Key Takeaways — Chapter 28

Core Concepts

1. Fission weapons require a prompt supercritical assembly of fissile material. Two designs exist: the gun-type (simple, reliable, HEU only, inefficient) and the implosion (complex, requires precision explosives, works with Pu, more efficient). Critical mass depends on material, geometry, reflector, and density ($M_c \propto 1/\rho^2$).

2. Critical mass estimates from one-speed diffusion theory give physically reasonable results: - ${}^{235}\text{U}$ bare sphere: $\sim 52\,\text{kg}$ ($R_c \approx 8.5\,\text{cm}$) - ${}^{239}\text{Pu}$ bare sphere: $\sim 10\,\text{kg}$ ($R_c \approx 5\,\text{cm}$) - Reflectors reduce $M_c$ by a factor of 2–3; compression reduces $M_c$ as $1/\rho^2$.

3. Thermonuclear weapons (Teller-Ulam): A fission primary compresses a fusion secondary via radiation coupling. Lithium-6 deuteride serves as both fuel and tritium source. Yields from kilotons to megatons; no upper limit in principle.

4. Enrichment is the industrial bottleneck. Gas centrifuge: $\alpha \approx 1.20$ per stage ($\sim 70$ enriching stages to WGU). $\sim 230\,\text{SWU/kg}$ of WGU. Thousands of centrifuges operating continuously are required, but the facility is smaller and lower-power than gaseous diffusion, making it harder to detect.

5. Plutonium production requires a reactor (any type with ${}^{238}\text{U}$ fuel) and a reprocessing plant. Weapons-grade Pu ($> 93\%$ ${}^{239}\text{Pu}$) requires low burnup. Both the reactor and reprocessing plant are detectable.

6. The NPT (1968) rests on three pillars: nonproliferation, disarmament, and the right to peaceful nuclear energy. IAEA safeguards enforce compliance through material accountancy, containment and surveillance, and environmental sampling.

7. Environmental sampling is the most powerful safeguards tool: SIMS analysis of individual $\sim 1\,\mu\text{m}$ particles can measure ${}^{235}\text{U}/{}^{238}\text{U}$ ratios with $\sim 1\%$ precision, distinguishing LEU from HEU.

8. Nuclear forensics identifies the origin and history of nuclear material from isotopic signatures: - ${}^{235}\text{U}/{}^{238}\text{U}$: enrichment level - ${}^{236}\text{U}$: irradiation/recycling indicator - ${}^{240}\text{Pu}/{}^{239}\text{Pu}$: burnup and grade (weapons vs. reactor) - ${}^{241}\text{Am}/{}^{241}\text{Pu}$: nuclear chronometer (time since last chemical separation, $t_{1/2} = 14.33\,\text{yr}$) - Trace elements: chemical processing fingerprint

9. Radiation detection for security uses NaI, LaBr$_3$, and HPGe detectors for gamma spectroscopy, and ${}^{3}\text{He}$ or alternatives for neutron detection. The primary challenge is distinguishing threat materials from NORM in limited measurement time.

10. The dirty bomb (RDD) disperses radioactive material with conventional explosives. No nuclear chain reaction occurs. Primary impact is economic and psychological (area denial), not mass casualty. Doses are generally modest.

Essential Numbers to Remember

The Threshold Concept

The barrier to nuclear proliferation is not the physics — the physics is well known and publicly available. The barrier is the industrial scale of producing fissile material (enriched uranium or plutonium), reinforced by the detectability of that industrial activity and the international safeguards regime. Understanding this distinction is essential: proposals to "control the physics" (e.g., by restricting physics education) are futile and counterproductive. Effective nonproliferation controls the materials, not the knowledge.

Connections to Other Chapters