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Quantum excitation is the effect in circular
accelerators Accelerator may refer to: In science and technology In computing *Download accelerator, or download manager, software dedicated to downloading *Hardware acceleration, the use of dedicated hardware to perform functions faster than a CPU ** Gr ...
or storage rings whereby the discreteness of photon emission causes the charged particles (typically electrons) to undergo a
random walk In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb ...
or
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
process.


Mechanism

An
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...
moving through a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...
emits
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, vi ...
. The expected amount of radiation can be calculated using the classical power. Considering quantum mechanics, however, this radiation is emitted in discrete packets of photons. For this description, the distribution of number of emitted photons and also the energy spectrum for the electron should be determined instead. In particular, the spectrum of a bending magnet is given by : S(\xi)=\frac\xi\int_0^\infty K_(\bar \xi) d\bar \xi The diffusion coefficient is given by : d= \dot N\langle u^2\rangle The result is : d= \frac\alpha \frac\frac


Further reading

For an early analysis of the effect of quantum excitation on electron beam dynamics in storage rings, see the article by Matt Sands. The Physics of Electron Storage Rings: An Introduction by Matt Sands


References

Accelerator physics {{accelerator-stub