Cherenkov amplification of guided graphene surface plasmons by a relativistic electron beam

We investigate Cherenkov-resonant amplification of guided terahertz graphene surface plasmons in a graphene parallel-plate waveguide driven by a relativistic electron beam. The structure consists of two graphene-coated dielectric interfaces separated by a micrometer-scale air gap supporting a strongly confined symmetric plasmon mode with reduced phase velocity. When the electron-beam velocity satisfies the Cherenkov synchronism condition, efficient phase-matched energy transfer gives rise to beam-driven instability and growth of the guided plasmon mode. A self-consistent analytical model is developed to describe the coupled beam–plasmon dispersion, mode confinement, and instability growth as functions of the waveguide geometry and beam parameters. The results show that subwavelength confinement enhances the beam–plasmon interaction, enabling efficient terahertz plasmon excitation and providing favorable conditions for amplification at moderate beam energies accessible with compact electron sources. Unlike Smith–Purcell radiation and electron-energy-loss excitation of graphene plasmons, which predominantly produce spontaneous emission, the proposed scheme exploits coherent beam–plasmon interaction within a compact graphene waveguide. The analysis establishes a theoretical framework for beam-driven graphene plasmonics and provides a promising route toward compact, tunable on-chip terahertz plasmonic amplifiers and coherent radiation sources.