Nuclear Fusion

Full definition

Why does the Sun shine? For centuries, no answer. In the 19th century, Helmholtz and Kelvin calculated that gravitational contraction alone could power the Sun for only about 30 million years — far shorter than Earth's geological age, already estimated in the billions. Something didn't add up. The answer came in 1920 with Arthur Eddington: nuclear fusion. Twenty years later, Hans Bethe worked out the exact reactions.

Fusion is the opposite of fission. In fission, a heavy nucleus (uranium, plutonium) splits into two lighter ones. In fusion, two very light nuclei (hydrogen, helium) merge into a heavier nucleus. In both cases part of the mass converts into energy via Einstein's equation E = Δm·c² — but fusion releases about 4 times more energy per kilogram of fuel than fission.

In the Sun's core, 600 million tons of hydrogen become 596 million tons of helium every second. The missing 4 million tons are converted into energy — mostly gamma photons that, after a ~200,000-year random walk through the outer layers, finally emerge as visible light. That energy sustains the star for its entire life and pours into the cosmos.

Stellar fusion has one major consequence: it FORGES the elements. Hydrogen + hydrogen → helium. Helium → carbon. Carbon + helium → oxygen, neon, magnesium... all the way to iron. Every carbon atom in your body, every oxygen atom in the air, every iron atom in your blood was made in a star by fusion. As Carl Sagan put it: 'we are star stuff'.

The process: energy and conditions

To fuse, two positive nuclei must overcome their electrostatic repulsion (Coulomb barrier). In stellar conditions this requires:

Temperature: typically 10⁷ K (10 million degrees). Nuclei then carry enough kinetic energy to approach each other. At this scale, quantum tunneling (discovered by Gamow in 1928) helps by letting a few nuclei cross the barrier without reaching its classical height.

Pressure/Density: in the Sun, ~150 g/cm³ in the core (10 times the density of lead) at 15 × 10⁶ K.

Energy balance: 4 protons → 1 helium-4 nucleus + energy. Δm/m ≈ 0.7 %, i.e., 26.7 MeV per reaction. This efficiency exceeds any chemical energy source by several orders of magnitude: 1 g of fused hydrogen releases ~6 × 10¹¹ J, versus ~4 × 10⁴ J for 1 g of burned gasoline.

Schematic equation (p-p chain, dominant in the Sun): 4 ¹H → ⁴He + 2 e⁺ + 2 ν_e + 2 γ. A fraction of the energy leaves as neutrinos (≈ 2 %), the famous solar neutrinos detected by Kamiokande, Super-Kamiokande, and SNO (Nobel Prizes 2002 and 2015).

Note a crucial asymmetry: fusion releases energy ONLY for elements lighter than iron (⁵⁶Fe). Beyond iron, fusion ABSORBS energy. That is why very massive stars producing iron in their core lose their energy source in a few days and collapse in a supernova.

The stellar reactions step by step

Proton-proton chain (p-p). Dominant in low-mass stars (< 1.3 M☉, including the Sun). Three steps: 1. p + p → ²H + e⁺ + ν_e (very slow — it sets the pace) 2. ²H + p → ³He + γ 3. ³He + ³He → ⁴He + 2 p

CNO cycle (carbon-nitrogen-oxygen). Dominant in more massive stars (> 1.3 M☉) and in the Sun's outer layers. Carbon acts as a catalyst. More efficient at high temperature, scaling as T¹⁷ (hence extremely sensitive).

Triple-alpha process. Once hydrogen is exhausted in the core and temperature passes ~10⁸ K, three helium nuclei fuse into carbon-12. Active in red giants. This step is enabled by an excited resonant state of ¹²C predicted by Fred Hoyle in 1953 — one of the most elegant theoretical predictions later confirmed experimentally.

Further fusions. At increasing temperatures: C+α → O, O+α → Ne, Ne+α → Mg, Si+Si → Fe. Each step burns hotter and briefer. A 25 M☉ star fuses hydrogen for 7 × 10⁶ years, but silicon for... just a few hours before collapse.

s- and r-processes. The formation of elements heavier than iron no longer proceeds by fusion (endothermic) but by neutron capture: the s-process (slow, in AGB giants) and the r-process (rapid, in supernovae and neutron-star mergers). Copper, silver, gold, uranium come from this. GW170817 (2017) provided the first direct observational evidence of the r-process.

How do we observe fusion?

We don't observe fusion itself (it happens at 10⁷ K inside opaque cores), but its many signatures.

Solar neutrinos. The neutrinos produced by the p-p chain escape the Sun directly without interaction. Their detection at the Homestake Mine (Davis, 1964-1994), then Kamiokande/Super-Kamiokande (Japan), SNO (Canada), Borexino (Italy) directly proved that the Sun shines by fusion. Nobel Prizes 2002 (Davis, Koshiba) and 2015 (Kajita, McDonald) crowned these discoveries, including the solution of the 'solar neutrino problem' through the discovery of neutrino oscillations.

Stellar spectroscopy. Analysis of absorption lines measures the composition of stellar atmospheres and traces the history of fusion in each star. Carbon stars (type C) show surface carbon, barium stars show barium... signatures of dredge-up from fusing cores.

Helioseismology. Global oscillations of the Sun, observed by SOHO (1995-) and GOLF, constrain core structure and validate fusion models to better than 1 %.

Cosmochemistry. Element abundances in stars, nebulae and meteorites tell the story of stellar nucleosynthesis since the Big Bang. Nucleosynthesis models (BBN + stellar + supernovae + kilonovae) reproduce the abundance of every element in the periodic table.

Fusion on Earth. Tokamaks (JET, ITER) and inertial fusion (NIF) attempt to reproduce stellar fusion in the lab. In December 2022, NIF (Livermore) reached 'ignition' for the first time (fusion energy > incoming laser energy). The road to a commercial reactor is still long.

What about amateur astronomy? Every star in the night sky is a natural fusion reactor. Our Solar System tool lets you contemplate our Sun, its fusion source 150 million km away.

Not to be confused with

Nuclear vocabulary regularly causes confusion.

Nuclear fission. The OPPOSITE operation: a heavy nucleus (²³⁵U, ²³⁹Pu) splits into two lighter ones, releasing energy. It is the principle of today's nuclear power plants and weapons. It does NOT occur in stars (which lack abundant fissile heavy elements). Fusion releases ~4 times more energy per kg of fuel and produces far less problematic radioactive waste.

Chemical reaction. Chemical reactions (combustion, photosynthesis) involve electrons, not nuclei. Energy released ~10⁶ times smaller than fusion. A liter of burned gasoline releases the equivalent of 0.6 mg of fused hydrogen.

Radioactive decay. Spontaneous transformation of an unstable nucleus by emitting α, β or γ. Needs no high temperature and releases little energy per nucleus (~MeV) compared with fusion (26.7 MeV for 4 protons).

Thermonuclear supernova (Ia). Explosive, uncontrolled fusion of the carbon/oxygen of a white dwarf that exceeds the Chandrasekhar limit. Fusion is the event, not the steady process that sustains an ordinary star.

Matter-antimatter annihilation. Another theoretical nuclear energy source — 100 % of the mass converted to energy, vs 0.7 % for H→He fusion. Rare in stars, but present in pulsar magnetospheres and near active black holes.

r- / s-process. Neutron-capture mechanisms producing elements heavier than iron. Not fusion in the strict sense (different energies involved, no fusing of charged nuclei) but part of the complete cosmic nucleosynthesis chain.