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-consistent collective oscillations, excited in a charged particle beam with nonlinear 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 waterbag equilibrium beam have been found in previous work (Sean Strasburg and R.C. Davidson, Phys. Lett. A 269 (2000) 40) using the smooth-focusing approximation and assuming axisymmetric perturbations. These eigenmodes, in combination with the nonlinear equilibrium charge-density and applied fields, cause areas of phase space to break into islands and, in the case of sufficiently large-amplitude perturbations and intense beams, to become stochastic. Nonlinear shifts in the transverse oscillation frequency are determined analytically. Using this frequency shift and the eigenmode frequencies, the location of resonant islands as a function of particle orbit amplitude, beam intensity, and mode number is predicted analytically and confirmed numerically. The dependence of island width on perturbative mode amplitude and beam intensity is explored numerically. Using the Poincare technique, the particle phase space in the beam core and the beam halo region is investigated by numerically integrating the test particle equations over long periods