Nonlinear coupling between breathing and quadupole-like oscillations in magnetically focused beams*

A nonlinear stability analysis of breathing beams considering nonaxysymmetric perturbations is performed. It is shown that the breathing oscillations of an initially round beam may nonlinearly induce quadrupole-like oscillations, with a consequent increase of the beam size along one direction. The instability mechanism and its relevance to beam particle losses are discussed. Self-consistent simulations are performed to verify the findings.