For thermonuclear fusion to become a practical source of energy, a fusion reactor must produce substantially more energy than is required to sustain the fusion plasma. It is therefore important to know what plasma conditions are necessary for net fusion energy gain. This question was addressed in 1955 by the British engineer and physicist John D. Lawson.

The idea is simple: suppose that we have a fusion reactor that heats the fusion fuel. The fuel must reach a very high temperature. As the temperature rises, the particles move faster and the probability of fusion increases. However, the plasma also loses energy through various processes, including electromagnetic radiation such as bremsstrahlung. An appropriate operating temperature must therefore be reached for each fusion reaction.

The other parameter is density — the denser the fuel, the higher the probability that particles will collide and fuse. However, no confinement system is perfect and the plasma continually loses energy through particle transport, radiation and other processes. The third important parameter is therefore the energy confinement time, which describes how long the plasma can retain its thermal energy.

The energy confinement time describes how long the plasma retains its thermal energy before that energy is lost and must be replaced. External heating is therefore required unless the fusion reactions themselves provide enough self-heating. The ratio of the fusion power produced to the external heating power supplied to the plasma is called the fusion energy gain factor, Q.

Fusion Energy Gain Factor, Q

If Q is lower than 1, the fusion power produced is lower than the external heating power supplied to the plasma.

Scientific breakeven corresponds to Q = 1, when the fusion power produced equals the external heating power supplied to the plasma. In inertial confinement fusion, an analogous milestone was achieved at NIF in 2022, when the fusion energy produced exceeded the laser energy delivered to the target. This is an important scientific milestone, but it is still far from the conditions required for a practical fusion power plant.

Q much greater than 1 is required for a fusion power plant because the plant must also cover conversion losses and the power consumed by its auxiliary systems before electricity can be supplied to the grid.

Ignition occurs when Q approaches infinity. The fusion plasma then sustains its temperature without external heating.

In order to get Q to at least one, the density (n), energy confinement time (τ_E) and temperature (T) have to be in a relationship that is:

n × τ_E = f (T)

For a deuterium–tritium plasma, the Lawson criterion is often expressed using the fusion triple product:

nTτ_E ≳ 3 × 10²¹ keV·s·m⁻³

at a plasma temperature of roughly 10–20 keV (about 100–200 million kelvin).

The Lawson criterion can be satisfied in two fundamentally different ways. Magnetic confinement uses plasma of relatively low density (n ≈ 10²⁰ m⁻³) confined for relatively long periods, with energy confinement times of the order of seconds. In inertial confinement, the fuel is compressed to extremely high densities for only a tiny fraction of a second. These two approaches form the basis of magnetic and inertial confinement fusion.