Chapter IV - RADIATION OF A MOVING PARTICLE

Abstract

This chapter discusses motion and radiation in an ondulator. It describes motion in a magnetic field. The chapter presents the radiation reaction and the limits of applicability of the classical theory. It explains radiative losses when charged particles move in a magnetic field. The radiation of a nonrelativistic particle (v « c) differs very appreciably and even in a qualitative manner from that of relativistic particles. If a charged particle moves in vacuo , it emits radiation only when it is accelerated and in the nonrelativistic case, when the velocity v«c = 3×10 10 cm/s, the radiation has most often a dipole character. Quadrupole radiation is usually important only if the dipole moment of the system is zero or anomalously small. The radiation when a charge executes a nonrelativistic circular motion in a magnetic field is the same as for two mutually perpendicular harmonic oscillators, which are shifted in phase by ½ π or which is the same for a constant electric dipole with dipole moment er H at right angles to the magnetic field, rotating with a frequency ω H . In the relativistic case, the radiation is mainly in the forward direction, in the direction of the velocity. The recoil, or reaction, must be in the backward direction as directed radiation carries momentum.