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 or diffusion process.
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 the number of emitted photons and also the energy spectrum for the electron should be determined instead.
In particular, the normalized power spectrum emitted by a charged particle moving in a bending magnet is given by This result was originally derived by Dmitri Ivanenko and Arseny Sokolov and independently by Julian Schwinger in 1949.
), the average number of emitted photons by the particle can be expressed as where
is The photon number curve and the power spectrum curve intersect at the critical energy where γ = E/e0, E is the total energy of the charged particle, ρ is the radius of curvature, re the classical electron radius, e0 = mec2 the particle rest mass energy, ℏ the reduced Planck constant, and c the speed of light.
However, the particle motion perturbation (diffusion) is mainly related by the variance of the quantum energy
The diffusion coefficient at a given position s is given by For an early analysis of the effect of quantum excitation on electron beam dynamics in storage rings, see the article by Matt Sands.