACTIVITYDOE-HDBK-1019/2-93 Reactor Theory (Nuclear Parameters)Example:The number of neutrons in the core at time zero is 1000 and keff = 1.002. Calculate thenumber of neutrons after 50 generations.Solution:Use Equation (3-4) to calculate the number of neutrons.Nn No keffnN50 1000 neutrons1.002501105 neutronsReactivityIf there are Noneutrons in the preceding generation, then there are No(keff) neutrons in thepresent generation. The numerical change in neutron population is (Nokeff - No). The gain orloss in neutron population (Nokeff - No), expressed as a fraction of the present generation (Nokeff),is shown below.No keff NoNo keffThis relationship represents the fractional change in neutron population per generation and isreferred to as reactivity(r). Cancelling out the term No from the numerator and denominator,the reactivity is determined as shown in the equation below.(3-5)r keff 1keffFrom Equation (3-5) it may be seen that r may be positive, zero, or negative, depending uponthe value of keff. The larger the absolute value of reactivity in the reactor core, the further thereactor is from criticality. It may be convenient to think of reactivity as a measure of a reactor'sdeparture from criticality. NP-03Rev. 0Page 18
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