Space charge effects on the intrabunch motion under large chromaticity at the main ring in the Japan Proton Accelerator Research Complex

In general, optimizing chromaticity and transverse feedback parameters is important in suppressing beam instabilities for stable operation in high-intensity proton machines. Meanwhile, space charge effects impact the intrabunch motion of the proton bunch within a large chromaticity region in the machines, such as the main ring (MR) in the Japan Proton Accelerator Research Complex (J-PARC). To address this issue, the decoherence and recoherence of the transverse motion of the particles comprising the proton bunch are investigated. The analysis reveals that the space charge effects have a significant influence on the recoherence period through the chromaticity. Nevertheless, the relationship between the maximum frequency in the bunch and the chromaticity is not affected by the space charge effects. These findings are demonstrated with particle tracking simulations, including the direct and indirect space charge effects, and the impedance source of the J-PARC MR. Furthermore, we illustrate the influence of the indirect space charge effect on particle motion by examining the excitation patterns of radial and head-tail modes.