Nuclear Fusion

The Sun shines by squeezing hydrogen into helium. Doing the same on Earth would give almost limitless, cleaner energy, if only we could hold a gas hotter than the Sun’s core in place.

Fusing light nuclei#

Bring two light nuclei within about 1 fm and the nuclear force can merge them into one heavier nucleus. Because B/A rises steeply for light nuclei, this releases energy: nuclear fusion. The difficulty is getting them that close. Atoms are about 10⁵ fm across, their electrons repel, and even bare nuclei repel each other strongly.

The answer is to heat the gas until the electrons are stripped off (a plasma) and the nuclei move so fast that some collide hard enough to fuse. Such reactions are called thermonuclear.

The Sun’s core is only about 1.5 × 10⁷ K, a hundred times cooler, yet it runs on fusion. Two reasons: in a hot gas some particles have far more than the average energy, and nuclei with too little energy can still tunnel through the Coulomb barrier occasionally.

Fusion in stars#

The proton–proton cycle

In the Sun and cooler stars (up to about 10⁷ K):

The Sun has been shining for about 4.5 × 10⁹ years, and its hydrogen should last roughly another 5 × 10⁹.

The carbon cycle

In hotter stars (about 10⁸ K), carbon-12 acts as a catalyst: it captures protons step by step (forming ¹³N, ¹³C, ¹⁴N, ¹⁵O, ¹⁵N, with two β⁺ decays) and finally gives back ¹²C plus a ⁴He. The net result is again four protons turned into one helium nucleus.

Heavier nuclei need hotter cores because Coulomb repulsion grows with Z. Hot enough stars fuse helium (3 ⁴He → ¹²C + γ) and so on up to the iron region, where B/A peaks. Elements heavier than iron are built by neutron capture followed by β decay.

Fusion on Earth#

Stars are held together by gravity. On Earth no solid wall can contain a plasma at fusion temperatures, so confinement is the main problem. The most practical reactions use deuterium and tritium:

The Lawson criterion

J. D. Lawson showed that to get out more energy than you put in, the plasma density n and confinement time τ must satisfy

Magnetic confinement: the tokamak

A tokamak holds the plasma in a doughnut-shaped (toroidal) chamber with carefully shaped magnetic fields: whenever a charged particle heads for the wall, the force qv × B turns it back. The plasma is heated with high-frequency currents, and fusion proceeds in pulses. Large machines such as JET in Europe have approached Q ≈ 1, and ITER is being built to go further; smaller ones such as Aditya at the Institute for Plasma Research, Ahmedabad, study plasma behaviour.

Inertial confinement

Intense laser pulses hit a tiny deuterium–tritium pellet from all sides. They vaporize it into plasma and compress it to 10³–10⁴ times its normal density, heating it so fast that fusion occurs before it can fly apart. The α particles produced stay inside and heat the plasma further.