  We present the electromagnetic design study of a multi cell, \beta_g= 0.9,
650 MHz elliptic superconducting radiofrequency cavity, which can be used for
accelerating 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 that we describe in the 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 break up instability due to dipole modes has been estimated. Lorentz force
detuning 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 Lorentz force detuning.
