Fields excited by a beam in a smooth toroidal chamber

We study the fields produced by a beam circulating in a smooth toroidal chamber with walls of finite conductivity. At high frequencies the beam can excite resonant modes of the chamber having phase velocity equal to the particle velocity. The frequencies of these synchronous modes are widely spaced and depend sensitively on the revolution frequency ω0. The associated longitudinal coupling impedance, Z(n, nω0), has relatively broad peaks as a function of the azimuthal mode number n. In typical cases Re Z(n, nω0)/n reaches values of several ohms in the lowest modes. The lowest mode has n somewhat greater than πR3/2/w1/2h, where R is the trajectory radius, and the cross section of the chamber is a rectangle of width w and height h. Although the frequencies are typically quite high, it is not excluded that the large coupling impedance could lead to fast microwave instabilities of a short bunch. (author) 25 refs., 18 figs., 1 tab