  We consider the interaction between a particle beam and a propagating
electromagnetic wave in the presence of a metamaterial. We show that the
introduction of a metamaterial gives rise to a novel dispersion curve which
determines a unique wave particle relationship, via the frequency dependence of
the metamaterial and the novel ability of metamaterials to exhibit simultaneous
negative permittivity and permeability. Using a modified form of Madey's
theorem we find that the novel dispersion of the metamaterial leads to a
amplification of the EM wave power.
