Synchrotron radiation occurs when a charge moving at
relativistic speeds follows a curved trajectory. In this
section, formulas and supporting graphs are used to
quantitatively describe characteristics of this radiation for
the cases of circular motion (bending magnets) and sinusoidal
motion (periodic magnetic structures). We will first discuss the
ideal case, where the effects due to the angular divergence and
the finite size of the electron beam—the emittance effects—can
be neglected. The angular distribution of radiation emitted by
electrons moving through a bending magnet with a circular
trajectory in the horizontal plane is given by ŠB = photon flux
(number of photons per second) q = observation angle in the
horizontal plane y = observation angle in the vertical plane a =
fine-structure constant g = electron energy/mec2 (me = electron
mass, c = velocity of light) w = angular frequency of photon (e
= Ów = energy of photon) I = beam current e = electron charge =
1.602 ´ 10–19 coulomb y = w/wc = e/ec wc = c