E.4 · IB Physics
Nuclear reactor control
Move the control rods, change the fuel and the moderator, and watch how the neutron multiplication factor k decides whether the chain reaction dies away, holds steady or grows.
k = k₀ × (1 − 0.30 f)
P(t+Δt) = P(t) × e^((k − 1)Δt/τ)
f = fraction of rod inserted, k₀ set by fuel and moderator, τ = 0.1 s (effective generation time incl. delayed neutrons)
- k
- 1.000
- Power
- 100 %
- Rod position
- 50.0 %
- State
- Critical
- Trend
- steady
Try this
- From Reset (k = 1.000), withdraw the rods to 49.0 %. Read k and check the doubling time against τ ln2 / (k − 1).
- Set the moderator to None. Explain why k falls far below 1 even though the fuel has not changed.
- Tick temperature feedback, then withdraw the rods to 47.0 %. Watch the power settle at a new level and note the value of k once it is steady.
Common error: writing that control rods ‘slow down’ neutrons — the moderator slows neutrons by collisions, while control rods absorb them and so reduce k.