PP_{o}e^{t /}¯effeff¯effReactor Theory (Reactor Operations)DOE-HDBK-1019/2-93REACTOR KINETICSRev. 0NP-04Page 11ReactorPeriod( )The reactor periodis defined as the time required for reactor power to change by a factor of"e," where "e" is the base of the natural logarithm and is equal to about 2.718. The reactorperiod is usually expressed in units of seconds. From the definition of reactor period, it ispossible to develop the relationship between reactor power and reactor period that is expressedby Equation (4-6).(4-6)where:P= transient reactor powerP= initial reactor powero= reactor period (seconds)t= time during the reactor transient (seconds)The smaller the value of , the more rapid the change in reactor power. If the reactor period ispositive, reactor power is increasing. If the reactor period is negative, reactor power isdecreasing.There are numerous equations used to express reactor period, but Equation (4-7) shown below,or portions of it, will be useful in most situations. The first term in Equation (4-7) is the promptterm and the second term is the delayed term.(4-7)where:*= prompt generation lifetime= effective delayed neutron fraction= reactivity= effective delayed neutron precursor decay constanteff= rate of change of reactivityEffectiveDelayedNeutronFractionRecall that , the delayed neutron fraction, is the fraction of all fission neutrons that are bornas delayed neutrons. The value of depends upon the actual nuclear fuel used. As discussedin Module 1, the delayed neutron precursors for a given type of fuel are grouped on the basisof half-life. The following table lists the fractional neutron yields for each delayed neutrongroup of three common types of fuel.