Analog analysis of π-mode structures: Results and implications

The cavities of choice for high-energy synchrotrons and for medium-beta and high-beta accelerating superconducting structures around the world are π-mode structures. A coupled-circuit analysis, allowing for errors in cell frequencies and cell coupling constants, has been used to determine relative on-axis electric field amplitudes between cells, operating frequencies, end-cell tuning, relative on-axis field phase shifts, and field tilts when operated off resonance. Formulas are given for the above information as well as specific examples showing sensitivities and machining/assembly/control tolerances. A method to determine relative field amplitudes on the basis of the mode spectra was developed.