2 - Fields of a moving charge

Summary

Introduction

In the previous chapter we used some qualitative arguments to estimate the basic nature of synchrotron radiation. The results of this exercise are very useful for understanding the underlying physics, estimating the quantities involved, and judging the validity of certain approximations we will make. Now synchrotron radiation is treated in a quantitative manner. We will distinguish between the time t at which the radiation is observed and t′ when it was created by the moving charge at a distance r. Since the relation between the two is in general rather complicated, some of the derivations are lengthy. As final results we obtain expressions for the radiation field and the emitted power, which will be applied to calculate synchrotron and undulator radiation in the next two parts. Treatments of synchrotron radiation can be found in many books, journal publications, articles, proceedings of conferences and workshops, and laboratory reports. The first book on the topic of synchrotron radiation [3] was published in 1912. Complete coverage of the topic is presented in [4–8], some of which give also a quantum-mechanical treatment. Many books on electrodynamics treat the radiation from relativistic particles and cover also theoretical aspects of synchrotron radiation [9–13].