Subscribe options

Select your newsletters:

Please enter your email address:

@

Your email address will only be used for the purpose of sending you the ITER Organization publication(s) that you have requested. ITER Organization will not transfer your email address or other personal data to any other party or use it for commercial purposes.

If you change your mind, you can easily unsubscribe by clicking the unsubscribe option at the bottom of an email you've received from ITER Organization.

For more information, see our Privacy policy.

News & Media

Latest ITER Newsline

  • Thermal shield repair | Where are we at?

    Fitting the vacuum vessel sectors like a jacket, lining the inner wall of the cryostat, or covering the sides of vertical coil gravity supports, ITER's thermal [...]

    Read more

  • Assembly prep | Reviewing plans for in-vessel installation

    A thorough review of all 'in-vessel' assembly scope was organized by the ITER Machine Assembly Program in early February, with the active participation of senio [...]

    Read more

  • Image of the week | Last measurements before campaign

    In order to precisely identify the bevel regions that need to be rectified, metrologists from the SIMANN (SIMIC-Ansaldo) consortium are performing ultra-precise [...]

    Read more

  • Neutral Beam Test Facility | After upgrades, SPIDER testbed set to restart

    After a two-year shutdown for upgrades, the SPIDER testbed at the ITER Neutral Beam Test Facility in Padua, Italy, is preparing for commissioning and operation. [...]

    Read more

  • ITER Research Plan | Jointly preparing a new blueprint

    As part of work underway to update the ITER Project Baseline, a group of experts nominated by the Members met in February to evaluate the new blueprint for achi [...]

    Read more

Of Interest

See archived entries

Lawson's magic formula

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 EUROfusion website.


return to the latest published articles