Reduced Order Models for Beam-Wave Interaction in High Power Microwave Sources

Abstract

We apply an asymptotic analysis to show that corrugated waveguides can be represented as cylindrical waveguides with smooth metamaterial coatings when the corrugtions are subwavelength. Here the metamaterial delivers an effective anisotropic surface impedance, effective dielectric constant, and imparts novel dispersive effects on signals traveling inside the waveguide. These properties arise from the subwavelength resonances of the metamaterial. For sufficiently deep corrugations, the waveguide exhibits backward wave propagation, which can be understood in the present context as a multi-scale phenomenon resulting from local resonances inside the subwavelength geometry. Our approach is well suited to numerical computation and we provide a systematic investigation of the effect of corrugation geometry on wave dispersion, group velocity, power flow, and gain factor per period.