Longitudinal stability of a coasting beam in a corrugated resistive vacuum chamber

An analysis is made of the electromagnetic fields excited by longitudinal density fluctuations of an unbunched relativistic particle beam drifting in a corrugated vacuum chamber of circular cross section. From these fields the coupling impedance is calculated, which is a measure of the reaction of an oscillating beam upon itself, and determines its stability. The coupling impedances of bellows and cross-section variations are investigated as functions of various geometric and beam parameters. Corrugations of a vacuum chamber may become resonant cavities at higher frequencies. The coupling impedance (divided by the mode number) may become several orders of magnitude larger than its value at lower frequencies, and severely endanger beam stability. The resonant coupling impedances can be found directly by computer solution of the matrix equations for the field coefficients. (11 refs).