Electromagnetic Design of a $\beta_{g} = 0.9$ 650-MHz Superconducting-Radio-Frequency Cavity

We present the electromagnetic design study of a multicell
$\beta_{g} = 0.9$
650-MHz elliptic superconducting-radio-frequency cavity, which can be used for accelerating
$\hbox{H}^{-}$
particles in the linear accelerator part of a spallation neutron source. The design has been optimized for maximum achievable acceleration gradient by varying the geometry parameters of the cavity, for which a simple and general procedure is evolved which we describe in this paper. For the optimized geometry, we have studied the higher order modes supported by the cavity, and the threshold current for the excitation of the regenerative beam breakup instability due to dipole modes has been estimated. Lorentz force detuning (LFD) studies have also been performed for the optimized design, and the calculations are presented to find the optimum location of the stiffener ring to compensate for the LFD.