Beam halo studies using a 3-dimensional particle-core model

In this paper we present a study of beam halo based on a three-dimensional particle-core model of an ellipsoidal bunched beam in a constant focusing channel. For an initially mismatched beam, three linear envelope modes-a high frequency mode, a low frequency mode and a quadrupole mode-are identified. Stroboscopic plots are obtained for particle motion in the three modes. With higher focusing strength ratio, a 1:2 transverse parametric resonance between the test particle and core oscillation is observed for all three modes. The particle-high mode resonance has the largest amplitude and presents potentially the most dangerous beam halo in machine design and operation. For the longitudinal dynamics of a test particle, a 1:2 resonance is observed only between the particle and high mode oscillation, which suggests that the particle-high mode resonance will also be responsible for longitudinal beam halo formation