¯
eff
¯
I
¯
eff
¯
Reactor Theory (Reactor Operations)
DOE-HDBK-1019/2-93
REACTOR KINETICS
Rev. 0
NP-04
Page 13
where:
=
effective delayed neutron fraction
=
average delayed neutron fraction
I
=
importance factor
In a small reactor with highly enriched fuel, the increase in fast non-leakage probability will
dominate the decrease in the fast fission factor, and the importance factor will be greater than
one. In a large reactor with low enriched fuel, the decrease in the fast fission factor will
dominate the increase in the fast non-leakage probability and the importance factor will be less
than one (about 0.97 for a commercial PWR).
Effective Delayed Neutron Precursor Decay Constant
Another new term has been introduced in the reactor period ( ) equation. That term is eff
(pronounced lambda effective), the effective delayed neutron precursor decay constant. The
decay rate for a given delayed neutron precursor can be expressed as the product of precursor
concentration and the decay constant ( ) of that precursor. The decay constant of a precursor
is simply the fraction of an initial number of the precursor atoms that decays in a given unit
time. A decay constant of 0.1 sec , for example, implies that one-tenth, or ten percent, of a
-1
sample of precursor atoms decays within one second. The value for the effective delayed
neutron precursor decay constant,
, varies depending upon the balance existing between the
eff
concentrations 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 equilibrium
value. During an up-power transient, however, the shorter-lived precursors decaying at any
given instant were born at a higher power level (or flux level) than the longer-lived precursors
decaying at the same instant. There is, therefore, proportionately more of the shorter-lived and
fewer of the longer-lived precursors decaying at that given instant than there are at constant
power. The value of
is closer to that of the shorter-lived precursors.
eff
During a down-power transient the longer-lived precursors become more significant. The
longer-lived precursors decaying at a given instant were born at a higher power level (or flux
level) than the shorter-lived precursors decaying at that instant. Therefore, proportionately
more of the longer-lived precursors are decaying at that instant, and the value of
approaches
eff
the values of the longer-lived precursors.
Approximate values for
are 0.08 sec for steady-state operation, 0.1 sec for a power
eff
-1
-1
increase, and 0.05 sec for a power decrease. The exact values will depend upon the materials
-1
used for fuel and the value of the reactivity of the reactor core.
