Beam Transport and Beam-Current Loss in Emittance-Dominated High-Frequency Tubes

Emittance effects are becoming increasingly important in high-frequency electron devices, especially in recent and proposed high-frequency traveling wave tubes and klystrons. The ratio of beam radius to the beam pipe, typically referred to as “fill factor,” is a critical parameter for high-frequency tubes. Fill factors, typical of lower frequency tubes, such as 0.5–0.8, can lead to significant beam current loss in high-frequency tubes when transported over long distances in the beam pipe because the beam in such tubes is more subject to emittance effects. The increased beam loss, in turn, leads to large dissipation of beam power at the RF circuit, damaging the circuit itself and limiting tube’s duty cycle. Traditionally, the beam emittance has been largely studied and measured in linear accelerators (linacs) where emittance effects are larger than space-charge effects at high beam energy. In this paper, we apply the beam physics developed for linacs to high-frequency tubes for the first time. We provide necessary theoretical tools to determine the fundamental limit of the beam pipe sizes for a desired limit of beam interception. Specifically, the effect of both space charge and emittance is incorporated into iterative solution of equilibrium distributions of charge densities in the presence of a uniform focusing axial magnetic field. The numerical solutions and tools provided here can be used to determine the beam pipe size for any beam emittance. The theoretical formulation and results are expected to be particularly useful for devices operating from mm-wave to subterahertz frequency regimes.