Cherenkov radiation by an electron bunch that moves in a vacuum above a left-handed material

Cherenkov radiation by a nonrelativistic electron bunch that moves above an interface of a vacuum-left-handed material has been investigated theoretically. The electron density of the bunch is described by a Gauss distribution. Cherenkov radiation for the frequency range where the refractive index is negative is shown to lead to simultaneous excitation of both bulk and surface electromagnetic waves over one and the same frequency range. In this case the wave vector magnitude in the plane of the interface of surface electromagnetic waves is larger than the corresponding wave vector magnitude of bulk electromagnetic waves. The energy flows in a left-handed material have been calculated. The spectral density and the radiation pattern have been investigated.