Particle accelerators are technological devices which allow studies at both infinitely small scale, e.g. particles responsible for elementary forces, and extremely large scale, e.g. the origin of cosmos. This work is concerned with area-preserving maps modelling ring accelerators. We prove a theorem on control allowing us to build two new maps. These systems exhibit excellent dynamical properties : wider dynamical aperture, reduction of chaos and a reduced frequency space. The results have a strong analitical basis and are validated numerically with the normal form theory (NF), the chaos indicator SALI and the frequency map analysis (FMA). Finally we present a very new direction in the control of dynamical systems : controlling dissipative systems that are perturbations of integrable ones. We give a detailed presentation of the first theoretical and numerical results through the van der Pol model.
| la date de réponse | 25 oct. 2013 |
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| langue originale | Anglais |
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| L'institution diplômante | |
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| Superviseur | Teo Carletti (Promoteur), Anne Lemaitre (Jury), Joseph Winkin (Président), Duccio Fanelli (Jury) & Michel Vittot (Jury) |
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Control theory of area preserving maps - Application to particle accelerator systems
Boreux, J. (Auteur). 25 oct. 2013
Student thesis: Doc types › Docteur en Sciences