Quantum excitation is the effect in circular accelerators 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 Z ...

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

electron The electron ( or ) 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 particles because they have no kn ...

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 to ...

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, visi ...

. 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 A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...

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

References

Accelerator physics {{accelerator-stub

Mechanism

Further reading

References