Recent Progress on Nonlinear Beam Manipulations in Circular Accelerators

In recent years, transverse beam splitting by crossing a stable resonance has become the operational means to perform MultiTurn Extraction (MTE) from the CERN PS to the SPS. This method delivers the high-intensity proton beams for fixed-target physics at the SPS. More recently, further novel manipulations have been studied, with the goal of devising new techniques to manipulate transverse beam properties. AC magnetic elements can allow beam splitting to be performed in one of the transverse degrees of freedom. Crossing 2D nonlinear resonances can be used to control the sharing of the transverse emittances. Furthermore, cooling the transverse emittance of an annular beam can be achieved through an AC dipole. These techniques will be presented and discussed in detail, considering future lines of research.