Incoherent effects of space charge and sum resonances on particle beams in a storage ring

In the past years, several studies, numerical and experimental, have been carried out for enlightening the effect of space charge and resonances on particle beams stored in accelerators. The last effort of this quest focused on the third-order coupled resonances, emphasizing the existence of the periodic crossing of fixed lines induced by space charge. In this article, the theory of nonlinear sum resonances in coasting beams in the presence of space charge is presented and applied to unravel the key features of the four-dimensional coupled dynamics in high-intensity bunched beams