Nuclear Physics and Reactor Theory Fundamentals
This domain tests neutronics and core physics: how fission releases energy, how a chain reaction is sustained, and how reactivity is quantified and fed back.
Core rules
- Binding energy per nucleon peaks near iron-56; fission of U-235 releases about 200 MeV, or roughly 3.2×10^-11 J per fission.
- Criticality is defined by k_eff, the ratio of neutron production to loss. Critical is k = 1; subcritical k < 1; supercritical k > 1.
- Reactivity is ρ = (k − 1)/k. It is expressed in pcm (1 pcm = 10^-5) or in dollars, where $1 = ρ/β and β is the delayed-neutron fraction.
- For U-235, β is about 0.0065; for Pu-239 it is about 0.0021. Prompt criticality occurs when ρ exceeds β.
- In a thermal reactor, k∞ is often decomposed with the six-factor formula: ε, p, f, η, plus leakage through buckling.
- Feedback matters: Doppler broadening gives a negative fuel-temperature coefficient; the PWR moderator coefficient is normally negative but depends on boron and temperature; void coefficients vary by design.
Worked example
A core has k = 1.005 and β = 0.0065. Find reactivity in pcm and dollars, and state whether it is prompt critical.
ρ = (1.005 − 1)/1.005 = 0.004975. In pcm this is 497.5 pcm. In dollars it is 0.004975/0.0065 = 0.765 $. Since 0.765 $ is below 1 $, the core is not prompt critical; it is supercritical on delayed neutrons, so power rises with a finite period rather than a prompt excursion. If k were 1.01, ρ would be 0.0099, or about 1.52 $, which is prompt critical.
Traps
Using k − 1 instead of (k − 1)/k introduces error that matters at large reactivity. Mixing pcm and percent is common: 500 pcm is 0.5%, not 5%. Do not assume every reactor has a negative void coefficient. Do not ignore leakage in small cores, and do not use U-235 β for a plutonium-dominated core.
Key points
- k = 1 is critical; ρ = (k − 1)/k.
- 1 $ = β; prompt critical means ρ ≥ β.
- U-235 fission yields about 200 MeV.
- Doppler feedback is negative and fast.
- Void and moderator coefficients are design-specific.
- Six-factor formula separates multiplication from leakage.