Trapped modes in waveguides with many small discontinuities.

Abstract

It has been demonstrated recently [G. V. Stupakov and S. S. Kurennoy, Phys. Rev. E 49, 794 (1994)] that a single small discontinuity (such as an enlargement or a hole) on a smooth waveguide can result in the appearance of trapped electromagnetic modes with frequencies slightly below the waveguide cutoff frequencies. The present paper studies a similar phenomenon for a waveguide with many small discontinuities, which is a good model for the vacuum chamber of large accelerators. Frequencies of trapped modes and their contributions to the coupling impedance are calculated. The frequencies for the cases of a few discontinuities or a periodic structure coincide well with those from numerical simulations. The trapped modes produce sharp resonance peaks of the coupling impedance near the cutoff frequencies. The magnitude of these peaks, as well as the existence itself of a trapped mode, strongly depends on the distribution of discontinuities, or on the distance between them if a regular array is considered. The impedance in the extreme case can be as large as ${\mathit{N}}^{3}$ times that for a single discontinuity, where N is the number of discontinuities.