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.
The
term (pronounced betabar) is the average
delayed neutron fraction. The value of is the weighted average of the total delayed
neutron fractions of the individual types of fuel. Each total delayed neutron
fraction value for each type of fuel is weighted by the percent of total
neutrons that the fuel contributes through fission. If the percentage of
fissions occurring in the different types of fuel in a reactor changes over the
life of the core, the average delayed neutron fraction will also change. For a
light water reactor using low enriched fuel, the average delayed neutron
fraction can change from 0.0070 to 0.0055 as uranium235 is burned out and
plutonium239 is produced from uranium238.
Delayed
neutrons do not have the same properties as prompt neutrons released directly
from fission. The average energy of prompt neutrons is about 2 MeV. This is
much greater than the average energy of delayed neutrons (about 0.5 MeV). The
fact that delayed neutrons are born at lower energies has two significant
impacts on the way they proceed through the neutron life cycle. First, delayed
neutrons have a much lower probability of causing fast fissions than prompt
neutrons because their average energy is less than the minimum required for
fast fission to occur. Second, delayed neutrons have a lower probability of
leaking out of the core while they are at fast energies, because they are born
at lower energies and subsequently travel a shorter distance as fast neutrons.
These two considerations (lower fast fission factor and higher fast nonleakage
probability for delayed neutrons) are taken into account by a term called the importance
factor (I). The importance factor relates the average delayed
neutron fraction to the effective delayed neutron fraction.
The
effective
delayed neutron fraction (_{eff})
is defined as the fraction of neutrons at thermal energies which were
born delayed. The effective delayed neutron fraction is the product of the
average delayed neutron fraction and the importance factor.
where:
In a small reactor with highly enriched fuel, the increase
in fast nonleakage 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 nonleakage probability and the importance factor will
be less than one (about 0.97 for a commercial PWR).
