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

The aim of this study is to make the parameter space of zero-current phase advance greater than 90?? 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 crz0 is larger than 90?? and the depressed phase advance crz is less than 90??, 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.