Editing Synchrotron radiation (section)

==Description==
A direct consequence of [[Maxwell's equations]] is that accelerated charged particles always emit electromagnetic radiation. Synchrotron radiation is the special case of charged particles moving at relativistic speed undergoing acceleration perpendicular to their direction of motion, typically in a magnetic field. In such a field, the force due to the field is always perpendicular to both the direction of motion and to the direction of field, as shown by the [[Lorentz force|Lorentz force law]].

The power carried by the radiation is found (in [[SI units]]) by the [[Larmor formula#Relativistic generalization|relativistic Larmor formula]]:<ref>{{cite book |last1=Wilson |first1=E. J. N. |title=An introduction to particle accelerators |date=2001 |publisher=Oxford University Press |location=Oxford |isbn=0-19-850829-8 |pages=221–223}}</ref><ref>{{cite book|first1=Richard|language=en|last1=Fitzpatrick |page=299|title=Classical Electromagnetism|url=https://farside.ph.utexas.edu/teaching/jk1/Electromagnetism.pdf}}<!-- auto-translated by Module:CS1 translator --></ref>

<math display="block">P_\gamma = \frac{q^2}{6 \pi \varepsilon_0 c^3} a^2 \gamma^4 = \frac{q^2 c}{6 \pi \varepsilon_0} \frac{\beta^4 \gamma^4}{\rho^2} ,</math>
where
* <math>\varepsilon_0</math> is the [[vacuum permittivity]],
* <math>q</math> is the particle charge,
* <math>a</math> is the magnitude of the acceleration,
* <math>c</math> is the speed of light,
* <math>\gamma</math> is the [[Lorentz factor]],
* <math>\beta = v/c</math>,
* <math>\rho</math> is the [[radius of curvature]] of the particle trajectory.

The force on the emitting electron is given by the [[Abraham–Lorentz–Dirac force]].

When the radiation is emitted by a particle moving in a plane, the radiation is [[linearly polarized]] when observed in that plane, and [[circularly polarized]] when observed at a small angle. However, in quantum mechanics, this radiation is emitted in discrete packets of photons, which introduces [[Quantum fluctuations of synchrotron radiation|quantum fluctuations in the emitted radiation]] and the particle's trajectory. For a given acceleration, the average energy of emitted photons is proportional to <math>\gamma^3</math> and the emission rate to <math>\gamma</math>.{{cn|date=May 2025}}