The triple product and the Lawson criterion

Fusion gain tells you how much energy came out for what went in. It can only be measured once a plasma produces a meaningful amount of fusion. The triple product measures something earlier: how close a plasma’s conditions are to the point where fusion could sustain itself. It can be compared across machines of very different sizes and designs, which is why the benchmark ranks it.

The three factors

Density (n). The number of fuel ions in each cubic metre of plasma. More ions mean more collisions and more fusion. Magnetic-confinement plasmas run at about 10²⁰ ions per cubic metre. See plasma density.

Ion temperature (T). How fast the fuel nuclei are moving, given in kiloelectronvolts (keV). One keV is about 11.6 million kelvin, so a “100 million degree” plasma is about 8.6 keV. See ion temperature.

Energy confinement time (τ_E). The energy stored in the plasma divided by the rate at which it loses energy. Put simply: if the heating were switched off, roughly how long before the plasma’s energy drained away. In the best tokamaks it is about a second or less; the longest in this dataset is 0.8 seconds, on JET in 1991. See energy confinement time.

Multiply the three and the result, n·T·τ_E, is the triple product, in units of keV·seconds per cubic metre.

The Lawson criterion

In 1955 the British physicist John Lawson worked out the conditions a fusing plasma must meet to produce more energy than it loses. His paper was classified and then published in 1957. In its original form the criterion is a threshold on density times confinement time, n·τ_E, now called the Lawson parameter. Folding temperature in gives the triple product.

For deuterium-tritium fuel, the plasma ignites (the fusion reactions heat it enough to keep it going with no external heating) once the triple product reaches about 3 × 10²¹ keV·s·m⁻³, at an ion temperature of about 14 keV. Short of ignition, lower values still give useful gain, and Wurzel and Hsu chart the triple product needed for each level of scientific gain.

Other fuels need more. Proton-boron-11 needs at least an order of magnitude more triple product than D-T, which is one reason the fusion fuels guide treats aneutronic claims with care.

A worked check

The benchmark requires a triple product to agree with its own parts where the dataset holds them. TFTR shot 83546, 17 February 1995, from the Wurzel and Hsu compilation:

• density 6.6 × 10¹⁹ m⁻³
• ion temperature 43 keV
• energy confinement time 0.28 s

6.6 × 10¹⁹ × 43 × 0.28 = 7.9 × 10²⁰ keV·s·m⁻³, matching the recorded value. That is about a quarter of the ignition threshold (7.9 × 10²⁰ ÷ 3 × 10²¹ ≈ 0.26), and it is the highest measured magnetic-confinement triple product in the dataset.

A unit trap sits in the same table. The Max Planck Institute for Plasma Physics reported Wendelstein 7-X’s 2017 record as 6 × 10²⁶ kelvin·s·m⁻³. Dividing by 11.6 million kelvin per keV gives about 5.2 × 10¹⁹ keV·s·m⁻³. The institute’s own parts agree: 0.8 × 10²⁰ m⁻³, about 40 million kelvin (3.4 keV) and 0.2 seconds give 5.5 × 10¹⁹. Read without conversion, the kelvin figure looks nearly a million times larger than TFTR’s. Converted, it is about one fifteenth.

Reading the leaderboard

The leaderboards page ranks devices by triple product, in units of 10²¹ keV·s·m⁻³ so that 1.0 would be close to a third of the way to ignition. The top of the table, as the dataset stands:

Rank	Device	Value (10²¹ keV·s·m⁻³)	Date
1	TFTR	0.79	17 Feb 1995
2	Joint European Torus	0.61	2 Nov 1991
3	JT-60U	0.56	1998
4	DIII-D	0.37	1997
5	Alcator C	0.12	1984
6	C-Mod	0.074	2016
7	Wendelstein 7-X	0.052	2017

Five things to know when reading it.

1. Each device appears once, at its best value in the source. Most rows come from the Wurzel and Hsu compilation: Table 1 for tokamaks and spherical tokamaks, Table 2 for other magnetic devices. The compilation often lists several shots for one device, and the benchmark takes the highest value it lists. That is not necessarily the device’s own record.
2. Every row is “claimed”, none “achieved”. The status reflects how the value was obtained, not doubt about the machine. Wurzel and Hsu flag many rows as partly inferred: for example, TFTR’s confinement time was derived from a differently defined measurement. The benchmark keeps those flags in each row’s note.
3. The best results are old. The top four are from 1991 to 1998, from large tokamaks that ran deuterium-tritium or pushed ion temperatures above 15 keV. Newer machines are mostly built for other goals: long pulses, superconducting magnets, or testing wall materials.
4. Design targets are excluded. ITER’s projected 7.4 × 10²¹ and SPARC’s projected 6.2 × 10²¹ are in the dataset as planned, and appear on no ranking.
5. Inertial fusion is not on this board yet. Wurzel and Hsu do compute triple products for inertial experiments, using a confinement time defined differently for a plasma that lasts nanoseconds, but the dataset has not recorded them. The National Ignition Facility’s results appear as gain on the gain page.

Plasma duration is not confinement time

A frequent error in fusion coverage is to treat how long a plasma lasted as how long it held its energy. They are different quantities and differ by orders of magnitude.

• EAST sustained a high-confinement plasma for 1,066 seconds on 20 January 2025. The longest energy confinement time this dataset holds for EAST is 0.054 seconds (2015). The ratio is about 20,000.
• Wendelstein 7-X ran for 480 seconds on 15 February 2023. Its record triple product in 2017 came with a confinement time of about 0.2 seconds.

Long duration matters: a power plant must run for hours. But duration says nothing on its own about how good the confinement is. The benchmark keeps plasma duration as a separate metric with its own leaderboard, and never folds it into the triple product.

Peak and sustained

Temperature and duration figures carry a qualifier. A peak ion temperature, held for a moment, is a different achievement from one sustained for tens of seconds. TFTR reached a peak of 510 million degrees, about 44 keV; its operator’s page gives no date, so the dataset records none. KSTAR in Korea sustained ions at 100 million degrees (about 8.6 keV) for 48 seconds in its December 2023 to February 2024 campaign. The first is hotter. The second is held far longer. Neither is simply “better”.

Sources

• Wurzel and Hsu, “Continuing progress toward fusion energy breakeven and gain as measured against the Lawson criteria”, arXiv:2505.03834 (2025), tables
• Wikipedia, Lawson criterion
• Max Planck Institute for Plasma Physics, Wendelstein 7-X world record for fusion product (2018)
• Max Planck Institute for Plasma Physics, Wendelstein 7-X 480-second discharge (2023)
• Chinese Academy of Sciences, EAST sets new record (21 January 2025)
• Korea Institute of Fusion Energy via EurekAlert, 28 March 2024
• Creely et al., “Overview of the SPARC tokamak”, Journal of Plasma Physics 86 (2020)