Stability of a Uniform-Density Breathing Beam with Circular Cross Section

An analysis of the stability of a breathing beam of uniform density and circular cross section is presented. Theoretical results are obtained for the form of the modes involving nonuniform charge density. In particular, the mismatch-tune depression space is explored to determine the limits beyond which exponential growth is predicted, and the corresponding growth rates. These results for what is believed to be the most unstable modes are confirmed in detail by numerical particle-in-cell simulations. Their practical implications with regard to beam halo formation for high current linacs are discussed.