Alexander Figotin, Guillermo Reyes
We advance here the Pierce theory of travelling wave tubes by constructing a Lagrangian for a multi-transmission-line coupled to the electron beam (MTLB system). This theory yields in particular (i) the Euler-Lagrange equations governing the dynamics of the MLTB system, and (ii) exact expressions for the conserved energy and its flux distributions obtained from the Noether theorem. We identify in the Lagrangian a specific term associated with beam which is the origin of the mathematical mechanisms of amplification and the energy transfer from the beam to microwave radiation.
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http://arxiv.org/abs/1304.5397
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