Hamiltonian Nonlinear Beam Dynamics

  • Helmut Wiedemann
Part of the Advanced Texts in Physics book series (ADTP)


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.


Perturbation Term Chromatic Aberration Phase Ellipse Nonlinear Field Resonant Term 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Helmut Wiedemann
    • 1
  1. 1.Applied Physics Department and Synchrotron Radiation LaboratoryStanford UniversityStanfordUSA

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