Stability and halo formation of a breathing axisymmetric uniform-density beam

An analysis of the stability and halo formation is presented for a breathing axisymmetric beam of uniform density [Kapchinsky-Vladimirsky (KV) beam] in a uniform focusing channel. Theoretical results are obtained for the form of modes involving nonuniform charge density. In particular, the mismatch-tune depression space is explored, both analytically and by numerical particle-in-cell simulations, to determine the stability limits and growth rates of the most unstable modes. The implications for halo formation are then explored. Halo parameters obtained by simulations are compared with predictions of an analytical model for halo formation from the breathing KV beam developed earlier. The practical applications of the results for high-current linear accelerators are discussed.