Resonant Normal Forms and Applications to Beam Dynamics
Recent developments in accelerator physics have raised new interest in the formalism of symplectic maps and the related perturbation theory, based on normal forms. The use of superconducting magnets in order to reach higher energies has caused the introduction of strong nonlinearities in the magnetic fields needed to focus the particles on the orbit. Therefore, modern accelerators are nonlinear machines which need new numerical and analytical tools to study problems like the maximization of the stability domain and the lifetime of the beam1,2. For hadron colliders since the synchrotron radiation can be neglected, the system is conservative and has many analogies with the well known problem of celestial mechanics concerning the stability of the orbits of the planets.
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