Excitation of a corrugated vacuum chamber by a proton beam

An expression is derived for the longitudinal impedance of the vacuum chamber of a proton synchrotron consisting of short corrugated sections separated by smooth-walled inserts. When the corrugated sections are in a periodic arrangement, this impedance becomes a superposition of several narrow resonances. The longitudinal impedance of the vacuum chamber of the accelerator of the Institute of High Energy Physics is calculated as an example. The result of this calculation explains the complex spectral structure of the microwave radiation which has been found experimentally at that accelerator