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Particle Accelerator Physics II pp 127–162Cite as

Hamiltonian Nonlinear Beam Dynamics

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Abstract

Deviations from linear beam dynamics in the form of perturbations and aberrations play an important role in accelerator physics. Beam parameters, quality and stability are determined by our ability to correct and control such perturbations. Hamiltonian formulation of nonlinear beam dynamics allows us to study, understand and quantify the effects of geometric and chromatic aberrations in higher order than discussed so far. Based on this understanding we may develop correction mechanisms to achieve more and more sophisticated beam performance. We will first discuss higher-order beam dynamics as an extension to the linear matrix formulation followed by specific discussions on aberrations. Finally, we develop the Hamiltonian perturbation theory for particle beam dynamics in accelerator systems.

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Authors and Affiliations

  1. Applied Physics Department and Stanford Synchrotron Radiation Laboratory, Stanford University, 94309-0210, Stanford, CA, USA

    Professor Dr. Helmut Wiedemann

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  1. Professor Dr. Helmut Wiedemann
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© 1995 Springer-Verlag Berlin Heidelberg

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Wiedemann, H. (1995). Hamiltonian Nonlinear Beam Dynamics. In: Particle Accelerator Physics II. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97550-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-97550-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-97552-3

  • Online ISBN: 978-3-642-97550-9

  • eBook Packages: Springer Book Archive

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