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We present the theory of a new amplification regime in Travelling Wave Tubes(TWTs) composed of a slow-wave periodic structure that supports multipleelectromagnetic modes that can all be synchronized with the electron beam. Theinteraction between the multimodal slow-wave structure and the electron beam isquantified using a Multi Transmission Line approach (MTL) based on ageneralized Pierce model and transfer matrix analysis leading to theidentification of modes with complex Bloch wavenumber. In particular, weaddress a new possible operation condition for TWTs based on the supersynchronism between an electron beam and four modes exhibiting a degeneracycondition near a band edge of the periodic slowwave MTL. We show aphenomenological change in the band structure of periodic MTL where we observeat least two growing modal cooperating solutions as opposed to a uniform MTLinteracting with an electron beam where there is rigorously only one growingmodal solution. We discuss the advantage of using such a degeneracy conditionin TWTs that leads to larger gain conditions in amplifier regimes and also tovery lowstarting beam current in high power oscillators.

Theory and New Amplification Regime in Periodic Multi Modal Slow Wave Structures with Degeneracy Interacting with an Electron Beam