Cavity height dependence of the longitudinal impedance for a pillbox cavity at high frequency

The longitudinal coupling impedance for a cylindrically symmetric structure which consists of a pillbox connected to a beam pipe was previously studied by Gluckstern using an integral equation method. The solution of the integral equation was found to be independent of the outer cavity radius b for 2k(b - a)2/g >> 1, where the frequency is kc, the pipe radius is a, and the cavity length is g. In this paper, the requirement 2k(b - a)2/g >> 1 is relaxed, yielding a more general expression for the impedance for a pillbox with dependence on (b - a). In addition, it is shown that the analytic results agree well with the numerical data obtained using the scheme where the fields are matched in the transverse planes at the beginning and end of the pillbox. (author). 5 refs., 2 figs