One of the conditions for distributed beam-wave interaction to occur is phase velocity smaller than c. It is possible to satisfy this condition by loading the waveguide with a dielectric material, however the problem with dielectrics is that they are susceptible to breakdown at relatively low electric fields therefore it is difficult to generate high power microwave radiation with regular materials. Another difficulty is the electric charge which accumulates on the surface and must be drained for adequate operation. Consequently, in many microwave sources metallic structures with periodic boundary are preferred as the central component which facilitates the interaction. The periodic geometry can be conceived as a set of obstacles delaying the propagation of the wave due to the multi-reflection process and, as will be shown during our discussion on Floquet’s theorem, an infinite spectrum of spatial harmonics develops. A few of these harmonics may propagate with a phase velocity larger or equal to c but the absolute majority have a smaller phase velocity.
KeywordsDispersion Relation Phase Velocity Periodic Structure Spatial Harmonic Magnetic Vector Potential
Unable to display preview. Download preview PDF.