Theory of high-harmonic rectangular gyrotron for TEmnmodes

In this paper, the linearized relativistic Vlasov equation is solved and a dispersion relation is calculated for the interaction between a relativistic electron beam and the electromagnetic fields of a rectangular waveguide supporting TE
mn
modes. The dispersion relation is simplified to the special case of a frame of reference moving with the electrons and the resulting coupling coefficient
\epsilon\min{mn}\max{l}
is calculated for various TE
mn
modes. The dependence of
\epsilon\min{mn}\max{l}
on the parity of the harmonic number l and various mn modes of the waveguide are discussed.