Perturbation Analysis of Maxwell's Equations

In this chapter, the authors present a perturbation analysis of Maxwell's equations to describe the interaction of an electron beam with a metamaterial a slow wave structure. They apply a two‐scale perturbation analysis to the Maxwell system used to model beam wave interaction inside the infinitely long amplifier. The authors model a finite‐size traveling wave tube amplifier (TWTA) loaded with an effective dielectric as a short Cherenkov system comprised of three components: a feeding waveguide, a finite length TWTA region, and an output waveguide. They consider grounded beam wave interaction structures made by deep corrugations on the surface of the waveguide. The authors investigate rectangular corrugation profiles as well as sawtooth, sinusoidal, and infinitely thin rib profiles. The electrodynamics for the short traveling wave tube (TWT) is modeled within the transmission line approximation. The support structure itself can affect TWT performance, introducing multiple hybrid modes and shifting the frequency of operation.