Particle Orbits in Quadrupole-Duodecapole Halo Suppressor

Dynamics of continuous space-charged-dominated beam propagating through a periodic quadrupole-duodecapole focusing channel is studied both numerically and analytically using test-particle-core model and Particle-In-Cell (PIC) simulation code TOPOPIC. The results of TOPOPIC indicate that with initially matched beam, utilization of quadrupole-duodecapole channel results in less beam emittance growth and fewer halo particles than that in a pure quadrupole channel. The Poincare section of plot obtained from the test-particle-core model is used to systematically determine the beam intensity dependent resonant dominated behavior of the test-particles, which reveals the mechanism of the halo suppression in quadrupole-duodecapole channel. Results of study show that, for appropriate field strength, the nonlinear duodecapole force removes the resonant structures due to space charge. Motions of particles, originally trapped in the nonlinear resonant island or chaos region related to space charge, turn out to be along regular tori and these particles have less probability to get into beam halos.