435 research outputs found
Analysis of adiabatic trapping phenomena for quasi-integrable area-preserving maps in the presence of time-dependent exciters
In this paper, new results concerning the phenomenon of adiabatic trapping
into resonance for a class of quasi-integrable maps with a time-dependent
exciter are presented and discussed in detail. The applicability of the results
about trapping efficiency for Hamiltonian systems to the maps considered is
proven by using perturbation theory. This allows determining explicit scaling
laws for the trapping properties. These findings represent a generalization of
previous results obtained for the case of quasi-integrable maps with parametric
modulation as well as an extension of the work by Neishtadt \textit{et al.} on
a restricted class of quasi-integrable systems with time-dependent exciters
Hamiltonian theory of the crossing of the 2Qxâ2Qy=0 nonlinear coupling resonance
In a recent paper, the adiabatic theory of Hamiltonian systems was
successfully applied to study the crossing of the linear coupling resonance,
. A detailed explanation of the well-known phenomena that occur
during the resonance-crossing process, such as emittance exchange and its
dependence on the adiabaticity of the process was obtained. In this paper, we
consider the crossing of the resonance of nonlinear coupling
using the same theoretical framework. We perform the analysis using a
Hamiltonian model in which the nonlinear coupling resonance is excited and the
corresponding dynamics is studied in detail, in particular looking at the
phase-space topology and its evolution, in view of characterizing the emittance
exchange phenomena. The theoretical results are then tested using a symplectic
map. Thanks to this approach, scaling laws of general interest for applications
are derived
Probing the diffusive behaviour of beam-halo dynamics in circular accelerators
Circular particle accelerators at the energy frontier are based on superconducting magnets that are extremely sensitive to beam losses as these might induce quenches, i.e. transitions to the normal-conducting state. Furthermore, the energy stored in the circulating beam is so large that hardware integrity is put in serious danger, and machine protection becomes essential for reaching the nominal accelerator performance. In this challenging context, the beam halo becomes a potential source of performance limitations and its dynamics needs to be understood in detail to assess whether it could be an issue for the accelerator. In this paper, we discuss in detail a recent framework, based on a diffusive approach, to model beam-halo dynamics. The functional form of the optimal estimate of the perturbative series, as given by Nekhoroshevâs theorem, is used to provide the functional form of the action diffusion coefficient. The goal is to propose an effective model for the beam-halo dynamics and to devise an efficient experimental procedure to obtain an accurate measurement of the diffusion coefficient
PLATO: A Program Library for the Analysis of 4D Nonlinear Transverse Motion
The PLATO (Perturbative Lattice Analysis and Tracking tOols) program, a program library for analyzing four-dimensional betatronic motion in circular particle accelerators is presented. The routines included in this library provide both the resonant and the nonresonant perturbative series that approximate nonlinear motion (normal forms); standard numerical tools such as the Lyapunov exponent, frequency analysis and evaluation of the dynamic aperture are also available. To ensure the highest flexibility, the code is fully compatible with standard tracking programs commonly used in the accelerator physics community
Towards a Statistical Physics of Human Mobility
In this paper, we extend some ideas of statistical physics to describe the
properties of human mobility. From a physical point of view, we consider the
statistical empirical laws of private cars mobility, taking advantage of a GPS
database which contains a sampling of the individual trajectories of 2% of the
whole vehicle population in an Italian region. Our aim is to discover possible
"universal laws" that can be related to the dynamical cognitive features of
individuals. Analyzing the empirical trip length distribution we study if the
travel time can be used as universal cost function in a mesoscopic model of
mobility. We discuss the implications of the elapsed times distribution between
successive trips that shows an underlying Benford's law, and we study the rank
distribution of the average visitation frequency to understand how people
organize their daily agenda. We also propose simple stochastic models to
suggest possible explanations of the empirical observations and we compare our
results with analogous results on statistical properties of human mobility
presented in the literature
Frequency map analysis of a three-dimensional particle in the core model of a high intensity linac
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
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