Quantitative analysis of trapping probability for quasi-integrable two degree of freedom maps

Abstract

A key ingredient for the Multi-Turn Extraction (MTE) at the CERN Proton Synchrotron is the beam trapping in stable islands of transverse phase space. In a previous paper a method allowing analytical estimation of the fraction of beam trapped into resonance islands as a function of the Hamiltonian parameters has been presented. Such amethod applies to one-degree of freedom models of betatronic motion. In this paper, the analysis is extended to the more realistic and challenging case of two-degree of freedom systems, in which the interplay between the horizontal and vertical motion is fully included. Numerical simulations are presented and the results are discussed in detail