Stochastic beam dynamics in quasi-isochronous storage rings

Abstract

We investigate effects of quantum fluctuation, potential well distortion, quantum lifetime, and Touschek lifetime of the quasi-isochronous ͑QI͒ dynamical system. The Fokker-Planck equation is employed to study the equilibrium bunch distribution. The quantum lifetime in the moderate damping regime is compared with analytical formulae. The effects of harmonic radio-frequency phase modulation on equilibrium distribution function, quantum lifetime reduction, and the occurrence of stochastic resonance are studied. The formula for the Touschek lifetime for the QI dynamical system is derived and studied.

Fuzzy H∞ Synchronization for Chaotic Systems with Time-Varying Delay

“…It has been widely explored in a variety of fields including physical, chemical, and ecological systems [2]. In the literature, various synchronization schemes, such as variable structure control [3], Ott-Grebogi-Yorke (OGY) method [4], parameters adaptive control [5], observer-based control [6], active control [7,8], time-delay feedback approach [9], backstepping design technique [10], complete synchronization [11], and so on, have been successfully applied to the chaos synchronization.…”

Microbunching Instability in Relativistic Electron Bunches: Direct Observations of the Microstructures Using Ultrafast YBCO Detectors

“…Assuming that the relevant motion occurs in the longitudinal direction [1][2][3], the state of each electron i at time t is defined by its instantaneous position z i ðtÞ and an energy variable δ i ðtÞ. The dynamics of the electrons can be described by the following model [18,19]:…”

Dynamics analysis of fractional order Yu-Wang system

“…Recently, it has been used in secure communication [46] and cryptography [10] also. Different approaches such as adaptive control [47], active control [48], OGY method [49], L 2 − L ∞ synchronization [50], adaptive H ∞ synchronization [51], delay feedback control [52,53] are proposed for chaos synchronization. Ahn and co-workers used fuzzy logic approach to propose different synchronization techniques for continuous time systems [54,55], chaotic neural networks [56,57] and so on.…”