Thermal axisymmetric waves in vortex-free beams from diodes and tetrodes

Summary form only given. A dispersion equation is being evaluated for axisymmetric waves in mildly warm vortex-free beams. Such beams are emitted from shielded cathodes found in diodes and tetrode type guns of W-band TWTs where cathode half-angles are small and grid scattering is absent or not significant. Such uniform-temperature beams can feature a bell-shaped density profile which is a transition stage between a hot-beam Gaussian profile and a cold-beam constant-density profile. Such bell-shaped density-profile beams can be approximated by warm, constant-density beam models for which a dispersion equation has been derived [1]. For the vortex-free beam, thermal components disappear from the transverse wavenumber and provide a dispersion equation that is like that for a zero-temperature beam. As a result, dispersion solutions for such warm beams can be obtained from T=0 surface-wave dispersion solutions by using alternate interpretations of the variables. The T Φ 0 solutions improve upon T = 0 solutions by predicting larger plasma-frequency reduction factors with increasing beam temperature. For example, based on test data previously presented for a W-band high-average-power TWT [2], the reduced plasma frequency at the synchronous frequency βP/π = 1.37 is roughly twice that calculated from zero-temperature theory. Figure 1 shows how, by including temperatures, dispersion solutions can increase the reduced plasma frequencies to be more consistent with test data.