Xenon#
Xenon Evolution#
The Xenon evolution follows the following Bateman equations:
\[ \frac{dI^{135}}{dt} = FissionRate * \gamma_I - I^{135} \lambda_I \]
\[ \frac{dXe^{135}}{dt} = FissionRate * \gamma_{Xe} + I^{135} \lambda_I - Xe^{135} \lambda_{Xe} - \Phi_{Th} Xe^{135} \sigma_{Xe} \]
where \(\gamma\) is the fission yield, \(\lambda\) the decay constant, \(\Phi_{Th}\) the thermal neutron flux and \(\sigma_{Xe}\) the microscopic absorption cross section of the Xenon.
The FissionRate is computed from the thermal power:
\[ Power / Vfuel = FissionEnergy * FissionRate \]
and \(\Phi_{Th}\) from the FissionRate, taking into account a small amount of fast fissions:
\[ FissionRate = FastFissionFactor * \Phi_{Th} * \sigma_f * N_f \]
where FastFissionFactor is the ratio between the total number of fissions and the thermal ones, \(\sigma_f\) the microscopic fission cross-section of the fuel and \(N_f\) the density of fissil atoms in the fuel.
The used microscopic cross-section values should refer to the thermal neutron flux.