## Abstract

We study slow diffusion processes of orbits through thin chaotic layers of 2m (m ≥ 2)-dimensional symplectic maps (often referred to as Arnol'd diffusion) on a 4-dimensional mapping model of accelerator dynamics. Using a method proposed by Chirikov, we compute diffusion rates of vertical displacements, |y_{n}|, near the flat beam case, when the horizontal motion occurs within a thin chaotic layer of the corresponding 2-dimensional x_{n}, x_{n+1} map. Our computation distinguishes between regions of diffusive and quasiperiodic motion, in which the respective rates are found to differ by 10-12 orders of magnitude for N = 10^{8} iterations. For diffusion, |y_{n}| grows on the average with n (n ≤ 10^{8}, with a rate D(R) ∝ exp(aR) (a > 0, R^{2} = y^{2}_{0} + y^{2}_{1}), which gives accurate estimates of escape times N_{esc} ∝ D^{-1}. Modelling synchrotron oscillations by a periodic modulation on the "betratron" frequencies, we find that diffusion rates increase significantly and rapid escape occurs above certain thresholds in the ε, Ω parameter values, ε and Ω being the amplitude and frequency of the modulation respectively.

Original language | English |
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Pages (from-to) | 122-131 |

Number of pages | 10 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 71 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Feb 1 1994 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics