Analysis of the Longitudinal Coupling Impedance of a Rectangular Slot in a Thin Coaxial Liner

As previously discussed [Fedotov and Gluckstern, Phys. Rev. E 54, 1930 (1996)], for a long narrow slot whose length may be comparable with the wavelength, the usual static approximation for the polarizability and susceptibil-ity which enter into the impedance is a poor one. Therefore, finding semi-analytic expressions for the impedance of a rectangular slot in a broad frequency range is highly desir-able. We develop a general analysis based on a variational formulation, which includes both the realistic coaxial struc-ture of the beam-pipe and the effect of finite wavelength in the calculation of the coupling impedance of a rectangular slot in a liner wall of zero thickness. We then present a nu-merical study of the frequency dependence of the coupling impedance of a transverse rectangular slot.