Quantum excitation (accelerator physics)

An electron moving through a magnetic field emits 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 spectrum of a bending magnet is given by

${\displaystyle S(\xi )={\frac {9{\sqrt {3}}}{8\pi }}\xi \int _{0}^{\infty }K_{5/3}({\bar {\xi }})d{\bar {\xi }}}$

The diffusion coefficient is given by

${\displaystyle d={\dot {N}}\langle u^{2}\rangle }$

The result is

${\displaystyle d={\frac {55}{24{\sqrt {3}}}}\alpha {\frac {\hbar }{mc}}{\frac {\gamma ^{5}}{|\rho |^{3}}}}$

For an early analysis of the effect of quantum excitation on electron beam dynamics in storage rings, see the article by Matt Sands.[1]