Subscribe options

Select your newsletters:


Please enter your email address:

@

News & Media

Latest ITER Newsline

  • Rendezvous | D and T to meet at JET in 2020

    In 2020, for the first time in more than 20 years, a reaction that only occurs in the core of the stars will be produced on Earth in a man-made machine. In the [...]

    Read more

  • On site | MOMENTUM believes in recent graduates

    It is rare for students to leave university and immediately begin work on a globally significant project. But thanks to the graduate program run by the project' [...]

    Read more

  • Tokamak Pit | Big steel elbow in place

    A cryostat feedthrough delivered by the Chinese Domestic Agency has become the first metal component of the machine to be installed in the Tokamak Pit, in an op [...]

    Read more

  • Neutral beam source | Europe awards EUR 20 million contract

    The contract, awarded to ALSYOM-SEIV (ALCEN group, France), launches the manufacturing phase for the beam source that will come on line in 2022 as part of the f [...]

    Read more

  • Image of the week | US Under Secretary of Science tours site

    Five months, almost to the day, after the US Secretary of Energy Rick Perry visited ITER, his deputy, Under Secretary for Science Paul Dabbar, stood by the same [...]

    Read more

Of Interest

See archived entries

Lawson's magic formula

Phil Dooley, EFDA

In 1955, John D.Lawson (4 April 1923-15 January 2008) demonstrated that the conditions for fusion reactions relied on three vital quantities: temperature (T), density (n) and confinement time (τ). (Click to view larger version...)
In 1955, John D.Lawson (4 April 1923-15 January 2008) demonstrated that the conditions for fusion reactions relied on three vital quantities: temperature (T), density (n) and confinement time (τ).
In 1955 a young engineer working on nuclear fusion decided to work out exactly how enormous the task of achieving fusion is. Although his colleagues were optimistic about their prospects, he wanted to prove it to himself. His name was John Lawson, and his findings—that the conditions for fusion power relied on three vital quantities—became the landmark Lawson Criteria.

The genesis of Lawson's Criteria is simple enough—he calculated the requirements for more energy to be created than is put in, and came up with a dependence on three quantities: temperature (T), density (n) and confinement time (τ)*. With only small evolution thanks to some subtle changes of definition, this is basically the same figure of merit used by today's fusion scientists, the triple product, nτT.

The amount of energy created relies on particles colliding and fusing—the number of collisions is related to the number of particles in a certain region—thus n, the number density (not mass density) is Lawson's first criterion. This would seem encouraging for the prospective experiment, as creating high pressure is relatively easy. However there is a catch. At higher densities a process known as bremsstrahlung rears its ugly head, in which collisions between nuclei and electrons generate radiation. Bremsstrahlung can become so dominant that all the power in the plasma is radiated away; the optimum density conditions are surprisingly low, around a million times less dense than air.

Nonetheless the fusion collisions—between the nuclei—have to be at high speed. This allows the nuclei to overcome their electrostatic repulsion, and get close enough for the strong force that governs fusion to take over and stick the particles together. The speed of a gas or plasma particle is equivalent to its temperature: the second of Lawson's criteria.

Again there is a limit—if the two particles are moving really fast then the time they are in close enough proximity for fusion to occur decreases. The bremsstrahlung also increases at higher temperatures, due to faster moving electrons. The Goldilocks temperature turns out to be in the vicinity of 100—200 million degrees, a seemingly huge task in the fifties that has become a standard condition today.

* "τ" is the Greek letter tau (pronounced like "how").

Read more on the EFDA website.


return to the latest published articles