REACTIVITYDOE-HDBK-1019/2-93 Reactor Theory (Nuclear Parameters)Example:The number of neutrons in the core at time zero is 1000 and k_{eff} = 1.002. Calculate thenumber of neutrons after 50 generations.Solution:Use Equation (3-4) to calculate the number of neutrons.N_{n } N_{o }k_{eff}nN_{50 } 1000 neutrons1.002501105 neutronsReactivityIf there are N_{o}neutrons in the preceding generation, then there are N_{o}(k_{eff}) neutrons in thepresent generation. The numerical change in neutron population is (N_{o}k_{eff} - N_{o}). The gain orloss in neutron population (N_{o}k_{eff} - N_{o}), expressed as a fraction of the present generation (N_{o}k_{eff}),is shown below.N_{o} k_{eff } N_{o}N_{o} k_{eff}This relationship represents the fractional change in neutron population per generation and isreferred to as reactivity(r). Cancelling out the term N_{o} from the numerator and denominator,the reactivity is determined as shown in the equation below.(3-5)r k_{eff } 1k_{eff}From Equation (3-5) it may be seen that r may be positive, zero, or negative, depending uponthe value of k_{eff}. 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