Nonlinear Resonance and Halo Formation Induced by Space Charge

The relationship between the nonlinear resonance and halo formation induced by space charge has been studied by means of the particle core model in this paper. Using the Poincare surface of section technique, an analysis of a particle motion in the phase plane has been presented. The range of the nonlinear resonance versus space charge effects, and the space charge thresholds of halo formation excited by nonlinear resonance are derived. Some numerical results are also given.