The analysis of the electric field and the dispersion relationship of a folded waveguide traveling wave tube using the Fourier transform

Abstract

We are developing an analytical model for determining the dispersion curve of the folded waveguide traveling wave tube (FWTWT). A typical variation of the electric field at a particular time, shows that the electric field is a discontinuous rather than a continuous function, which would appear to make analyzing the waveform difficult mathematically. However the electric field can be thought of as being built up by a continuous sinusoidal wave, which is first sampled at the center of each gap, with every other sample value being flipped in sign to allow for the folding effect. These sample values are then convolved with a single rectangular pulse shape, which produces the required overall electric field variation. The Fourier transform method has been used to evaluate the spatial harmonics contents of the electric field along the interaction gaps axis of the FWTWT. The results show that the dispersion relationship of the electric field experienced by the electrons, is multi-valued, having many wavenumber values for a given operating frequency.