Radiation into transverse electric modes of rectangular waveguides from spatiotemporally modulated gyrating electron beams.

Abstract

A previously published analysis [J. L. Hirshfield, Phys. Rev. A 44, 6845 (1991)] of the first-order transfer of power into fields of a ${\mathrm{TE}}_{0\mathit{m}}$ rectangular waveguide from a relativistic electron beam carrying spatiotemporal modulation is extended to ${\mathrm{TE}}_{\mathit{l}\mathit{m}}$ modes. Non-axis-encircling orbits, circularly polarized excitations, and competing modes are incorporated into the expanded analysis. Selection rules and phase-matching conditions are found that govern the power transfer; these are shown to allow wave power to increase quadratically with both the interaction length and the dc beam current. Examples of fifth-harmonic conversion are presented for both ${\mathrm{TE}}_{32}$ and ${\mathrm{TE}}_{03}$ modes, the latter in a square waveguide supporting a circularly polarized wave. Power levels of 100 kW or more at 94 GHz appear to be achievable in a conceptual fifth-harmonic device using a 200-kV, 1-A beam. The circularly polarized mode appears to be relatively free of mode competition. Devices with lower beam energies are also shown to be capable of fifth-harmonic operation at 94 GHz, albeit with lower output power than for devices with higher beam energies.