There is an increasing demand for High Beam Current, High Radio-Frequency (RF) power S-band cavities in existing and new accelerator projects to produce a very brilliant, broadband, terahertz coherent synchrotron radiation source (CRS). The MIT/Bates South Hall Ring at the MIT/Bates Accelerator Center operating with a 2.856 GHz RF system is ideally suited to investigate in more depth the technical problems of the beam dynamic issues and the high circulating beam operation for a stable CRS operation. To achieve this goal, the RF cavities must be upgraded to a gap voltage of 1.5 MV in the limited space available in the machine, and this can be only achieved with a high gradient superconducting cavity.? An innovative approach was required because, at the present time there are no cavities and accessories designed to support the high beam currents of up to 100 mA and at the same time provide a high gap voltage at high frequency. In this Phase-I project, AMAC performed the calculations and optimization to determine the parameters to meet the requirements for the superconducting cavity, provided two alternate designs for the RF input couplers, performed a detailed Higher Order Modes (HOM) analysis, and proposed an HOM absorber concept to dampen the modes exited in the cavity due to the high beam current and high bunch intensity.