Warm-fluid collective mode excitations in intense charged particle beams with nonlinear equilibrium self-fields: test particle simulations

This paper examines analytically and numerically the effects of self-consis tent collective oscillations, excited in a charged particle beam with nonli near equilibrium self-fields, on the motion of a test particle in the beam core and halo region. The infinite set of linearized eigenmodes of a waterb ag equilibrium beam have been found in previous work (Sean Strasburg and R. C. Davidson, Phys. Lett. A 269 (2000) 40) using the smooth-focusing approxi mation and assuming axisymmetric perturbations. These eigenmodes, in combin ation with the nonlinear equilibrium charge-density and applied fields, cau se areas of phase space to break into islands and, in the case of sufficien tly large-amplitude perturbations and intense beams, to become stochastic. Nonlinear shifts in the transverse oscillation frequency are determined ana lytically. Using this frequency shift and the eigenmode frequencies, the lo cation of resonant islands as a function of particle orbit amplitude, beam intensity, and mode number is predicted analytically and confirmed numerica lly. The dependence of island width on perturbative mode amplitude and beam intensity is explored numerically. Using the Poincare technique, the parti cle phase space in the beam core and the beam halo region is investigated b y numerically integrating the test particle equations over long periods. (C ) 2001 Elsevier Science B.V. All rights reserved.