Analysis of a model for resonant extraction of intense beams by normal forms and frequency map - art. no. 114201

A simple 1D model is proposed to explore the resonant extraction of intense beams from a synchrotron as performed in the SIS synchrotron in GSI (Darms tadt). The model Hamiltonian consists of a constant focusing, a thin sextup ole, and a smooth space charge field. Hyperbolic normal forms are used to e stimate the extraction times and the emittance of the extracted beam; the q uality of the reconstruction is tested in absence of space charge. The effe ct of space charge on the dynamical behavior of the beam near the 1/3 betat ron resonance is numerically investigated using the frequency map analysis and qualitatively explained with perturbation theory. A polynomial approxim ation to the one turn map is obtained by replacing the exact space charge f orce with a sequence of polynomial kicks, and the resonant normal forms rep roduce quite accurately the nonlinear tunes and the fixed points position. At low order an analytical estimate of the area of the stable region is pro posed to recover the self- consistency of the model.