Note that, there is the consistency between the numerator in the definition of ε
and the denominator in the definition of Pf
.The fast non-leakage probability is for large reactor cores about 0.92 – 0.98 and this value is minimally affected (in comparison with the other factors) by operational changes except changes in the moderator temperature. It can be derived from the Fermi age theory, the probability that a neutron will remain in
the core and become a thermal neutron
without being lost by fast leakage, is also represented by following equation:
where τ is the fermi age of a neutron, B is the geometrical buckling (in case of critical state Bg = Bm), which depends only on the shape and size of the core. The value of B for small cores is higher than the value for large cores. So that, it is obvious, the fast neutrons leakage is higher for small cores and also depends of the macroscopic slowing down power of neutron moderator (leakage is higher for poor moderators).
The fast non-leakage probability
Total Non-leakage Probability
) and the thermal non-leakage probability
) 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 PNL
, and may be expressed by following equation:
For large reactors, we can rewrite this equation without a substantial loss of accuracy simply by replacing the diffusion length Ld and τ by the migration length M in the one group equation. The term B4 is very small for large reactors and therefore it can be neglected. We may then write.
where M is the migration area (m2). The migration length is defined as the square root of the migration area.
Main operational changes, that affect this factor:
Since both (Pf and Pt
) are affected by a change in moderator temperature
in a heterogeneous water-moderated reactor and the directions of the feedbacks is the same, the resulting total non-leakage probability
is also sensitive on the change in the moderator temperature. In result, an increase in the moderator temperature
causes that the probability of leakage increases
. This effect is one of two main effects causing the moderator temperature coefficient (MTC)
of most PWRs
to be negative.
The fast neutron leakage is also dependent on the core temperature (or moderator temperature). The moderator temperature influences macroscopic cross-sections for elastic scattering reaction (Σs=σs.NH2O) due to the thermal expansion of water. As the temperature of the core increases, the fast neutron leakage increases. This physical process is a part of the moderator temperature coefficient (MTC) and it is responsible for an increase in neutron flux measured by neutron detectors, which are situated around the reactor vessel.