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Recent Applications of Hamiltonian Dynamics to Accelerator Physics

  • Ezio Todesco
Part of the NATO ASI Series book series (NSSB, volume 331)

Abstract

The use of superconducting magnets in large hadron accelerators has raised new interest in the nonlinear effects in accelerator physics (Scandale and Turchetti, 1990): indeed, both analytical tools and reliable numerical methods are required to design future accelerators. The standard numerical approach is based on the concept of symplectic transfer maps (Iselin and Niederer, 1988; Schmidt, 1990); the corresponding analytical tool is the theory of normal forms (Turchetti, 1988; Bazzani et al., 1993a), which is the natural generalization of canonical perturbation theory for flows to transfer maps. Normal forms for symplectic maps have the big advantage of being easily implement able in computer codes (Servizi and Turchetti, 1984), allowing the automatic computation of high perturbative orders; moreover, even if the series are generically divergent such as in the hamiltonian case, a detailed analysis of the mechanism of divergence was carried out, allowing to use the approximation provided by truncated normal forms in judiciously chosen domains (Bazzani et al., 1993a and 1993b).

Keywords

Normal Form Stability Domain Nonlinear Motion Magnetic Lattice Accelerator Physic 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Ezio Todesco
    • 1
  1. 1.Department of Physics, INFN, Sezione di BolognaUniversity of BolognaBolognaItaly

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