A Simple Derivation of the Long Wavelength Edge Radiation from a Bending Magnet

A simple derivation of the “edge radiation” emitted by an electron beam going through a bending magnet in the directions of its entrance and exit from the magnet itself is presented. This radiation is characterized by wavelengths much longer than the synchrotron radiation critical wavelength in the same magnet. The far field radiation emitted by an electron following a curved trajectory inside a finite bending magnet can be approximated with any required accuracy by that produced by an electron following a segmented trajectory made of straight lines with sudden change of the velocity direction. The radiation field amplitude produced by a velocity direction change is that of a “prompt” bremsstrahlung in which the velocity module remains constant. The total amplitude is the sum of all the bremsstrahlung amplitudes with their relative phase difference. For long wavelengths and around the direction of entrance or exit from the magnet, only few terms are required to give a good description of the radiation as compared with exact calculations