Nuclear fusion

Nuclear fusion joins light nuclei into heavier nuclei. For sufficiently light elements, the products can be more tightly bound per nucleon, so the reaction releases energy. The central difficulty is getting positively charged nuclei close enough for the short-range nuclear force to act.

The Coulomb barrier

Two positively charged nuclei repel each other electrically. Higher temperature raises typical ion kinetic energies and increases the number of close encounters, but it does not remove the barrier. Quantum tunnelling is crucial: nuclei can have a finite probability of reaching fusion distances even when their classical energy is below the top of the electrostatic barrier.

High temperature helps, but tunnelling remains part of the physics. Fusion occurs only when nuclei approach to very short distances.

A reference reaction: deuterium and tritium

A commonly discussed laboratory reaction is ²H + ³H → ⁴He + n. It releases about 17.6 MeV: roughly 3.5 MeV goes to the helium nucleus and 14.1 MeV to the neutron. The neutron is neutral and therefore is not magnetically confined with the charged plasma.

Fusion releases energy when it moves light nuclei toward more tightly bound products. “Combining nuclei” by itself is not the reason.

Temperature, density and confinement all matter

A fusion plasma must contain enough reacting ions, with a suitable energy distribution, for long enough that fusion production can compete with energy losses. This is the logic behind the Lawson criterion and related triple-product measures. A spectacular temperature alone is not evidence that a plasma is producing net energy.

Stars and laboratory plasmas are not the same case

The Sun is confined by gravity and mainly converts hydrogen to helium through the proton-proton chain. Terrestrial fusion research often focuses on different reactions and uses magnetic confinement or rapid compression. These systems have different engineering routes, but the same basic physics remains: enough close nuclear encounters must occur before the plasma loses its useful energy.

Worked examples

1. Check nucleon bookkeeping

Solution

For ²H + ³H → ⁴He + n, mass numbers give 2 + 3 = 5 on the left and 4 + 1 = 5 on the right. Electric charge is also conserved: 1 + 1 = 2 + 0.

2. Why does temperature not suffice?

Solution

Temperature describes the ion energy distribution, but fusion yield also depends on density and confinement time. A hot but extremely dilute, short-lived plasma can still produce little fusion.

3. Use a Q-value

Solution

If a reaction has a mass defect of 0.010 u and 1 u c² ≈ 931.5 MeV, then Q ≈ 0.010 × 931.5 = 9.32 MeV.