Introduction

We consider the radiation emitted by a charged particle moving with constant, relativistic velocity on a circular arc. It is called synchrotron radiation, or sometimes also ordinary synchrotron radiation, abbreviated as SR, to distinguish it from the related case of undulator radiation, abbreviated as UR. We start with a qualitative discussion of synchrotron radiation in order to obtain some insight into its physical properties such as the opening angle, spectrum, and polarization. This will also help us to judge the validity of some approximations used in later calculations.

The physical properties of synchrotron radiation have their basis in the fact that the charge moves with relativistic velocity towards the observer. The charge and the emitted radiation travel with comparable velocities in about the same direction. The fields created by the charge over a relatively long time are received by the observer within a much shorter time interval. This time compression determines the spectrum of synchrotron radiation.

The opening angle

We consider a charge moving in the laboratory frame F on a circular trajectory with radius of curvature ρ, Fig. 1.1. We go into a frame F′ that moves with a constant velocity that is the same as that of the charge at the instant it traverses the origin.