Detecting chaos in particle accelerators through the frequency map analysis method

Abstract

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.

Landau Damping of Beam Instabilities by Electron Lenses

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What is the mechanism of power-law distributed Poincaré recurrences in higher-dimensional systems?

“…Chaotic transport in Hamiltonian systems is of great importance in a wide variety of applications, e.g., for predicting the stability of celestial motion and satellites [1][2][3], controlling the beams of particle accelerators [4][5][6][7], and to describe the dynamics of atoms and molecules [8][9][10][11][12][13]. Generic Hamiltonian systems are not fully chaotic but have a mixed phase space which also contains regular tori.…”

Long-term evolution and stability of Saturnian small satellites: Aegaeon, Methone, Anthe and Pallene

“…Frequency analysis is a powerful technique to quantify the weak chaotic behavior of a dynamical system with arbitrary degrees of freedom. Since its original formulation by Laskar (1990Laskar ( , 1993, who develop it in order to prove the chaotic nature of the solar system's secular evolution, it has been successfully applied to a wide variety of dynamical problems, going from planetary sciences (Nesvorný & Morbidelli 1998;Robutel & Laskar 2001) to galactic dynamics (Papaphilippou & Laskar 1998;Valluri & Merritt 1998), and even through fundamental particle physics (Nadolski & Laskar 2003;Papaphilippou 2014).…”