What happens to the reactor period as reactivity ρ approaches β_eff?

• A. The reactor period becomes undefined as ρ approaches β_eff.
• B. The reactor period shortens dramatically and the reactor becomes easier to control.
• C. The reactor period remains constant as ρ approaches β_eff.
• D. The period lengthens dramatically and tends to infinity as ρ approaches β_eff.

Answer: (D)

The period is governed by how close the reactivity is to the point where delayed neutrons just balance the system. When reactivity is approaching the delayed-critical value set by the effective delayed-neutron fraction β_eff, the net driving force for change becomes vanishingly small. In a point-kinetics picture that includes delayed neutrons, the slowest mode that controls the power change has a time constant that grows without bound as ρ → β_eff from below. So the reactor responds more and more slowly, and the period becomes very large, effectively tending to infinity. If ρ were to cross β_eff, the situation would shift to prompt-critical behavior with a much shorter, prompt-neutron–driven period, but right at the boundary the period diverges.