Effects of beam spinning on the fourth-order particle resonance of 3D bunched beams in high-intensity linear accelerators

Abstract

The aim of this study is to make the parameter space of zero-current phase advance greater than 90\ifmmode^\circ\else\textdegree\fi{} available to the high-intensity linear accelerator (linac) design and operation, which has been excluded to avoid the envelope instabilities and particle resonances. The earlier study of Cheon et al. [Nucl. Instrum. Methods Phys. Res., Sect. A 1013, 165647 (2021)] reported that the spinning of ion beams can mitigate the fourth-order particle resonance and the associated envelope instability in high-intensity linacs. In the present work, we further investigate the effects of beam spinning on the fourth-order particle resonance in the case of 3D bunched beams with fast acceleration. We also explore the space-charge-driven resonance in the longitudinal plane and confirm that the fourth-order particle resonance can be manifested when the longitudinal zero-current phase advance ${\ensuremath{\sigma}}_{z0}$ is larger than 90\ifmmode^\circ\else\textdegree\fi{} and the depressed phase advance ${\ensuremath{\sigma}}_{z}$ is less than 90\ifmmode^\circ\else\textdegree\fi{}, similar to the transverse case. The beam spinning effects are examined in both transverse and longitudinal planes during beam acceleration through periodic solenoid and quadrupole-doublet focusing channels.