Delayed Neutrons Fraction
The total yield of delayed neutrons per fission, vd, depends on:
- Isotope, that is fissioned (see table).
- Energy of a neutron that induces fission (see chart).
In LWRs the delayed neutron fraction decreases with fuel burnup. This is due to isotopic changes in the fuel. It is simple, fresh uranium fuel contains only 235U as the fissile material, meanwhile during fuel burnup the importance of fission of 239Pu increases (in some cases up to 50%). Since 239Pu produces significantly less delayed neutrons, the resultant core delayed neutron fraction of a multiplying system decreases (it is the weighted average of the constituent delayed neutron fractions). This is also the reason why the neutron spectrum in the core become harder with fuel burnup.
βcore= ∑ Pi.βi
where Pi is fraction of power generated by isotope i.Example:Let say the reactor is at the beginning of the cycle and approximately 98% of reactor power is generated by 235U fission and 2% by 238U fission as a result of fast fission. Calculate the core delayed neutron fraction.
βcore= ∑ Pi.βi = 0.98 x β235 + 0.02 x β238
= 0.98 x 0.0065 + 0.02 x 0.0157
= 0.0064 + 0.0003