P
P_{o} e^{t /}
¯
eff
eff
¯
eff
Reactor Theory (Reactor Operations)
DOEHDBK1019/293
REACTOR KINETICS
Rev. 0
NP04
Page 11
Reactor Period ( )
The reactor period is 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 reactor
period is usually expressed in units of seconds. From the definition of reactor period, it is
possible to develop the relationship between reactor power and reactor period that is expressed
by Equation (46).
(46)
where:
P
= transient reactor power
P
= initial reactor power
o
= 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 is
positive, reactor power is increasing. If the reactor period is negative, reactor power is
decreasing.
There are numerous equations used to express reactor period, but Equation (47) shown below,
or portions of it, will be useful in most situations. The first term in Equation (47) is the prompt
term and the second term is the delayed term.
(47)
where:
*
= prompt generation lifetime
= effective delayed neutron fraction
= reactivity
= effective delayed neutron precursor decay constant
eff
= rate of change of reactivity
Effective Delayed Neutron Fraction
Recall that , the delayed neutron fraction, is the fraction of all fission neutrons that are born
as delayed neutrons. The value of depends upon the actual nuclear fuel used. As discussed
in Module 1, the delayed neutron precursors for a given type of fuel are grouped on the basis
of halflife. The following table lists the fractional neutron yields for each delayed neutron
group of three common types of fuel.

