Symbol a
a is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Why this formula appears here
Electrons circulating in a storage ring undergo enormous proper acceleration — for an ultra-relativistic beam of Lorentz factor on a ring of radius r , the proper centripetal acceleration is a /r . For beam parameters typical of a large electron-positron collider, with of order 210^5 and r of order several kilometers, this works out to a 810^{23}\, , corresponding by the Unruh formula to = a/(2 c ) 310^3\, — a temperature scale that is, remarkably, not astronomically small, unlike the roughly 10^{-19}\, an Earth-bound laboratory accelerometer would need a planet’s worth of…
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Symbol gamma^2
gamm is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.
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Its accuracy depends on the assumptions and range of use described in the article.
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Published contexts (1)
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Equation 100 · Evolutionary Physics
No Particle Without a Cosigner
This equation gives an approximation: it relates the quantities while allowing an approximation.
Electrons circulating in a storage ring undergo enormous proper acceleration — for an ultra-relativistic beam of Lorentz factor on a ring of radius r , the proper centripetal acceleration is a /r . For beam parameters typical of a large electron-positron collider, with of order 210^5 and r of order several kilometers, this works out to a 810^{23}\, , corresponding by the Unruh formula to = a/(2 c ) 310^3\, — a temperature scale that is, remarkably, not astronomically small, unlike the roughly 10^{-19}\, an Earth-bound laboratory accelerometer would need a planet’s worth of…