Chapter VII - CHERENKOV EFFECT, DOPPLER EFFECT, TRANSITION RADIATION

Abstract

This chapter provides an overview of Cherenkov and Doppler effect. It describes Cherenkov emission and absorption in an isotropic and magneto-active plasma. The chapter discusses the transition radiation and application of the reciprocity theorem. The momentum of a photon in a medium is its total momentum, including both the field momentum and the momentum imparted to the medium in the emission of the wave. From a quantal point of view, the kinematics of the emission, that is, the conditions imposed upon the frequency and the direction of the emission, are determined by the energy and momentum conservation laws. For a wavepacket, consisting of wave-functions with different but approximately equal energies, the centre of mass of the packet in the energy scale diminishes. The difference between subluminal and superluminal motions lies in the rate at which the average energy changes and also in the nature of the spreading of the packet. The role of the system, which emits anomalous Doppler waves, can be played by electrons oscillating as a result from being acted upon by an applied field or moving along a helical path along a magnetic field, which is parallel to the axis of the beam. Cherenkov and Doppler effect from the quantal point of view. Radiation reaction in a medium. Cherenkov emission and absorption in an isotropic and magneto-active plasma. Cherenkov emission by dipoles. Emission in channels and gaps. Application of the reciprocity theorem. Transition radiation. † † Except for the part dealing with transition radiation we follow in the present chapter an earlier review paper ( Ginzburg, 1960 ). In the Russian literature the Cherenkov effect is called the Vavilov-Cherenkov effect.