Nonlinear resonances and chaotic behavior in a periodically focused intense charged-particle beam

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Abstract
It is shown that beam self-field effects induce nonlinear resonances and chaotic behavior in the envelope oscillations of an intense charged-particle beam propagating through a periodic focusing field. The resonance condition is derived and expressed in terms of the vacuum phase advance and the beam perveance. Certain correlations are found between such resonant and chaotic behavior and well-known instabilities in periodically focused high-current ion beams. The predicted nonlinear resonances and chaotic behavior are expected to be observable in beam transport experiments in which there is a mismatch between the beam and the periodic focusing field.