Wide energy bandwidth superconducting accelerating cavities

Superconducting cavities have been widely used in high intensity proton accelerators. In this paper, we discuss parameters that affect energy bandwidth of the accelerating cavity and propose a new energy averaged transit time factor to help choose transition energy between different sections and cavity geometry parameters in the linac design. These wide energy bandwidth superconducting cavities can potentially be used to accelerate a proton beam multiple times. A time-pass condition is defined to attain fixed RF phases during multiple passes of the beam. Such a superconducting recirculating proton linac could significantly reduce the number of RF cavities in the accelerator and lower construction and operational costs of the facility.