Effective Precursor Decay Constant – Lambda-Effective
The effective delayed neutron precursor decay constant (pronounced lambda effective) is a new term, which has to be introduced in the reactor period equation in case of a single precursor group model. For the purpose of creating a simple kinetic model conducive to understanding reactor behavior, it is useful to further reduce the precursors to a single group. But if we do this, the convention is to employ a constant precursor yield fraction and a variable precursor decay rate, as defined by lambda effective (λeff). In the single precursor group model the lambda effective is not a constant, but rather a dynamic property that depends on the mix of precursor atoms resulting from the reactivity.
The reason the constant decay constant cannot be used, is as follows. During power transients, there is a difference in the decay and the creation of short-lived and long-lived precursors.
During a power increase (positive reactivity), the short-lived precursors decaying at any given instant were born at a higher power level than the longer-lived precursors decaying at the same instant. The short-lived precursors become more significant. As the magnitude of the positive reactivity increases, the value of lambda effective increases closer to that of the short-lived precursors (let say 0.1 s-1 for +100pcm).
During a power decrease (negative reactivity), the long-lived precursors decaying at a given instant were born at a higher power level than the short-lived precursors decaying at that instant. The long-lived precursors become more significant. As the magnitude of the negative reactivity increases, the value of lambda effective decreases closer to that of the long-lived precursors (let say 0.05 s-1 for -100pcm).
If the reactor is operating at steady-state operation, all the precursor groups reach an equilibrium value and the λeff value is approximately 0.08 s-1.