About
The goal of this lecture is to present the contemporary methods and numerical tools of non-linear dynamical systems in order to analyse the motion in particle accelerators. After a short introduction to non-linear effects and their impact to beam performance, the lecture will briefly review elements of classical mechanics, essential for the study of non-linear dynamics, including the Lagrangian and Hamiltonian formalism, canonical transformation and simplicity. Starting from the relativistic Hamiltonian for E/M fields, elements of canonical perturbation theory will be presented, showing its limitation, for particle accelerators. In this respect, concepts of linear and non-linear beam transport will be introduced, represented by matrices or more generally maps. The Lie formalism will be employed in order to elaborate and analyse these maps through non-linear normal form construction. An introduction to Truncated Power Series through differential Algebra will be also given, as it is essential for constructing 1-term maps. Finally, elements of symplectic integration will be reviewed.
0:00:00 Slide 1
0:28:38 Slide 2
0:31:10 Slide 3
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0:34:22 Slide 5
0:36:12 Slide 6
0:38:07 Slide 7
0:40:53 Slide 8
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0:45:27 Slide 11
The talk
Credits and licence
- Institution
- CERN
- Department
- CAS - CERN Accelerator School
- Speaker
- Yannis Papaphilippou
- Year
- 2024
- Level
- Graduate
- Language
- English
- Subjects
- Mathematics, Physics
- Source
- CERN
- Licence
- CERN, as CERN states it. CERN's terms
- Attribution
- © CERN. CERN provides its audiovisual media free of charge for educational and informational use, credited to CERN; this lecture is shown in CERN's own player.
- Who can watch
- CERN gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed