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The RF design of a 325MHz {\beta}=0.37 superconducting double spoke cavity for China ADS has been finished. In this paper, the optimization of the spoke cavity is described in detail. The main goal in the RF design is to decrease the normalized surface field. We use the elliptic column instead of cylinder to decrease the normalized magnetic field. The RF simulation gives the optimum parameters Ep/Eacc of 4.39 and Bp/Eacc of 7.15mT/(MV/m), which meet the requirement of C-ADS.

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