¯eff¯I¯eff¯Reactor Theory (Reactor Operations)DOE-HDBK-1019/2-93REACTOR KINETICSRev. 0NP-04Page 13where:=effective delayed neutron fraction=average delayed neutron fractionI=importance factorIn a small reactor with highly enriched fuel, the increase in fast non-leakage probability willdominate the decrease in the fast fission factor, and the importance factor will be greater thanone. In a large reactor with low enriched fuel, the decrease in the fast fission factor willdominate the increase in the fast non-leakage probability and the importance factor will be lessthan one (about 0.97 for a commercial PWR).EffectiveDelayedNeutronPrecursorDecayConstantAnother new term has been introduced in the reactor period ( ) equation. That term is _{eff}(pronounced lambda effective), the effective delayed neutron precursor decay constant. Thedecay rate for a given delayed neutron precursor can be expressed as the product of precursorconcentration and the decay constant ( ) of that precursor. The decay constant of a precursoris simply the fraction of an initial number of the precursor atoms that decays in a given unittime. A decay constant of 0.1 sec , for example, implies that one-tenth, or ten percent, of a-1sample of precursor atoms decays within one second. The value for the effective delayedneutron precursor decay constant, , varies depending upon the balance existing between theeffconcentrations of the precursor groups and the nuclide(s) being used as the fuel.If the reactor is operating at a constant power, all the precursor groups reach an equilibriumvalue. During an up-power transient, however, the shorter-lived precursors decaying at anygiven instant were born at a higher power level (or flux level) than the longer-lived precursorsdecaying at the same instant. There is, therefore, proportionately more of the shorter-lived andfewer of the longer-lived precursors decaying at that given instant than there are at constantpower. The value of is closer to that of the shorter-lived precursors.effDuring a down-power transient the longer-lived precursors become more significant. Thelonger-lived precursors decaying at a given instant were born at a higher power level (or fluxlevel) than the shorter-lived precursors decaying at that instant. Therefore, proportionatelymore of the longer-lived precursors are decaying at that instant, and the value of approacheseffthe values of the longer-lived precursors.Approximate values for are 0.08 sec for steady-state operation, 0.1 sec for a powereff-1-1increase, and 0.05 sec for a power decrease. The exact values will depend upon the materials-1used for fuel and the value of the reactivity of the reactor core.

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