Cross-plane resonance: a mechanism for very large amplitude halo formation

In this paper we report on the possibility of very large amplitude halo formation due to a cross-plane resonance, based on a core/test-particle model. Previous analyses of halo formation in mismatched beams (which did not involve a coupling of the phase planes) have found that particles may be driven to amplitudes which are limited to typically three times the edge radius by a 2:1 parametric resonance. In the present paper, we systematically study the transverse halo as functions of the longitudinal-to-transverse focusing strength ratio and the longitudinal-to-transverse emittance ratio. We find that, in cases where the longitudinal focusing exceeds the transverse focusing, the parameters may lead to a new type of resonance, a coupled-plane resonance, where the transverse amplitude can be, in principle, unlimited. In this regime (in contrast to the usual in-plane resonance), the halo amplitude increases with a reduction of the space charge. This may have potential relevance to the future superconducting linac design where the longitudinal to transverse focusing ratio could be greater than one