# 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.

## Copyright © EDF 2002 - 2026  


## ThermoSysPro Version 4.2