The Higher Order Modes Calculation of RF Cavity with Finite Element Method

A previous paper has presented to calculate not only the fundamental and longitudical modes but also the transverse higher modes of RF cavity. But with this method higher modes are calculated one by one. In this paper we present a finite element method using triangulated elements, six points quadratic interpolation for improvement. At first, we obtain a tridiagonal coefficient matrix with the Householder method, then calculate its eigenvalues using half-divided method. With this method we can calculate any order eigenvalues(and resonant frequency values) and the responding eigenvectors (and field distribution) of a mode group simultaneously at one time. This method is convenient, accurate and economical for computing time.