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Synchronization in parametrically driven Hamiltonian systems

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Il Nuovo Cimento B (1971-1996)

Summary

Analytical and numerical techniques of non-linear dynamics are used to study synchronization in certain periodically modulated 2-dimensional Hamiltonian systems. Our model equation describes the behaviour of a «flat» particle beam passing through a periodic array of magnetic dipole focusing elements with sextupole non-linearities. Explicit expressions for the frequency of oscillations about the ideal path are obtained to second order in a small parameter, representing the strength of the instantaneous interactions. These expressions agree very well with the results of numerical computations of the corresponding periodic orbits. Finally, the stability properties of these so-called synchronized periodic solutions are studied numerically and their relevance to the problem of beam stability is discussed.

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References

  1. Chirikov B. V. andVecheslavov V. V., preprint 89-72 (1989), and preprint 86-98 (1980), Institute of Nuclear Physics, Novosibirsk.

  2. Bazzani A., Mazzanti P., Servizi G. andTurchetti G.,Nuovo Cimento,102 (1988) 51.

    Article  MathSciNet  Google Scholar 

  3. Chirikov B. V. et al., Physica D,14 (1985) 289.

    Article  MathSciNet  ADS  Google Scholar 

  4. Gerasimov A. L. et al., preprint 87-69, Institute of Nuclear Physics, Novosibirsk, 1987.

  5. Mahmoud G. M. andBountis T.,J. Appl. Mech.,55 (1988) 721.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Bountis T. andMahmoud G. M.,Part. Accel.,22 (1987) 129.

    Google Scholar 

  7. Mahmoud G. M.,Physica A,199 (1993) 87.

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Assiut, Assiut, Egypt

    G. M. Mahmoud

  2. Department of Mathematics, University of Patras, 26110, Patras, Greece

    T. Bountis

  3. Dipartimento di Fisica, Università di Bologna, Via Irnerio 46, I-40126, Bologna, Italy

    G. Turchetti

Authors
  1. G. M. Mahmoud
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  2. T. Bountis
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  3. G. Turchetti
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Additional information

Work supported in part by a Human Capital and Mobility CEE contract number ERBCHRXCT940480.

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Mahmoud, G.M., Bountis, T. & Turchetti, G. Synchronization in parametrically driven Hamiltonian systems. Nuov Cim B 110, 1311–1322 (1995). https://doi.org/10.1007/BF02723115

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  • DOI: https://doi.org/10.1007/BF02723115

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