In point kinetics, what best describes β_eff and its role?

• A. The prompt-neutron fraction; does not include delayed neutrons.
• B. The effective delayed-neutron fraction; the sum of delayed neutron fractions weighted by precursor populations; used to control the speed of the reactor's response in kinetics.
• C. The total delayed-neutron fraction; defined as the sum of all per-group fractions without weighting.
• D. The delayed-neutron generation time; the average delay before emission.

Answer: (B)

In point kinetics, the slow part of the reactor’s response comes from delayed neutrons. β_eff is the effective delayed-neutron fraction, meaning it represents how many delayed neutrons are effectively available per prompt neutron, but it’s not just a simple sum of fractions. It is the sum of the delayed-neutron fractions weighted by the actual precursor populations present, which reflect how the different precursor groups contribute to neutron emission at that moment.

This weighted sum sets how strong the delayed-neutron source term is in the kinetics equations. Since delayed neutrons enter the neutron balance with a time delay, β_eff directly controls the time scale of the reactor’s dynamic response to a reactivity change. A larger β_eff means more neutrons come out later, slowing the overall response; a smaller β_eff means a faster response because fewer neutrons are delayed.

Why the other ideas aren’t right: the prompt-neutron fraction ignores the delayed-neutron contribution altogether; a simple unweighted sum of delayed fractions doesn’t capture how precursor populations weigh each group’s impact; and the delayed-neutron generation time is a separate parameter describing how long delays take, not the fraction of neutrons that are delayed.