Nuclear Fusion

Why fusion?

Property	Fission	Fusion
Fuel	U-235 (rare, mined)	D from water (effectively unlimited)
Energy/kg	~8 × 10¹³ J	~3 × 10¹⁴ J (4× more)
Long-lived waste	Yes (10⁵+ years)	No (decades)
Meltdown risk	Yes	No (loss of confinement just stops reaction)
Proliferation	U-235, Pu-239 weapons	None (no enrichment cascade)
Control	Long-established	Net energy just achieved (NIF 2022)

Common fusion reactions

Reaction	Energy released	Notes
D + T → He-4 + n	17.6 MeV	Easiest; main target
D + D → He-3 + n	3.27 MeV	Or D + D → T + p (4.03 MeV)
D + He-3 → He-4 + p	18.3 MeV	No neutrons, but He-3 is rare
p + p → D + e⁺ + ν	0.42 MeV	Sun's first step; very slow
p + B-11 → 3·He-4	8.7 MeV	Aneutronic, very high T needed

Lawson criterion

For ignition (self-sustained fusion):

n · τ · T > 10²¹ keV·s/m³  (for D-T)

where n is plasma density, τ is energy confinement time, T is ion temperature.

Approach	n (m⁻³)	τ (s)	T (keV)
Sun's core	~10³²	~10⁹	1.3
Tokamak (ITER target)	~10²⁰	~5	15
Inertial confinement (NIF)	~10³¹	~10⁻¹¹	~10

All three regimes can achieve the same n·τ·T target.

JavaScript — fusion calculations

// D-T fusion: energy per reaction
const Q_DT = 17.6e6 * 1.602e-19;  // J

// Energy per kg fully fused (D + T)
function fusionEnergy_DT_perKg() {
  // 1 kg of D + T mixture; ~5/2 = 2.5 g/mol effective
  // Actually: 2.014 + 3.016 = 5.03 u per pair; 1 kg → ~1.99e26 reactions
  const reactions = 1000 / 5.03 * 6.022e23;
  return reactions * Q_DT;
}

console.log(`1 kg D-T mix: ${(fusionEnergy_DT_perKg() / 1e14).toFixed(2)} × 10¹⁴ J`);
console.log(`= ${(fusionEnergy_DT_perKg() / 4.184e12).toFixed(0)} Mt TNT`); // ~80 Mt for 1 kg!

// Sun's energy output: how much H consumed?
function solarMassLoss(luminosity_W) {
  return luminosity_W / 9e16;  // kg/s
}

console.log(`Sun: ${solarMassLoss(3.828e26).toExponential(2)} kg/s lost (= 600 Mt H/s)`);

// Lawson criterion check
function lawsonProduct(n, tau, T_keV) {
  return n * tau * T_keV;  // m⁻³ · s · keV
}

// ITER target
console.log(`ITER target: nτT = ${lawsonProduct(1e20, 5, 15).toExponential(2)} keV·s/m³`);
// 7.5 × 10²¹ — should achieve ignition

// Coulomb barrier — temperature needed
function coulombTemp_keV(Z1, Z2, r_fm = 5) {
  // E_Coulomb = k·Z1·Z2·e²/r at closest approach
  // E in keV with r in fm: E_keV = 1.44 × Z1·Z2 / r_fm
  return 1.44 * Z1 * Z2 / r_fm;
}

console.log(`p-p Coulomb peak: ${coulombTemp_keV(1, 1).toFixed(2)} keV`);  // 0.288 keV
// But tunneling means lower T sufficient — Sun's 1.3 keV core is enough

// Fusion power density
function fusionPowerDensity(n_D, n_T, sigma_v_m3_per_s) {
  // P = n_D · n_T · <σv> · Q
  return n_D * n_T * sigma_v_m3_per_s * Q_DT;
}

// At T = 15 keV, <σv> ≈ 1.5e-22 m³/s for D-T
const sigmav_15 = 1.5e-22;
console.log(`At n_D = n_T = 5e19, T = 15 keV: power = ${fusionPowerDensity(5e19, 5e19, sigmav_15).toFixed(0)} W/m³`);
// Million W/m³ — but small reactor volumes ↔ MW power total

// Q-factor (gain)
function fusionGain(P_fusion, P_input) {
  return P_fusion / P_input;
}

// NIF 2022: 2.05 MJ in, 3.15 MJ out → Q ~ 1.54 (ignition)
console.log(`NIF Q = ${fusionGain(3.15e6, 2.05e6).toFixed(2)}`);
// ITER goal: Q = 10

Where fusion matters

• Stellar physics. Powers all main-sequence stars; nucleosynthesis creates elements heavier than H.
• Future power. ITER, SPARC (private), and others aim for commercial fusion power.
• Nuclear weapons. H-bombs use fusion stage; fusion provides bulk yield.
• Space propulsion. Theoretical fusion rockets (much higher Isp than chemical).
• Cosmology. Big Bang nucleosynthesis produced light elements; stellar fusion creates heavier.
• Materials testing. Fusion neutron sources for materials irradiation studies.
• Medical isotopes. Some isotopes produced via fusion-related reactions.

Common mistakes

• Confusing with fission. Different physics — fusion combines light, fission splits heavy. Both follow E = mc² but in different directions of binding-energy curve.
• Believing fusion is "30 years away" forever. Joke for decades; recent NIF Q > 1 (2022) is genuine breakthrough. ITER first plasma 2025-2026. Commercial harder.
• Treating all fusion approaches the same. Magnetic (tokamak), inertial (lasers), magnetic+inertial (Z-pinch), aneutronic (p-B11) — different physics, different challenges.
• Believing fusion is "cold" possible. Cold fusion (Pons-Fleischmann 1989) has not been reproducibly demonstrated. Current commercial efforts all require ~150 million K plasmas.
• Thinking fusion has no waste. Reactor components become activated by neutrons. Decommissioning still requires careful handling. But MUCH less long-lived than fission.
• Forgetting tritium scarcity. Tritium has 12-yr half-life — minimal natural quantity. Fusion reactors must "breed" tritium from lithium blankets. Engineering challenge.