Abstract
The paper investigates the nonlinear coupling of envelope modes of oscillation for intense bunched beams. Initially, the analysis concentrates on the case of spherically symmetric beams for which longitudinal and transverse focusing forces are assumed to be the same. It is investigated how externally induced spherically symmetric breathing oscillations may nonlinearly drive the growth of ellipsoidal modes which can break the spherical beam symmetry. Next, a more general case in which the focusing forces are not symmetric such that the matched beam already presents an ellipsoidal shape is studied. It is found that depending on the parameters of the system, even a very small mismatch amplitude can drive an instability, which leads to an effective coupling of longitudinal and transversal envelope oscillations by means of the space-charge forces. Use is made of Poincaré plots and the stability index of periodic orbits to perform a detailed analysis of the location of the instability in the parameter space and how it affects the beam transport. Self-consistent numerical simulations are performed in order to verify the onset of the nonlinear instability and its effect on the evolution of the RMS size and emittance of the beam.
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