The radiation of electromagnetic waves and the instability of electrons moving at super-light velocity in a medium

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Abstract
The features of the radiation of electromagnetic waves by particles or systems (atoms, molecules, etc.) moving in a medium or near a medium (the moderating system) at super-light velocity can often be successfully analysed by applying quantum considerations, even when the problem is a classical one. This is also the case for the radiation, absorption and amplification of waves in beams of particles, and for the study of their instability. We shall discuss questions of this kind in this paper, including the problem of the classical force of reaction of the radiation when a charge moves in a medium. Our basic result, which follows from both simple quantum considerations and classical calculations, is as follows: when the motion is at super-light velocity, the radiation reaction force which changes the amplitude of oscillation of a particle decreases, and in some cases even changes sign, i.e. responds to the building up of oscillations and not to ‘friction’. In accordance with this fact, when beams of particles are moving in a medium at super-light velocity they become unstable, and the electromagnetic waves are amplified.