Title :
Diffusion phenomena in simple Hamiltonian systems: some analytical and numerical results
Author :
Bazzani, A. ; Giovannozzi, M. ; Rambaldi, S. ; Turchetti, G.
Author_Institution :
Dipartimento di Matematica, Bologna Univ., Italy
Abstract :
We study both numerically and analytically some simple Hamiltonian systems perturbed by a random noise or by a periodic (or quasi-periodic) noise. In this way we simulate the effects of the ripple in the power supply on the betatronic motion in a particle accelerator. We consider the dependence of the diffusion in the phase space on the relevant parameters of our system like the nonlinear terms, the strength of the noise and, in the deterministic case, its modulation frequency. We discuss also the possibility of describing the evolution of a distribution function for an integral of motion of the unperturbed system, like the action or the energy, by means of a Fokker-Planck equation. The results are compared with numerical simulations
Keywords :
Fokker-Planck equation; beam handling equipment; beam handling techniques; diffusion; nuclear electronics; numerical analysis; particle accelerators; perturbation theory; power supplies to apparatus; random noise; Fokker-Planck equation; analytical results; betatronic motion; deterministic case; diffusion phenomena; distribution function; modulation frequency; motion integral; nonlinear terms; numerical results; particle accelerator; periodic noise; phase space; power supply ripple; quasiperiodic noise; random noise; simple Hamiltonian systems; unperturbed system; Apertures; Distribution functions; Frequency; H infinity control; Integral equations; Nonlinear equations; Numerical simulation; Optical modulation; Orbits; Stochastic processes;
Conference_Titel :
Particle Accelerator Conference, 1993., Proceedings of the 1993
Conference_Location :
Washington, DC
Print_ISBN :
0-7803-1203-1
DOI :
10.1109/PAC.1993.308942
