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Beam Stability in Modern Light Sources via Frequency Map Analysis

Final Activity Report Summary - BSMLSFMA (Beam Stability in Modern Light Sources via Frequency Map Analysis)

The main objective of the project was the application of well-established methods of non-linear Hamiltonian dynamics, such as the frequency map analysis (FMA), in order to understand the beam stability properties in modern light sources in theory, simulations and experiments. To this end an efficient tracing code based on symplectic integration schemes was build, allowing the fast and accurate simulation of orbits of single particles in models of various real machines like the ESRF storage ring (Grenoble, France), and the Compact Linear Collider (CLIC) damping rings (CERN, Geneva, Switzerland). The acquired simulation data, as well as experimental measurements were analysed through FMA.

In the case of experimental beam position measurements special attention was given to the problem of the decoherence of the beam, which diminishes drastically the number of turns for the tune determination, with data above the noise level. One of the main results of the project was that analysing data from equally spaced beam position monitors (BPMs) not having the same optics, or even from many BPMs that are not even equally spaced, a fast and accurate tune determination is obtained.

The main source of nonlinear effects in beam dynamics is the presence of sextupoles. A basic outcome of our study is that the 'thin lense' approximation of sextupoles (i.e. the act of the sextupole is considered to be an instantaneous 'kick' of the beam), which is often used in dynamical studies of accelerator models, influences strongly the frequency maps, and thus it should be avoided when the understanding of nonlinear effects is needed.

Another outcome of the project was the introduction and application of the generalised alignment index (GALI) method for the rapid detection of chaos, as well as for the determination of the dimensionality of regular motion in multi-dimensional Hamiltonian systems.