Analytical study of higher order modes of elliptical cavities using oblate spheroidal eigenvalue solution

The oblate spheroidal shape is close to the commonly used elliptical rf cavity shape employed in accelerators. Here we solve the oblate spheroidal radial and angular wave functions to obtain the frequencies of the axisymmetric TM and TE modes. We develop a semianalytic formalism to calculate the characteristic parameters, such as shunt impedance, of higher order modes (HOMs). Our formulation is applied to calculate the HOM frequencies of the INDUS-2 and ILC cavities, and the agreement with three-dimensional finite element calculations is excellent. Using this formalism we investigate the effect of changing the oblate shape, and predict an optimized range of � 0 (one of the key parameters to define the geometry), to reduce the number of significant HOMs.