Operational changes that affect the diffusion length
The diffusion coefficient is very important parameter in thermal reactors and its magnitude can be changed during reactor operation. Since the diffusion coefficient is dependent on the macroscopic scattering cross-section, Σs, we will study impacts of operational changes on this parameter.
Change in the moderator temperature
The diffusion coefficient, D, is sensitive especially on the change in the moderator temperature.
In short, as the moderator temperature increases, the diffusion coefficient also slightly increases.
This increase in the diffusion coefficient is especially due (Σs=σs.NH2O) to a decrease in the macroscopic scattering cross-section, Σs=σs.NH2O, caused by the thermal expansion of water (a decrease in the atomic number density).
Calculation of Diffusion Coefficient
The scattering cross-section of carbon at 1 eV is 4.8 b (4.8×10-24 cm2). Calculate the diffusion coefficient and the transport mean free path.
We will calculate the diffusion according to the advanced formula:
First, we have to determine the atomic number density of carbon and then the scattering macroscopic cross-section.
MC = 12
NC = ρ . Na / MC
= (2.2 g/cm3)x(6.022×1023 nuclei/mol)/ (12 g/mol)
= 1.1×1023 nuclei / cm3
the microscopic cross-section
σs12C = 4.8 b
the macroscopic cross-section
Σs12C = 4.8×10-24 x 1.1×1023 = 0.528 cm-1
the diffusion coefficient is then:
D = 1 / (3 x 0.528 x 0.9445) = 0.668 cm
the transport mean free path
λtr = 3 x D = 2.005 cm