Frequency sensitivity of the passive third harmonic superconducting cavity for SSRF

A 1.5 GHz passive third harmonic superconducting cavity was proposed to improve the beam quality and lifetime in the Shanghai Synchrotron Radiation Facility Phase-II beamline project. Lifetime improvement highly depends on the resonant frequency of the passive third harmonic superconducting cavity. It is important that the operating frequency of the cavity is within the design range and the cavity has reasonable mechanical stability. A simulation method for the multiphysics coupled analysis has been developed based on the ANSYS code. Multiphysics coupled simulations have been performed under different conditions, such as etching, evacuation, cooling, and preloading. Analyses of mechanical modes and structural stress have been executed. A possible stiffening ring method for the two-cell superconducting niobium cavity has been investigated. In this paper, we present a multiphysics coupled analysis of the third harmonic cavity using a finite element analysis code. The results of the analysis show that a reliable frequency for the cavity after electron beam welding is 1498.033 MHz, and the corresponding frequency of the pre-tuning goal is 1496.163 MHz. A naked cavity is a reasonable option based on structural stress and mechanical modal analyses. A frequency range of +/- 500 kHz and limiting tolerable displacement of +/- 0.35 mm are proposed for the design of the frequency tuner.