Abstract
Particles in electromagnetic fields behave like oscillators and are conservative systems as long as we ignore statistical effects like the emission of quantized photons in the form of synchrotron radiation. Even in such cases particles can be treated as conservative systems on average. In particular, particle motion in beam transport systems and circular accelerators is oscillatory and can be described in terms of perturbed oscillators. The Hamiltonian formalism provides a powerful tool to analyze particle motion and define conditions of stability and onset of instability. In this chapter we will derive the Lagrangian and Hamiltonian formalism with special consideration to particle beam dynamics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Goldstein: Classical Mechanics (Addison-Wesley, Reading 1950)
L.D. Landau, E.M. Lifshitz: Mechanics, 3rd edn. (Pergamon, Oxford 1976)
L.D. Landau, E.M. Lifshitz: The Classical Theory of Fields, 4th edn. (Pergamon, Oxford 1975)
L. Lur’é Mécanique Analytique (Librairie Universitaire, Louvain 1968)
H. Wiedemann: Particle Accelerator Physics I (Springer, Berlin, Heidelberg 1993)
A. Schoch: Theory of linear and non linear perturbations of betatron oscillations in alternating gradient synchrotrons. CERN Rpt. CERN 57–23 (1958)
G. Guignard: The general theory of all sum and difference resonances in a three dimensional magnetic field in a synchrotron. CERN Rpt. CERN 76–06 (1976)
S. Ohnuma: Quarter integer resonance by sextupoles. Int. Note, Fermilab TM- 448 040 (1973)
E.D. Courant, M.S. Livingston, H.S. Snyder: Phys. Rev. 88, 1190 (1952)
J. Safranek: SPEAR lattice for high brightness synchrotron radiation, Ph.D Thesis (Stanford University, Stanford 1992)
B. Chirikov: A universal instability of many-dimensional oscillator systems. Phys. Repts. 52, 263 (1979)
Nonlinear Dynamics Aspects in Particle Accelerators. Lect. Notes Phys., Vol.247 (Springer, Berlin, Heidelberg 1986)
Physics of Particle Accelerators, AIP Conf. Proc., Vol.184 (American Institute of Physics, New York 1989)
J.M. Greene: A method for determining a stochastic transition. J. Math. Phys. 20, 1183 (1979)
Nonlinear Dynamics and the Beam-Beam Interaction, ed. by M. Month, J.C. Herrera. AIP Conf. Proc., Vol.57 (American Institute of Physics, New York 1979)
Phase Space Dynamics. Lect. Notes Phys., Vol.296 (Springer, Berlin, Heidelberg 1988)
E.D. Courant, H.S. Snyder: Theory of the alternating-gradient synchrotron. Annals Phys. 3, 1 (1958)
H. Poincaré: Nouvelle Méthods de la Mécanique Celeste (Gauthier-Villars, Paris 1892) Vol.1, p.193
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wiedemann, H. (1995). Hamiltonian Formulation of Beam Dynamics. In: Particle Accelerator Physics II. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97550-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-97550-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-97552-3
Online ISBN: 978-3-642-97550-9
eBook Packages: Springer Book Archive