Reactor Theory (Nuclear Parameters)DOE-HDBK-1019/2-93NEUTRON LIFE CYCLEWhen the multiplication factor of a reactor is not equal to exactly one, the neutron flux willchange and cause a change in the power level. Therefore, it is essential to know more abouthow this factor depends upon the contents and construction of the reactor. The balance betweenproduction of neutrons and their absorption in the core and leakage out of the core determinesthe value of the multiplication factor. If the leakage is small enough to be neglected, themultiplication factor depends upon only the balance between production and absorption, and iscalled the infinite multiplication factor (k) since an infinitely large core can have no leakage.When the leakage is included, the factor is called the effective multiplication factor (k_{eff}).The effective multiplication factor (k_{eff}) for a finite reactor may be expressed mathematically interms of the infinite multiplication factor and two additional factors which account for neutronleakage as shown below.k_{eff}= kftFastNon-LeakageProbability(_{f})In a realistic reactor of finite size, some of the fast neutrons leak out of the boundaries of thereactor core before they begin the slowing down process. The fast non-leakage probability(_{f})is defined as the ratio of the number of fast neutrons that do not leak from the reactor core tothe number of fast neutrons produced by all fissions. This ratio is stated as follows. f number of fast neutrons that do not leak from reactornumber of fast neutrons produced by all fissionsThermalNon-LeakageProbability(_{t})Neutrons can also leak out of a finite reactor core after they reach thermal energies. Thethermal non-leakage probability(_{t}) is defined as the ratio of the number of thermal neutronsthat do not leak from the reactor core to the number of neutrons that reach thermal energies. Thethermal non-leakage probability is represented by the following.t number of thermal neutrons that do not leak from reactornumber of neutrons that reach thermal energiesThe fast non-leakage probability (_{f}) and the thermal non-leakage probability (_{t}) may becombined into one term that gives the fraction of all neutrons that do not leak out of the reactorcore. This term is called the total non-leakage probability and is given the symbol _{T}, whereT= ft. _{f}and _{t}are both effected by a change in coolant temperature in a heterogeneouswater-cooled, water-moderated reactor. As coolant temperature rises, the coolant expands. Thedensity of the moderator is lower; therefore, neutrons must travel farther while slowing down.This effect increases the probability of leakage and thus decreases the non-leakage probability.Consequently, the temperature coefficient (defined later) for the non-leakage probabilities isnegative, because as temperature rises, _{f}and _{t}decrease.Rev. 0NP-03Page 9

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