Analog analysis ofπ-mode structures: Results and implications

Abstract

The cavities of choice for high-energy synchrotrons and for medium-beta and high-beta accelerating superconducting structures around the world are p-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.

CLUSTER: A high-frequency H-mode coupled cavity linac for low and medium energies

“…The numerical value of L E is chosen in order to reproduce the right field modulation, with the same amplitude in each gap. In agreement with [30], one obtains L E = 2L 1 . On the other hand, a suitable scheme for the coupling cell is a mutual inductance.…”

One-step tuning algorithm forπ-mode cavities

“…III C of Ref. [1] showed that dimensional tolerances were a factor of 10 smaller for frequency requirements than for coupling constant requirements. Since frequency tolerances are much more stringent, it is assumed that relative field errors in a cavity are mainly related to frequency errors.…”

“…Terminology and information developed in Ref. [1] are used extensively in the following discussion. Equation development [1] for relative fields in a p-mode cavity made it possible to determine methods for evaluating fields in a cavity with errors and for the actions required to make fields as equal as possible cell-to-cell.…”

“…[1] are used extensively in the following discussion. Equation development [1] for relative fields in a p-mode cavity made it possible to determine methods for evaluating fields in a cavity with errors and for the actions required to make fields as equal as possible cell-to-cell. Solving for relative fields using a stepwise method and determination of the p-mode frequency correction factor a were two significant steps making it possible to develop the theory for a one-step tuning algorithm that achieves flat fields in a p-mode cavity.…”

“…(4) of Ref. [1] is simplified by eliminating terms whose effects are less than several percent of the main correction term. Using the absolute value for the cell field amplitude expression (taking into account cell frequency errors) gives…”