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Residual decay power kinetics.

Up to now, the nuclear power density ft (W/cm³) was calculated from the fission neutron source sf (neutr/cm³/s) by (1) where κ/ν (skn) is tabulated along with the other neutronic properties.

Actually, sf represents the total "potential" fission neutron source which includes the prompt neutrons emitted at fission time, and the delayed neutron emitted by subsequent decay of radioactive fission product emitters cj generated at fission time.
We remind (2) the balance equation of precursor cj with decay constant λj.
For stationary condition, (4) applies, which implies (5).
A strict mathematical similitude may be established between the delayed neutron precursors and the power decay fission product (FP) emitters. The concentration cyj (the added "y" stands for power deca"Y") satisfies (7), where βyj is the number of FP emitters of type j with decay constant λyj.
(8) holds for steady-sate.;
The power density fyj deposited by emitters yj decay is proportional (factor μ) to the decay rate (9).
At steady-state, from (8) and (9) , we obtain (10) which shows that if we set (11), fyj could be interpreted as well as the steady-state ratio of cyj generated decay power fyj to the total potential power ft.
The actual fyj in transient condition is (12), and f (13) the actual instant power.
In (13), βyp is the prompt (major) fraction.
For yj emitters with time constant (1/ λyj) much larger than the application duration, the contribution of those emitters should more conveniently be approximated by a constant part βy0 ft0 of the initial power. At steady state, f=ft=ft0 and (8) holds.
Conceiving the power decay model as a strict analogy to the delayed neutron model allows taking profit of the existing coding. However, as power production is no longer synchronous whith neutron flux, modeling the interaction between neutronic and power effects (for example, the power feedback to reactivity) is more complicated
Power decay model is activated under Lstcy and Lstcyj lists. (be=β, am=λ).

For most of the transients at power, the effect of decay power is just reflected by a small time lagging and smoothing of power production behind the neutron flux and the activation of the effect is not worthwhile; the normal model is probably conservative.

For safety evaluation of the core immediately after shutdown however, the residual power depends of previous reactor operation history and the delayed neutron produced by remaining precursors may contribute to some fission power. Then the decay power model is necessary.

The prompt fraction beyp must not be entered: it is calculated from bey0 and the behj by means of (14).