Lawson Criterion

The Lawson criterion states the minimum threshold that a plasma’s density, temperature, and energy confinement time must satisfy simultaneously in order to achieve a net energy gain from fusion.

Simple Definition (High School)

Picture a campfire. To get a fire going, you need to gather enough fuel, make it hot enough, and keep the heat from escaping too quickly. If the wood is spread too thin, or the wind carries the heat away too fast, the fire goes out before it can catch. Fusion works the same way: only when the fuel (the plasma) is dense, hot, and able to hold its heat long enough does the energy produced by reactions exceed the heat that leaks away. The Lawson criterion bundles these three conditions into a single rule of thumb: “with this much, the fire will catch.” The British physicist John Lawson derived it in the 1950s.

Precise Definition (Undergraduate and Above)

The Lawson criterion is formulated as the condition under which the energy produced by fusion reactions exceeds the energy lost from the plasma. In practice, the triple product $n \, T \, \tau_E$, obtained by multiplying the density $n$, temperature $T$, and energy confinement time $\tau_E$, is used as the figure of merit.

For a deuterium-tritium (D-T) reaction at the optimal temperature (roughly 10 to 20 keV, about 100 to 200 million degrees), the triple product required for ignition is approximately:

$$n \, T \, \tau_E \gtrsim 3 \times 10^{21} \ \text{keV} \cdot \text{s} / \text{m}^3$$

This means that the product of the density $n$ (number of particles per unit volume), the temperature $T$, and the energy confinement time $\tau_E$ (a measure of how long the heat is retained) must exceed this value. The three quantities compensate for one another: if the density is low, the confinement time must be long; if the confinement time is short, the density must be high.

Role in Fusion Research

The Lawson criterion serves as a “passing line” common to every fusion approach, providing a yardstick for measuring a device’s performance. Magnetic confinement tokamaks keep the density modest while achieving a long confinement time, whereas inertial confinement completes the reaction in a very short time at extremely high density: each approach has a different strategy for accumulating the triple product. The state in which the energy generated by the reactions alone keeps the plasma temperature self-sustaining is called ignition, and the Lawson criterion is the standard for judging whether this ignition can be reached.

Learn More

• Lawson Criterion (Fundamentals)
• Plasma Transport

Related Terms

• Plasma - the state the Lawson criterion applies to
• Confinement - what determines the confinement time $\tau_E$
• Fusion Reaction - the source of energy gain
• Tokamak - a representative device aiming to meet the Lawson criterion