Search Results (4 total)

We consider the dynamical properties of a particle-core model for a uniformly filled triaxial ellipsoid in a periodic lattice of a high intensity linac. The mismatched oscillation modes are analytically computed in the smooth approximation and are compared with the numerical results of a tracking program. The study of the phase space in the mismatched case is performed by the frequency map analysis. In particular, we can analyze the effect of the nonlinear resonances between the envelope modes and the single particle sincrobetatron frequencies. A chaoticity criterion based on the frequency map analysis allows one to compute the stability region around the beam core. An estimate of the transport and its enhancement due to mismatch is provided by tracking orbits at the border of the stability region.

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 (Darmstadt). The model Hamiltonian consists of a constant focusing, a thin sextupole, and a smooth space charge field. Hyperbolic normal forms are used to estimate the extraction times and the emittance of the extracted beam; the quality of the reconstruction is tested in absence of space charge. The effect of space charge on the dynamical behavior of the beam near the 1/3 betatron resonance is numerically investigated using the frequency map analysis and qualitatively explained with perturbation theory. A polynomial approximation to the one turn map is obtained by replacing the exact space charge force with a sequence of polynomial kicks, and the resonant normal forms reproduce quite accurately the nonlinear tunes and the fixed points position. At low order an analytical estimate of the area of the stable region is proposed to recover the self-consistency of the model.

The network of resonances in the action plane for a four-dimensional map is obtained by computing the actions from the Fourier coefficients of the orbits, and it is compared with the results of Birkhoff normal forms. This method, which combines the positive features of standard frequency analysis and normal forms, is suitable to study the one turn map of a particle accelerator.

We investigate the diffusion in the action variable when the frequency of an integrable isochronous map is modulated. Purely stochastic, hyperbolic, or periodic deterministic modulations are considered. The diffusion coefficient in the invariant for the unperturbed map is exactly determined and shown to be nonzero, except in the last case, when the modulation is smooth and nonzero, due to the presence of topological barriers.