ABSTRACT
In previous chapters we have considered the emission of radiation by nonrelativistic moving particles. In particular, we determined the Stokes parameters for particles moving in linear or curvilinear paths. In this chapter we reconsider these problems in the relativistic regime. It is customary to describe the velocity of the charge relative to the speed of light using the ratio defined by the parameter β = v/c. (Note that we will be using this ratio in vector and magnitude form, i.e., β = |β| = |v|/c = v/c, where appropriate.)
For a linearly oscillating charge we saw that the emitted radiation was linearly polarized and its intensity dependence varied as sin2 θ. This result was derived for the nonrelativistic regime (|β| << 1). We now consider the same problem, using the relativistic form of the radiation field. Before we can do this, however, we must first show that for the relativistic regime (|β| ∼ 1) the radiation field continues to consist only of transverse components, Eθ and Eφ, and the radial or longitudinal electric component Er is zero. If this is true, then we can continue to use the same definition of the Stokes parameters for a spherical radiation field.
