Reactor Theory (Reactor Operations)DOE-HDBK-1019/2-93SUBCRITICAL MULTIPLICATIONInstead of plotting M directly, its inverse (1/M) is plotted on a graph of 1/M versus rod height.M 11 keff1M1 keffAs control rods are withdrawn and keff approaches one and M approaches infinity, 1/Mapproaches zero. For a critical reactor, 1/M is equal to zero. A true 1/M plot requiresknowledge of the neutron source strength. Because the actual source strength is usuallyunknown, a reference count rate is substituted, and the calculation of the factor 1/M is throughthe use of Equation (4-5).(4-5)1MCRoCRwhere:1/M=inverse multiplication factorCRo=reference count rateCR=current count rateIn practice, the reference count rate used is the count rate prior to the beginning of the reactivitychange. The startup procedures for many reactors include instructions to insert positivereactivity in incremental steps with delays between the reactivity insertions to allow time forsubcritical multiplication to increase the steady-state neutron population to a new, higher leveland allow more accurate plotting of 1/M. The neutron population will typically reach its newsteady-state value within 1-2 minutes, but the closer the reactor is to criticality, the longer thetime will be to stabilize the neutron population.Example:Given the following rod withdrawal data, construct a 1/M plot and estimate the rodposition when criticality would occur. The initial count rate on the nuclearinstrumentation prior to rod withdrawal is 50 cps.Rod Withdrawal(inches)Count Rate(cps)25546768681201019212500Rev. 0NP-04Page 7
Integrated Publishing, Inc. - A (SDVOSB) Service Disabled Veteran Owned Small Business
