Lawsoncriterium

The Lawson criterion is a condition for achieving net energy from controlled thermonuclear fusion. It states that a fusion plasma must reach a sufficiently high product of plasma density, temperature, and energy confinement time, known as the triple product, in order to produce more energy from fusion reactions than is lost to the surroundings.

For deuterium–tritium fusion in magnetic confinement devices, the criterion is commonly expressed in two equivalent forms. A practical two-parameter form is n τ_E ≳ 1×10^20 s·m^-3 at an optimal temperature around 10 keV (about 100 million kelvin). In the three-parameter form, the constraint is n T τ_E ≳ 3×10^21 keV·s·m^-3, where T is the plasma temperature in keV. The precise thresholds depend on the fusion reaction, the energy losses considered, and the confinement method. These thresholds balance the rate of fusion energy production against conductive, radiative, and other losses, and they conceptually serve as a target for reactor design.

The criterion is named after John D. Lawson, who proposed it in the 1950s as a measure of breakeven viability for magnetic confinement fusion. It remains a fundamental benchmark in tokamak and stellarator research and informs assessments of approaches to achieve ignition or breakeven. Different confinement schemes use related formulations; in inertial confinement fusion, analogous requirements involve areal density and rapid energy deposition, with thresholds that differ from magnetic confinement.