Reactor Theory (Nuclear Parameters)
NEUTRON LIFE CYCLE
When the multiplication factor of a reactor is not equal to exactly one, the neutron flux will
change and cause a change in the power level. Therefore, it is essential to know more about
how this factor depends upon the contents and construction of the reactor. The balance between
production of neutrons and their absorption in the core and leakage out of the core determines
the value of the multiplication factor. If the leakage is small enough to be neglected, the
multiplication factor depends upon only the balance between production and absorption, and is
called the infinite multiplication factor (k
) since an infinitely large core can have no leakage.
When the leakage is included, the factor is called the effective multiplication factor (keff).
The effective multiplication factor (keff) for a finite reactor may be expressed mathematically in
terms of the infinite multiplication factor and two additional factors which account for neutron
leakage as shown below.
keff = k
Fast Non-Leakage Probability (
In a realistic reactor of finite size, some of the fast neutrons leak out of the boundaries of the
reactor core before they begin the slowing down process. The fast non-leakage probability ( f)
is defined as the ratio of the number of fast neutrons that do not leak from the reactor core to
the number of fast neutrons produced by all fissions. This ratio is stated as follows.
number of fast neutrons that do not leak from reactor
number of fast neutrons produced by all fissions
Thermal Non-Leakage Probability (
Neutrons can also leak out of a finite reactor core after they reach thermal energies. The
thermal non-leakage probability ( t) is defined as the ratio of the number of thermal neutrons
that do not leak from the reactor core to the number of neutrons that reach thermal energies. The
thermal non-leakage probability is represented by the following.
number of thermal neutrons that do not leak from reactor
number of neutrons that reach thermal energies
The fast non-leakage probability ( f) and the thermal non-leakage probability ( t) may be
combined into one term that gives the fraction of all neutrons that do not leak out of the reactor
core. This term is called the total non-leakage probability and is given the symbol T, where
. f and t are both effected by a change in coolant temperature in a heterogeneous
water-cooled, water-moderated reactor. As coolant temperature rises, the coolant expands. The
density of the moderator is lower; therefore, neutrons must travel farther while slowing down.
This effect increases the probability of leakage and thus decreases the non-leakage probability.
Consequently, the temperature coefficient (defined later) for the non-leakage probabilities is
negative, because as temperature rises, f and t decrease.