Reactor Theory (Reactor Operations)DOE-HDBK-1019/2-93SUBCRITICAL MULTIPLICATIONThe equation for N1 can be divided by the equation for N2.N1N2S11 k1S11 k2N1N21 k21 k1Because the source strength appears in both the numerator and denominator, it cancels out ofthe equation. Therefore, the neutron level at any time can be determined based on the neutronlevel present at any other time provided the values of keff or reactivity for both times are known.The neutron level in a shutdown reactor is typically monitored using instruments that measurethe neutron leakage out of the reactor. The neutron leakage is proportional to the neutron levelin the reactor. Typical units for displaying the instrument reading are counts per second (cps).Because the instrument count rate is proportional to the neutron level, the above equation canbe restated as shown in Equation (4-4).(4-4)CR1CR21 k21 k1where:CR1= count rate at time 1CR2= count rate at time 2k1= keffat time 1k2= keffat time 2Equation (4-4) is very useful during the shutdown operation of a reactor. Before adding positivereactivity to a reactor, it is possible to predict the effect the reactivity addition will have on theneutron level. Example:A reactor that has a reactivity of -1000 pcm has a count rate of 42 counts per second(cps) on the neutron monitoring instrumentation. Calculate what the neutron level shouldbe after a positive reactivity insertion of 500 pcm from the withdrawal of control rods.Rev. 0NP-04Page 5
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