Diffusion phenomena in simple Hamiltonian systems: some analytical and numerical results

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 t...

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Bibliographic Details
Main Authors: Bazzani, A., Giovannozzi, M., Rambaldi, S., Turchetti, G.
Format: Conference Proceeding
Language:English
Subjects:
Apertures
Distribution functions
Frequency
H infinity control
Integral equations
Nonlinear equations
Numerical simulation
Optical modulation
Orbits
Stochastic processes
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Summary: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.< >
DOI:10.1109/PAC.1993.308942