Interaction a tube beam of charged particles with a dispersive medium of cylindrical configuration

The interaction between a tubular beam of charged particles and a dispersive medium of cylindrical configuration has been investigated. This medium may have negative permittivity and negative permeability simultaneously over a certain frequency range. The dispersion equation for the eigenmodes spectra of a medium and the coupled modes spectra of the system have been derived and numerically analyzed. It has been found that the absolute beam instability of bulk-surface waves occurs because of peculiarities of the eigenmodes spectra of a left-handed metamaterial. The resonant frequency behavior of the permeability causes the emergence of the sections of dispersion curves with anomalous dispersion. The obtained results allow us to propose the left-handed metamaterial as the delaying medium in oscillators of electromagnetic radiation without a need to provide an additional feedback in the system.