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Beam–beam interaction models under narrow-band random excitation

Author

Listed:
  • Xu, Yong
  • Xu, Wei
  • Mahmoud, Gamal M.
  • Lei, Youming

Abstract

The aim of this paper is to continue our previous investigations on beam–beam interaction models in particle accelerators by considering these models under narrow-band random excitation. In this investigation the multiple scale and the moment methods are used. The equations of modulation of the amplitude and the phase are derived and perturbation techniques are used to seek approximate steady-state solutions. Two special cases are considered to illustrate this study and excellent agreement is found between analytical and numerical results. Other cases can be similarly studied. The effects of noise and detuning parameters are examined numerically and theoretically and we find that the system demonstrates a diffused limit cycle as the intensity of noise increases. The numerical results show that the multiple scale method is effective for these stochastic systems.

Suggested Citation

  • Xu, Yong & Xu, Wei & Mahmoud, Gamal M. & Lei, Youming, 2005. "Beam–beam interaction models under narrow-band random excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 372-386.
    • Handle: RePEc:eee:phsmap:v:346:y:2005:i:3:p:372-386
    DOI: 10.1016/j.physa.2004.08.073
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    References listed on IDEAS

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    1. Mahmoud, Gamal M., 1997. "Stability regions for coupled Hill's equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 239-249.
    2. Mahmoud, Gamal M., 1995. "Beam-beam interaction models with a small stochastic perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(4), pages 445-451.
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    Cited by:

    1. Li, Wei & Li, Jiaorui & Chen, Weisheng, 2012. "The reliability of a stochastically complex dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(13), pages 3556-3565.
    2. Li, Wei & Xu, Wei & Zhao, Junfeng & Wu, Haibo, 2007. "The study on stationary solution of a stochastically complex dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 465-472.
    3. Xu, Yong & Zhang, Huiqing & Xu, Wei, 2007. "On stochastic complex beam–beam interaction models with Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 259-272.

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