Pi-mode structures - results and implications for operation

Pi-mode structures are the type chosen for high-energy synchrotrons and for medium- and high-beta accelerating superconducting structures. A coupled-circuit analysis, allowing for errors in cell frequencies and cell coupling constants, has been used to determine relative on-axis fields between cells, operating frequencies, end-cell tuning, relative on-axis field phase shifts and field tilts when operated off resonance. Formulae are given for the above information as well as specific examples to show sensitivities and machining/assembly/control tolerances.