Vavilov-Cherenkov Effect and "Bohr Radiation" Produced by a Beam of Charged Particles in a Dispersive Medium

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Abstract
An electron beam interacting with a dispersive (atomic or molecular) medium produces two intense sources of instability that are represented by a growing longitudinal wave and a growing transverse wave. The longitudinal wave has frequencies that are equal to the atomic binding frequencies of the surrounding medium and is designated as the "Bohr wave." The transverse wave has frequencies determined by the Vavilov-Cherenkov criterion and is similar to the Vavilov-Cherenkov wave produced by a single particle interacting with the medium. These sources of instability are "continued" into lower frequency ranges in which they produce growing waves of a "hybrid" type that are characterized by an electric vector having both longitudinal and transverse components. The longitudinal and transverse waves represent the "fundamental modes" that exist in the medium in the absence of the beam. The perturbation produced by the beam is responsible for the instability of the fundamental modes and for the occurrence of the coupling between these modes. The coupling produces electromagnetic waves in which the electric field has a longitudinal component. The conditions for coupling and the character of the instabilities are investigated.