Nonlinear Transverse Beam Dynamics in Synchrotron Accelerators with Emphasis on the Interaction of the Beam with Pockets of Ions.

摘要

The authors calculate the Poincare map for the equation of motion of a particle in an accelerator under the action of nonlinear forces and they discuss the problem of the dynamic aperture. They derive analytical expressions for the electrostatic potential induced by the particle beam. These expressions allow an accurate location of potential wells and the study of the dynamics of ions from the residual gas. They analyze the beam dynamics in the presence of another beam or of pockets of ions. They deduce stability conditions and conclude that both the integer part of the tune as well as the location of the ion pockets determine the stability. For small amplitudes, they derive an analytical expression for the variation of the tune with the amplitude. They introduce the technique of averaging of differential equations to study the reduction of the density of ions through the application of an electric field--beam shaking. By building a simple model for the beam-ions interaction, they conclude on the existence of a pattern of nonlinear resonance. They propose a new procedure for beam shaking which consists on a suitable periodic variation of the exciting frequency--'frequency pumping' and present numerical evidence of its efficiency.