Space charge effects on coupled-bunch instability in high-intensity proton rings

High-intensity proton accelerators are utilized for neutron, neutrino, and hadron sources. Increasing the beam intensity is important for science that utilizes these particles. However, as beam intensity increases in these proton accelerators, beam instability has emerged as a limiting factor. Coupled-bunch instability, resulting from impedance with frequency components near or below the revolution frequency, stemming from the electrical resistance of beam chambers, ceramic chambers in rapid cycling synchrotrons, and kicker magnets, poses a significant challenge in these proton accelerators. The oscillation frequency of beams observed during operation with chromaticity is considerably higher than the impedance frequency. Space charge forces exhibit significant strength, with a tune shift exceeding 0.1 as an absolute value. In single-bunch behavior, space charge forces dominate, influencing the oscillation modes of instability. It is inevitable that the effect will extend to coupled-bunch modes. This paper provides a theoretical discussion on the coupled-bunch instability of beams subjected to intense space charge forces.