Self-consistent renormalized phonons in metallic and nonmetallic solids

The interaction of charged particle beam with non-linear “cubic” type media has been studied; the dielectric permeability of such media depends on the square strength of the electric field produced by the beam-excited wave. The processes of the Cherenkov excitation of the medium by a modulated definite current are investigated as well as the polarization of longitudinal oscillations of the medium excited by the current. The equations are obtained to determine the dependence of fields excited by the current on the amplitude of the exciting current. It is found that under certain circumstances (near the radiation cut-off) the conditions of Cherenkov radiation may be violated due to non-linearities of the medium and the particle radiation loss vanish. The amplification of longitudinal waves in an arbitrary isotropic medium with “cubic” non-linearity by a monoenergetic particle beam is studied when the frequencies of amplified oscillations are close to the resonance frequencies of the medium.