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Triple Product

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.

Reviewed Last reviewed: 9 Aug 2026 · Category: Concepts & Physics

Definition

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]

Ignition threshold (D–T fuel):
n · T · τE ≥ 3 × 1021 keV · s · m−3
(at the optimal temperature of approximately 14 keV)

Physical Basis

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]

The Three Factors

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]

Experimental Progress

The triple product achieved in laboratory plasmas has increased by more than four orders of magnitude since the 1960s. Verified experimental results:[2]

Significance

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]

Sources

  1. Lawson, J.D. "Some Criteria for a Power Producing Thermonuclear Reactor." Proceedings of the Physical Society B, vol. 70, no. 1, 1957, pp. 6–10.
  2. Wurzel, S.E. and Hsu, S.C. "Progress toward fusion energy breakeven and gain as measured against the Lawson criterion." Physics of Plasmas, vol. 29, 2022, 062103.
  3. Wesson, J. Tokamaks. 4th edition, Oxford University Press, 2011.
  4. ITER Physics Expert Groups et al. "Chapter 1: Overview and summary." Nuclear Fusion, vol. 39, no. 12, 1999, pp. 2137–2174.

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