In cylindrically symmetric accelerator cavities equipped with higher order mode (HOM) couplers, the two polarizations of each deflecting mode are often fixed by the couplers themselves, leaving one polarization inadequately damped. This problem can be overcome by deliberate breaking of the cell's cylindrical symmetry. We describe a quasi-cylindrical cavity profile in which the polarization of the dipole, quadrupole, and sextupole HOM's are fixed at ±¿/4, ±¿/8, ±¿/12 with respect to the intended coupler orientation, providing a maximally favorable situation for damping by a single coupler. A single cell S-band cavity was built to test the practicality of our design. The experimental data, in the range 3-7 GHz, conclusively shows that the mode polarizations can be controlled with only minor perturbations to the cell's cylindrical symmetry.
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