Some Facts About Neutron and Reactor Physics - The Risks of Nuclear Energy Technology - page 17

Fig. 2.5 Square lattice cell with fuel rod, cladding and moderator of a LWR-fuel element

2.4 Criticality or Effective Multiplication Factor k eff

The ratio between the number of newly generated neutrons by fission and the
number of neutrons absorbed in the reactor core or escaping from the reactor is
called the criticality factor or effective multiplication factor, k eff .
When k eff ¼

1, the reactor core is critical and can be operated in steady state. At

k eff < 1 the reactor core is subcritical, e.g. with control or absorber rods fully

inserted in the core.
Boron, Cadmium or Gadolinium etc. can be used as absorber materials, either as
metallic alloys in control rods or as burnable poisons in ceramic form in fuel rods
and special poison rods or as a fluid, e.g. boric acid in the coolant of an LWR [ 1 - 4 ].
For a k eff > 1 the reactor core is supercritical. More neutrons are produced than

are absorbed in the reactor core or do escape from the core. The neutron chain
reaction is ascending (reaction rates and the number of neutrons and, thus, reactor
power increase as a function of time).
The criticality or effective multiplication factor k eff of a reactor core is deter-
mined by the proper choice of its geometrical dimensions (diameter and spacing
of the fuel rods, diameter and height of the reactor core), by the choice of the
moderator and coolant as well as by the choice of the fuel and structural materials.
The choice of the U-235 enrichment of the fuel is of decisive importance for LWRs.

2.5 Neutron Density and Power Distribution

Figure 2.6 displays the spatial distribution of the neutron density in the range of
thermal energies for a Pressurized Water Reactor (PWR). The distribution of fission
reaction rates or of the power generated by fissions is essentially proportional to the