Abstract
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 ${\ensuremath{\xi}}_{0}$ (one of the key parameters to define the geometry), to reduce the number of significant HOMs.
Highlights
The solution for the eigenfrequencies of any rf cavity depends on its boundary shape
Our formulation is applied to calculate the higher order modes (HOMs) 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, to reduce the number of significant HOMs
Shaped rf cavities have been modeled as oblate spheroids, to obtain the analytical solutions of HOMs and related parameters in order to study the effect of the cavity geometry on HOMs
Summary
The solution for the eigenfrequencies of any rf cavity depends on its boundary shape. In -mode structures the cavity gap is =2, where is the ratio of particle velocity to the velocity of light and is the wavelength of the cavity resonating frequency Such elliptical shaped cavities resemble the spheroidal oblate shape, where it is possible to obtain the analytical solution by solving the wave equation in spheroidal coordinates. Zhang and Jin [13] have provided FORTRAN programs for accurate calculation of these functions These solutions have been used for applications such as wave propagation using antennas [5,14] and fluid dynamics [15], and have not yet been used to obtain the eigenfrequencies of oblate spheroidal shapes with large eccentricity. We find that deviations in the higher-order mode frequencies are within 5%–10%, which gives us confidence in the usefulness of our analytic approach
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