Coupling impedance structure above the tube cut-off frequency

Previous studies of the equations for the beam induced electromagnetic fields, which occur when a smooth vacuum chamber is disturbed by a periodic sequence of double discontinuities, are extended. From these equations the coupling impedance of the beam to these cavity-like discontinuities is obtained directly. A method is proposed for handling the equations in the microwave region (above the cutoff frequency for chamber propagation). It is shown how field singularities develop as the cutoff frequency is crossed. In fact for a single cutoff mode, the lowest being the TM01 mode, many resonances arise with a close but regular spacing in frequency. Their high multiplicity and close spacing give these tube resonances a quality very different from the 'normal' cavity resonances. Resistive loading leads to a decrease in the resonant impedance with the resulting resonance width being very narrow. The resonant coupling impedance is studied in detail as a function of frequency including the parametric dependence on the cavity dimensions, the ring and tube radii, and the resistive loading of the cavity. In addition to demonstrating clearly these tube resonances the mathematical procedure developed here can be used to study the frequency dependence of the induced fields and the corresponding coupling impedance in general. (Auth.)