Nuclear Explosion Physics

A nuclear explosion releases the energy binding atomic nuclei together — on time scales of microseconds, in a volume initially smaller than a grapefruit. The physics spans quantum mechanics, neutron transport, radiation hydrodynamics, and plasma physics, and understanding it clearly is essential to comprehending both the historical event and the scientific principles underlying nuclear deterrence and nonproliferation.

1. Nuclear Fission and the Chain Reaction

Nuclear fission: ²³⁵U + n \to [²³⁶U]* \to ⁹²Kr + ¹⁴¹Ba + 3n + ~200 MeV (per fission) (or many other fission fragment pairs) Energy released: Mass defect: Δm = m(²³⁵U) + m(n) - m(Kr) - m(Ba) - 3m(n) Δm \approx 0.00085 u per fission E = Δm\cdotc² \approx 0.00085 \times 931.5 MeV/u \approx 200 MeV per fission Compare: TNT \approx 1 kcal/mol \to ~0.04 eV per molecule Ratio: 200 MeV / 0.04 eV \approx 5\times10⁹ \to nuclear energy ~5 billion\times chemical energy 1 kg of ²³⁵U completely fissioned: N = (1000 g)/(235 g/mol) \times 6.022\times10²³ = 2.56\times10²⁴ fissions E = 2.56\times10²⁴ \times 200\times10⁶ \times 1.6\times10⁻¹⁹ J = 8.2\times10¹³ J \approx 20 kT TNT Chain reaction: Each fission releases 2-3 neutrons. These neutrons can induce further fissions. Fast neutron spectrum (unmoderated): ²³⁵U fissionable by fast neutrons. Multiplication factor k: k = (neutrons produced) / (neutrons absorbed or lost) k < 1: subcritical — chain dies out k = 1: critical — sustained reaction (reactor) k > 1: supercritical — exponential growth In a weapon: k >> 1 (supercritical) \to exponential growth on nanosecond timescale

2. Critical Mass

Critical mass — minimum mass for self-sustaining chain reaction: Neutron mean free path in ²³⁵U: λ = 1/(n\cdotσ_f) where σ_f = fission cross-section (barns) For fast neutrons: σ_f \approx 1.2 barn = 1.2\times10⁻²⁴ cm² n(U235) = ρ\cdotN_A/A = 18.7 g/cm³ \times 6.022\times10²³ / 235 = 4.79\times10²² atoms/cm³ λ \approx 1/(4.79\times10²² \times 1.2\times10⁻²⁴) \approx 17 cm (rough estimate) For a sphere of radius R: Leakage probability \propto R² (surface) Absorption \propto R³ (volume) Critical when geometry balances leakage vs absorption Pure ²³⁵U sphere: m_c \approx 52 kg (bare sphere, uncompressed) Pure ²³⁹Pu sphere: m_c \approx 10 kg (smaller — higher σ_f) Tamper effect: surrounding the fissile material with ²³⁸U or beryllium reflects neutrons back \to reduces critical mass by factor ~3-4 Implosion compression: doubling density \to reduces critical mass by factor ~4 \to Fat Man used only ~6 kg of Pu (combined tamper + implosion)

3. Weapon Designs: Gun-Type vs Implosion

Gun-type (Little Boy, Hiroshima, Aug 6 1945): A sub-critical mass of ²³⁵U (enriched to ~80%) is fired through a cylinder into another sub-critical piece. When assembled, the combined mass exceeds critical. Simple, reliable — but requires ~50 kg of ²³⁵U (inefficient). Cannot be used with ²³⁹Pu (pre-detonation problem — trace ²⁴⁰Pu causes premature chain reaction during assembly). Yield: 15 kT.
Implosion design (Fat Man, Nagasaki, Aug 9 1945; Trinity, July 16 1945): A sub-critical sphere of ²³⁹Pu is surrounded by shaped high-explosive lenses. Simultaneous detonation from all sides generates a spherically symmetric convergent shock wave compressing the Pu core to ~2-3× normal density. This reduces the critical mass below the assembled amount → supercriticality. A polonium-beryllium initiator (urchin) at centre releases a neutron burst precisely at maximum compression. The technical challenge of simultaneous detonation (within microseconds) required extensive testing — hence Trinity. Yield: 21 kT (Fat Man).

