Analytical and numerical studies of transverse beam splitting used for the CERN PS Multi-Turn Extraction

In view of the programme of reduction of beam losses in the PS for the high intensity beams, in particular that for the CNGS experiment, a novel extraction method was designed for beam transfer between the PS to the SPS. This method, called Multi-Turn Extraction (MTE) is based on the splitting of the proton beam in the horizontal transverse phase space by means of sextupoles and octupoles, using a specific tune variation. The split beam exhibits five beamlets: the core and four islands where a fraction of the beam is trapped. This work analyses numerically and analytically the properties of the beam splitting in view of proposing possible optimizations regarding the trapping of the particles in the islands. We first introduce theoretical models describing this process, from the point of view of the Hamiltonian theory and the transfer map formalism of beam dynamics. The generalized Hénon mapping is then considered to describe the dynamics of the MTE method. We then use the Normal Form approach to analytically obtain properties of that model. In order to explore the properties of the MTE method, we simulate numerically the evolution of the beam in the framework of the 2D and 4D Hénon models. We present a tracking code that we developed to assess the properties of the splitting process. An extensive 2D simulation campaign has been performed to understand the effects of the parameters of the mappings on the fraction of particles trapped in the islands and on the emittances of the different beamlets. We determine the influences of physical parameters (strength of the nonlinearities and tune variation) on the trapping process and we propose ways to improve the trapping and the emittance sharing. In addition, we present results obtained from 4D simulations to investigate new effects introduced by the nonlinear coupling between the horizontal and vertical planes.