Reactor Theory (Reactor Operations)DOE-HDBK-1019/2-93SUBCRITICAL MULTIPLICATIONThe equation for N_{1} can be divided by the equation for N_{2}.N_{1}N_{2}S11 k_{1}S11 k_{2}N_{1}N_{2}1 k_{2}1 k_{1}Because 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 k_{eff} 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)CR_{1}CR_{2}1 k_{2}1 k_{1}where:CR_{1}= count rate at time 1CR_{2}= count rate at time 2k_{1}= k_{eff}at time 1k_{2}= k_{eff}at 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