Concise expression of a classical radiation spectrum.

Abstract

In this paper we present a concise expression of the classical electromagnetic radiation spectrum of a moving charge. It is shown to be equivalent to the often used and much more complicated form derived from the Lienard-Wiechert potentials when the observation distance R satisfies the condition R\ensuremath{\gg}\ensuremath{\gamma}\ensuremath{\lambda}. The expression reveals a relationship between the radiation spectrum and the motion of the radiation source. It also forms the basis of an efficient computing approach, which is of practical value in numerical calculations of the spectral output of accelerated charges. The advantages of this approach for analytical and numerical applications are discussed and the bending-magnet synchrotron radiation spectrum is calculated according to the approach.