Waves in Warm Constant-Density Cylindrical Electron Beams

A dispersion equation is derived for waves in a warm constant-density cylindrical electron beam where electrons exhibit 3-D orbits in a uniform magnetic field and where the rigid-rotor beam model has transverse temperatures confined to the beam interior to provide a cold sharp beam edge suitable for matching RF fields. The equation solutions for surface waves in a warm beam emitted from a magnetically shielded gun can be obtained immediately from solutions for surface waves in a cold beam. Validation of such warm-beam solutions was made using TWT hot-test data and particle-in-cell-code simulations. Standard transcendental-equation solutions are found for surface waves in warm small-vorticity beams and space-charge waves in warm large-vorticity beams. Reduced plasma frequencies are increased for surface waves and decreased for space-charge waves by increasing the transverse-temperature thermal parameter. Beam temperatures were included in a Pierce-theory determinantal equation in the small-transverse-wavenumber limit.