Electron beam propagation in linearly polarized undulators: The effect of the anharmonicity on the spatial and phase-space distributions

G. Dattoli, P.L. Ottaviani

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The betatron part of the equations of motion of an electron beam, propagating in a linearly polarized undulator, can be derived from a quartic anharmonic oscillator Hamiltonian coupling the vertical and radial components. The relevant Liouville equation is solved, providing the evolution of the e-beam phase-space distribution, and analyze the variation, during the transport of quantities of physical interest. In particular, radial and vertical phase-space contour plots which exhibit distortions, due to nonlinear effects, and consequent emittance growth are discussed. The integration method employed is based on a symmetric split technique of the evolution operator associated to the Liouville equation under study. Previous results from a macroparticle simulation are used as benchmark. Finally, the split operator technique naturally leads to area preserving maps. © 1995 American Institute of Physics.
Original languageEnglish
Pages (from-to)1348 - 1357
Number of pages10
JournalJournal of Applied Physics
Issue number2
Publication statusPublished - 1995
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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