NEUTRON LIFE CYCLE
DOE-HDBK-1019/2-93
Reactor Theory (Nuclear Parameters)
As temperature varies, each absorption and fission microscopic cross section varies according to
the 1/v relationship (see Module 2). Since both the numerator and the denominator change
equally, the net change in h is zero. Therefore, h changes only as uranium-235 enrichment
changes. h increases with enrichment because there is less uranium-238 in the reactor making
it more likely that a neutron absorbed in the fuel will be absorbed by uranium-235 and cause
fission.
To determine the reproduction factor for a single nuclide rather than for a mixture, the
calculation may be further simplified to the one shown below.
h sf n
sa
Effective Multiplication Factor
The infinite multiplication factor can fully represent only a reactor that is infinitely large,
because it assumes that no neutrons leak out of the reactor. To completely describe the neutron
life cycle in a real, finite reactor, it is necessary to account for neutrons that leak out. The
multiplication factor that takes leakage into account is the effective multiplication factor (keff),
which is defined as the ratio of the neutrons produced by fission in one generation to the number
of neutrons lost through absorption and leakage in the preceding generation.
The effective multiplication factor may be expressed mathematically as shown below.
keff
neutron production from fission in one generation
neutron absorption in the
preceding generation
neutron leakage in the
preceding generation
So, the value of keff for a self-sustaining chain reaction of fissions, where the neutron population
is neither increasing nor decreasing, is one. The condition where the neutron chain reaction is
self-sustaining and the neutron population is neither increasing nor decreasing is referred to as
the critical condition and can be expressed by the simple equation keff = 1 .
If the neutron production is greater than the absorption and leakage, the reactor is called
supercritical. In a supercritical reactor, keff is greater than one, and the neutron flux increases
each generation. If, on the other hand, the neutron production is less than the absorption and
leakage, the reactor is called subcritical. In a subcritical reactor, keff is less than one, and the
flux decreases each generation.
NP-03
Rev. 0
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