Production of halo particles by excitation of collective modes in high-intensity charged particle beams

This paper examines analytically and numerically the effects of self-consistent collective oscillations excited in a high-intensity charged particle beam on the motion of a test particle in the beam core. Even under ideal conditions, assuming a constant transverse focusing force (smooth focusing approximation), and perturbations about a uniform-density, constant radius beam, it is found that collective mode excitations, in combination with the applied focusing force and the equilibrium test fields, can eject particles from the beam core to large radii. Test particle orbits are calculated for collective oscillations with $n=1\mathrm{}$ and 2 radial mode structure, and an estimate is obtained for the range of initial conditions for which particles will be expelled from the beam interior. Resonances for meridional particles are found to be unimportant, while a class of particles with nonzero angular momentum are found to participate in resonant behavior. Once expelled from the beam, numerical solutions of the orbit equations indicate that Kolmogorov-Arnold-Moser curves, phase space spanning integrals of motion, confine particles within 1.5 times the beam radius for moderately low mode amplitudes, but are successively destabilized for higher amplitudes.