Shaping transverse beam distributions by means of adiabatic crossing of resonances

Non-linear effects are responsible for peculiar phenomena in the dynamics of charged particles in circular accelerators. Recently, they have been extensively used to propose novel beam manipulations where it is possible to modify the transverse beam distribution in a controlled way, with the goal to fulfil the constraints posed by new applications. One example is the resonant beam splitting used at CERN for the Multi-Turn Extraction (MTE), which is used to transfer proton beams from the PS to the SPS. The theoretical description of these effects relies on the formulation of the particle’s dynamics in terms of Hamiltonian systems and symplectic maps, and on the theory of adiabatic invariance and resonant separatrix crossing. Close to a resonance, new stable regions and new separatrices appear in the phase space. As non-linear effects do not preserve the linear Courant-Snyder invariant, it is possible for a particle to cross a separatrix, changing the value of its adiabatic invariant. This process opens the path to new possibilities in terms of beam manipulations. This thesis deals with a variety of possible effects that can be used to shape, in a controlled fashion, the transverse beam dynamics, starting from 2D and then moving to 4D models of the particles’ motion. We show the possibility of performing beam splitting using a resonant external exciter, as well as combin- ing the action of an exciter with mte-like tune modulation close to resonance. Non-linear effects can also be used to cool a beam by acting on its transverse beam distribution. We discuss the special case of a beam with an annular distribution, showing how its emittance can be reduced by means of modulating the amplitude and frequency of a resonant oscillating dipole. We then consider 4D models where the motion in the two transverse planes is coupled when acting close to resonance. This fact can be exploited to operate on the transverse emittances by means of a controlled crossing of a 2D resonance. Depending on the resonance, the result is an emittance exchange between the two planes, or an emittance sharing. These phenomena are described and understood in terms of adiabatic invariance theory.