Nonlinear coupling between breathing and quadrupole-like oscillations in the transport of mismatched beams in continuous magnetic focusing fields

Abstract

A nonlinear analysis of the transport of breathing beams considering nonaxisymmetric perturbations is performed. It is shown that large-amplitude breathing oscillations of an initially round beam may couple nonlinearly to quadrupole-like oscillations, such that the excess energy initially constrained to the axisymmetric breathing oscillations is allowed to flow back and forth between breathing and quadrupole-like oscillations. In this case, the beam develops an elliptical shape with a possible increase in its size along one direction as the beam is transported. This is a highly nonlinear phenomenon that occurs for large mismatch amplitudes on the order of 100% and is found to be particularly relevant for space-charge-dominated beams with K k0 , where K is the beam perveance, k0 is the vacuum phase advance per unit axial length, and is the emittance of the beam. A simple model based on mapping techniques is used to clarify the mechanism that leads to the energy exchange between the modes and is tested against results from direct integration of the envelope equations.