The basic fuel element of light water reactors is a fuel rod
which contains fuel pellets
made of uranium dioxide
. For example, an 1100 MWe (3300 MWth) reactor core
may contain 157 fuel assemblies
composed of over 45,000 fuel rods
and some 15 million fuel pellets
. The neutron moderator
surrounds these fuel rods. The spatial self-shielding
is phenomenon primarily connected with this heterogeneity of the reactor core
The fission neutrons are born in the fuel, but they are primarily moderated (slowed down) in the moderator. Thermal and epithermal neutrons return back into the fuel to be absorbed and to cause further fission. With the aid of energy self-shielding neutrons are more likely absorbed by the nuclei near the fuel surface. In this case the surface layers of the fuel geometrically shields the inner layers from neutron flux, leading to a relatively lower neutron flux inside the fuel rod. For neutron energies near resonances (energy self-shielding) the depression of the energy dependent flux is dramatical.
The spatial and energy self-shielding, that take place primarily in heterogeneous reactor cores, causes a significant increase in the resonance escape probability (“p” from four factor formula) in comparison with homogeneous cores. Without the spatial self-shielding provided by the separation of fuel and moderator, values of keff = 1 are possible with natural uranium fuel only if heavy water is used as the moderator.
In nuclear industry gadolinium is commonly used as a neutron absorber due to the very high neutron absorbtion cross-section of two isotopes 155Gd and 157Gd. In fact their absorption cross-sections are the highest among all stable isotopes. 155Gd has 61 000 barns for thermal neutrons (for 0.025 eV neutron) and 157Gd has even 254 000 barns. Some power plants use gadolinium as a burnable absorber diluted in the fuel matrix in the form of mixture Gd2O3 + UO2. Such the high absorption cross-section of gadolinium causes that the fuel rod is burning up layer by layer (from the surface to inner layers) and at the beginning of the cycle this fuel rod behaves like being from neutron black material. At the beginning of the cycle the higher content (i.e. from 4% to 6% of Gd2O3) of gadolinium causes minimal decrease in the overall compensation of the core reactivity. Only the higher amount of such rods with burnable absorber results in the overall decrease in core reactivity. This is also the example of very strong effect of self-shielding.
Self-shielding and Doppler Broadening
There is a further phenomenon connected with spatial and energy self-shielding
. The energy self-shielding is significantly affected by the material temperature
. It is closely connected with the Doppler broadening
and with the fuel temperature coefficient
(also known as the Doppler coefficient
). The material temperature affects the energy self-shielding through Doppler-broadening of the microscopic resonance cross-section. With an increase in fuel temperature also the thermal motion
of target nuclei increases resulting in the broadening of spectral lines
due to the Doppler effect. The wings of resonances are broadened while its peak magnitude decreases. The energy dependent neutron flux
closely follow the behavior of the changed resonances in a reverse manner
, leading to a reduction in the self-shielding
and an increase in the effective microscopic absorption cross-section. This in turn provides negative reactivity feedback
against fuel temperature increase.
An increase in temperature from T1
causes the broadening of spectral lines of resonances. Although the area under the resonance remains the same, the broadening of spectral lines causes an increase in neutron flux
in the fuel φf
(E), which in turn increases the absorption as the temperature increases.