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On stochastic complex beam–beam interaction models with Gaussian colored noise

Author

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  • Xu, Yong
  • Zhang, Huiqing
  • Xu, Wei

Abstract

This paper is to continue our study on complex beam–beam interaction models in particle accelerators with random excitations Y. Xu, W. Xu, G.M. Mahmoud, On a complex beam–beam interaction model with random forcing [Physica A 336 (2004) 347–360]. The random noise is taken as the form of exponentially correlated Gaussian colored noise, and the transition probability density function is obtained in terms of a perturbation expansion of the parameter. Then the method of stochastic averaging based on perturbation technique is used to derive a Fokker–Planck equation for the transition probability density function. The solvability condition and the general transforms using the method of characteristics are proposed to obtain the approximate expressions of probability density function to order ε.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:384:y:2007:i:2:p:259-272
    DOI: 10.1016/j.physa.2007.05.057
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    References listed on IDEAS

    as
    1. Yong Xu & Wei Xu & Gamal M. Mahmoud, 2005. "Generating Chaotic Limit Cycles For A Complex Duffing–Van Der Pol System Using A Random Phase," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(09), pages 1437-1447.
    2. 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.
    3. Mahmoud, Gamal M. & Aly, Shaban A.H., 2000. "On periodic solutions of parametrically excited complex non-linear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 390-404.
    4. Cveticanin, L., 2001. "Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 348-360.
    5. Xu, Yong & Xu, Wei & Mahmoud, Gamal M, 2004. "On a complex beam–beam interaction model with random forcing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 347-360.
    6. 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.
    7. 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.
    8. Mahmoud, Gamal M., 1998. "Approximate solutions of a class of complex nonlinear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 211-222.
    Full references (including those not matched with items on IDEAS)

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