Evaluation of vortex fields in a non-linear slow-wave structure. II. The method of complex amplitudes

The method of complex amplitudes is suitable for spectral simulation of microwave tubes if RF signals are narrow-band. It based on quasi-continuous approximation of a delay line and interpretation of a vortex field as a wave with slowly varying in temporal t and longitudinal z directions parameters. The RF field is evaluated as product of a narrow-band complex envelope A(t,z), a fast harmonic carrier at base frequency ω_b and propagation factor β_b exp(iω_bt-iβ_bz) and a wave field unit structural function E_0ω(x,y,z).