The product of plasma density, temperature, and energy confinement time—the single figure of merit that determines how close a fusion plasma is to producing net energy.
The fusion triple product is the quantity n · T · τE, where n is the fuel ion number density, T is the ion temperature, and τE is the energy confinement time. It serves as the primary figure of merit for evaluating how close a confined plasma is to achieving net fusion energy production.[1]
A fusion plasma must be hot enough for fuel nuclei to overcome their mutual Coulomb repulsion and fuse, and retain that thermal energy long enough for sufficient reactions to occur. Lawson’s original criterion framed this as a minimum product of density and confinement time at a given temperature. The triple-product reformulation incorporates temperature explicitly, providing a single number that captures all three requirements simultaneously.[1]
Density (n): The fuel ion number density. Magnetic confinement devices typically operate at 1019–1021 m−3, while inertial confinement plasmas reach 1031–1032 m−3.[3]
Temperature (T): The ion temperature, where 1 keV ≈ 11.6 million °C. The optimal temperature for D–T ignition is approximately 14 keV (~160 million °C). Below roughly 4 keV, bremsstrahlung radiation losses exceed fusion power.[3]
Energy confinement time (τE): The timescale over which the plasma loses its stored thermal energy. In modern tokamaks, τE ranges from tens of milliseconds to several seconds.[3]
The triple product achieved in laboratory plasmas has increased by more than four orders of magnitude since the 1960s. Verified experimental results:[2]
The triple product provides a technology-independent metric for comparing fusion approaches. ITER is designed to achieve triple-product values well above the ignition threshold, targeting Q ≥ 10.[4]