Unavoidable trapped mode in the interaction region of colliding beams

We discuss the nature of the electromagnetic fields excited by the beams in the beam pipe of an interaction region. In trying to find an optimum geometry for this region with a minimum of electromagnetic wave excitation, we have discovered one mode, which remains even in a very smooth geometry. This mode has a longitudinal electrical component and can be easily excited by the beam. By analyzing the structure of this mode we have found a way to absorb this mode. The work was done in connection with a proposal for a future electron-positron collider.