The diffusion length is very important parameter in thermal reactors and its magnitude can be changed during reactor operation. Since the diffusion length is dependent on the diffusion coefficient (~Σs) and Σa, we will study impacts of operational changes on these parameters. For illustration, here are some examples of these operational changes and their impacts on L2, that may take place in PWRs.
Change in the moderator and fuel temperature
The diffusion length, L2, is sensitive especially on the change in the moderator temperature. Since diffusion in heterogeneous reactors occurs especially in the moderator, the change in the moderator temperature dominates over the change in the fuel temperature.
In short, as the moderator temperature increases, the diffusion length also increases.
The moderator temperature influences all macroscopic cross-sections (e.g. Σs=σs.NH2O) especially due to the thermal expansion of water, which results in a decrease in the atomic number density. In fact, the microscopic cross-sections also slightly changes with temperature, but not so much in thermal spectrum.
For the diffusion length there are two effects. Both processes have the same direction and together causes the increase in the diffusion lengths as the temperature increases. Since the diffusion length significantly influences the thermal non-leakage probability, it is of importance in reactor dynamics (it influences moderator temperature feedback).
- Macroscopic cross-sections for elastic scattering reaction Σs=σs.NH2O, which significantly changes due to the thermal expansion of water. As the temperature of the core increases, the diffusion coefficient (D = 1/3.Σtr) increases.
- The macroscopic cross-section for neutron absorption also decreases as the moderator temperature increases. This is especially due to thermal expansion of water, but also due to the changes in the microscopic cross-section (σa) for neutron absorption. As the temperature of the core increases, the absorption cross-section decreases.
Change in the boron concentration
The concentration of boric acid diluted in the primary coolant influences the diffusion length. For example, an increase in the concentration of boric acid (chemical shim) causes an addition of new absorbing material into the core and this causes an increase in the macroscopic absorption cross-section and this, in turn, causes a decrease in the diffusion length.