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.
Mechanism
An
electron moving through a
magnetic field emits
radiation called
synchrotron radiation. 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 normalized power spectrum emitted by a charged particle moving in a bending magnet is given by
This result has been derived originally by
Dmitri Ivanenko and
Arseny Sokolov and independently by
Julian Schwinger in 1949
[1]
By dividing each power of this power spectrum by the energy, we obtain the photon flux
The photon flux from this normalized power spectrum (of all energies) is then
That the above photon flux integral is finite implies discrete photon emission. It is in fact a
Poisson process. The emission rate is
- [photon/sec] from [4.4]
[2] [5.9]
[2] [5.12]
[2]
For a travelled distance at a speed close to (), the average number of emitted photons by the particle can be expressed as
- where is the
fine-structure constant
The probability that k photons are emitted over is
The photon number curve and the power spectrum curve intersect at the critical energy
where ,E is the total energy of the charged particle, is the
radius of curvature, the
classical electron radius, the particle rest mass energy, the reduced
Planck constant and the speed of light.
The mean of the quantum energy is given by and impact mainly the
radiation damping. However, the particle motion perturbation (diffusion) is mainly related by the variance of the quantum energy and leads to an equilibrium
emittance. The diffusion coefficient at a given position is given by
-
[3]
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.
[2]
References