Nero: a Code for Evaluation of Nonlinear Resonances in 4d Symplectic Mappings
نویسنده
چکیده
A code to evaluate the stability, the position and the width of nonlinear resonances in four-dimensional symplectic mappings is described. NERO is based on the computation of the resonant perturbative series through the use of Lie transformation implemented in the code ARES, and on the analysis of the resonant orbits of the interpolating Hamiltonian. The code is aimed at studying the nonlinear motion of a charged particle moving in a circular accelerator under the influence of nonlinear forces.
منابع مشابه
Some Numerical and Analytical Tools for the Analysis of 4d Betatronic Motion
We review the formalism of 4D symplectic mappings to analyse the betatronic motion in a circular hadron collider; diierent methods for the evaluation of the nonlinear frequencies are considered, and the usefulness of the analysis of the motion in the frequency space is underlined. Some analytical tools based on the perturbative theory of normal forms are sketched: the nonresonant formalism allo...
متن کاملLocal Analysis of Formal Stability and Existence of Fixed Points in 4d Symplectic Mappings
OF FIXED POINTS IN 4D SYMPLECTIC MAPPINGS E. Todesco INFN, Sezione di Bologna, Via Irnerio 46, 40126, Bologna, Italy. Abstract Symplectic mappings in a four-dimensional phase space are analysed; in the neighbourhood of an elliptic xed point whose eigenvalues are close to satisfy a double resonance condition, the perturbative tools of resonant normal forms are outlined. The analysis of the inter...
متن کاملEuropean Laboratory for Particle Physics Cern -sl Division Dynamic Aperture Estimates and Phase Space Distortions in Nonlinear Betatronic Motion
Symplectic mappings which modelize the 4D betatronic motion in a magnetic lattice are considered. We deene the dynamic aperture in terms of the connected volume in phase space of initial conditions which are bounded for a given number of iterations. Diierent methods for a fast estimate of this quantity are given; the analysis of the associated errors and the optimization of the integration step...
متن کاملVibration Analysis of a Nonlinear System with a Nonlinear Absorber under the Primary and Super-harmonic Resonances (TECHNICAL NOTE)
Abstract In vibratory systems, linear and nonlinear vibration absorbers can be used to suppress the primary and super-harmonic resonance responses. In this paper, the behavior of a nonlinear system with a nonlinear absorber, under the primary and super-harmonic resonances is investigated. The stiffnesses of the main system and the absorber are cubically nonlinear and the dampers are linear. M...
متن کاملEvaluation of Dynamic Aperture in the Presence of Phase Space Distortions
We study symplectic mappings which occur in the modelization of the 4D betatronic motion in a magnetic lattice and define the dynamic aperture in terms of the connected volume in phase space of initial conditions which are bounded for a given number of iterations. Different methods for a fast estimate of the dynamic aperture are outlined; the analysis of the associated errors and the optimizati...
متن کامل