Equilibrium beam distribution in electron storage rings near synchrobetatron coupling resonances

Based on the work [1],[2], we discuss the topic of finding the equilibrium beam distribution near synchrobetatron coupling resonances. We show how this framework reduces to the Sands results in the uncoupled case. A variety of damping/diffusion effects can be included. We discuss the case of IBS damping diffusion in detail, showing how it can be combined with our analytical treatment of emittance evolution. For the synchrobetatron coupled case, this formalism has been applied in detail to the case of dispersion at RF cavities and crab cavities.