Electromagnetic Fields Scattered by a Charge Moving on the Axis of a Semi-Infinite Circular Waveguide: Radiation Spectrum and Longitudinal Impedance

The electromagnetic field symmetric about the axis and excited by a charged particle bunch entering (or exiting) an open perfectly conducting smooth waveguide is found. The longitudinal impedance is expressed as the sum of the contributions from the wall and from the open end of the pipe (diffracted fields). The radiation spectrum is calculated for a wide range in frequency and particle energy.