4. Yield and Trinity

Yield (W): 1 kT TNT = 4.184×10¹² J 1 MT TNT = 4.184×10¹⁵ J Historical yields: Trinity (first test), July 16 1945: ~21 kT Little Boy (Hiroshima): ~15 kT Fat Man (Nagasaki): ~21 kT Tsar Bomba (Soviet, 1961): ~50 MT (largest ever detonated) Modern thermonuclear warhead (W88): ~475 kT Fission efficiency ("burn fraction"): Ideal (complete fission of 6 kg Pu): ~500 kT equivalent Fat Man yield: ~21 kT → burn fraction ~4% Modern designs: 15-30% efficiency Trinity observation (Fermi's estimate): Fermi dropped scraps of paper during the blast wave passage. Measured displacement: ~2.5 m at 10 km from detonation Used blast pressure-displacement formula → estimated ~10 kT Official estimate (instruments): 21 kT Fermi's rapid mental estimate was within factor of 2 — celebrated example of order-of-magnitude physics estimation ("Fermi estimation")

Thermonuclear (hydrogen) bombs: A fission primary stage compresses and heats a secondary stage containing lithium-6 deuteride. The fission explosion generates X-rays that ablate the secondary casing → implosion → temperature ~10⁸ K → deuterium-tritium fusion reactions (D + T → ⁴He + n + 17.6 MeV). The fusion neutrons also fission a ²³⁸U tamper → most yield actually comes from fission, not fusion. The Teller-Ulam design (1951) made megaton yields achievable in compact form. All strategic nuclear warheads are thermonuclear.

5. Explosion Phases: What Happens

After detonation, a nuclear explosion progresses through distinct phases driven by different physics:

t = 0–50 ns (Chain reaction): Fission proceeds exponentially. About 80 generations from initial neutron to full yield. Temperature rises to ~10⁸ K, density to ~10⁷ kg/m³. The bomb disassembles before all material can fission.
t = 50 ns–1 ms (Fireball / X-ray phase): Weapon material is fully vaporised plasma emitting intense X-rays and γ-rays. The X-ray mean free path is short → X-rays absorbed in nearby air → air superheated and re-radiates. Fireball radius grows to ~100 m for a 1 MT burst in ~1 ms. Shockwave separates from luminous fireball.
t = 1 ms–10 s (Blast wave): Supersonic shockwave propagates outward. Overpressure (+ΔP above atmospheric) devastates structures. 5 psi overpressure destroys most residential buildings. Negative pressure phase (underpressure) follows, creating inward wind.
t = 10 s–several minutes (Thermal phase): Fireball rises as a buoyant plume. Surface temperature ~8000 K → intense thermal radiation. Accounts for ~35% of total yield. Can cause flash burns at tens of km distance for megaton yields.
Fallout: Weapon debris, soil (if surface burst), and fission products lifted into mushroom cloud. Rainout and fallout deposits radioactive material downwind. ⁹⁰Sr and ¹³⁷Cs (half-lives 29 and 30 years) are principal long-term hazards.

6. Scaling Laws and Effects

Cube-root scaling law (Glasstone "Effects of Nuclear Weapons"): R = R_1 \cdot (W/W_1)^(1/3) Where R = radius of given effect, W = weapon yield, W_1 = reference yield. Example: 1 psi (moderate structural damage) radius for 1 kT burst: ~1.3 km For 1 MT (1000\times more energetic): R = 1.3 km \times (1000)^(1/3) = 1.3 \times 10 = 13 km \to 1 psi radius Thermal effects (R_thermal \propto W^(1/2) approximately, varies with visibility): For 3rd-degree burns in clear weather: 1 kT: ~0.5 km 1 MT: ~12 km (\times\sqrt1000 \approx 32\times, but atmospheric absorption limits high yields) Lethal ionising radiation from prompt gamma/neutrons: Significant only within ~1-2 km even for large weapons (dominated by blast/thermal at larger distances) EMP (Electromagnetic pulse): High-altitude burst (>40 km): Compton electrons from gamma rays spiral in Earth's magnetic field \to super-EMP field up to 50 kV/m over entire line-of-sight footprint (1000+ km for 400 km altitude) Damages unprotected electronics over continental scale

7. Historical Legacy and Non-Proliferation

Manhattan Project (1942–1946): ~130,000 people, $2 billion (~$30 billion today). Parallel plants at Oak Ridge (²³⁵U enrichment), Hanford (²³⁹Pu production), Los Alamos (weapon design, Oppenheimer). First demonstration of large-scale nuclear science engineering.
Nuclear testing: 2056 nuclear tests total (1945–1998). Over 500 atmospheric tests before the 1963 Partial Test Ban Treaty. Long-term ¹⁴C, ⁹⁰Sr, ¹³⁷Cs elevation in global environment. CTBT (Comprehensive Test Ban Treaty, 1996): not ratified by USA, China. Moratorium on testing broadly observed.
Deterrence and proliferation: 9 countries currently possess nuclear weapons (~12,500 warheads total, 2023). Non-Proliferation Treaty (NPT, 1968): 191 states parties. Challenge: North Korea tested weapons 2006–2017. Iran enrichment program. The IAEA safeguards system is the formal verification mechanism.
Humanitarian impact: Hiroshima + Nagasaki: 109,000–226,000 deaths by end of 1945. Hibakusha (survivors) carried radiological and psychological effects for generations. The International Campaign to Abolish Nuclear Weapons (ICAN) — Nobel Peace Prize 2017 — advocates for the Treaty on the Prohibition of Nuclear Weapons (TPNW, 2021).