Wave Energy Amplification in a Metamaterial based Traveling Wave Structure

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