Particle dynamics in quasi-isochronous storage rings

Riabko, A.; Bai, Mei; Brabson, B.; Chu, C. M.; Jeon, D.; Lee, S. Y.; Zhao, Xiaodong

doi:10.1103/physreve.54.815

Cited by 21 publications

(12 citation statements)

References 14 publications

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“…The physics of the alpha buckets is quite different from the "normal rf buckets," since their energy acceptance depends only on ja 1 ͞a 2 j [2], rather than p V rf ͞a 1 as in Eq. phase acceptance is given by [5] Df…”

Section: J B Murphy and S L Kramermentioning

confidence: 99%

First Observation of Simultaneous Alpha Buckets in a Quasi-Isochronous Storage Ring

Murphy

Kramer

2000

Phys. Rev. Lett.

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We present the first experimental evidence confirming the theoretical predictions of alpha buckets in an electron storage ring. By controlling both the first-and second-order momentum compaction factors, we succeeded in storing electrons simultaneously in a pair of alpha buckets or in either bucket alone. The two electron bunches are separated in energy by slightly less than 1% and the energy is tunable over a narrow range. The energy difference was directly measured using synchrotron light from an undulator. Simultaneous two-color light beams from an undulator were generated. By changing the rf voltage, we were able to vary the normally fixed longitudinal bunch separation. The physics of nonlinear longitudinal phase space has been understood for some time in proton accelerators, where crossing the so-called transition energy (vanishing phase slip factor) during acceleration can cause a loss of beam [1]. Electron accelerators do not have this problem since the velocity dependent term in the phase slip factor is usually negligible compared to the path lengthening term characterized by the momentum compaction factor, a ϵ a 1 1 a 2 d. As a result, electron rings nearly always operate well above the transition energy. Until now, a vanishing phase slip factor has been a concept to be avoided. However, recently several attempts have been made to generate short bunches in electron storage rings by reducing the first-order momentum compaction factor for the lattice and operating close to transition in a "quasi-isochronous mode" [2-4]. As the first-order term a 1 is reduced, the effect of the second-order term becomes important in determining the physics of the electron bunches. Additional stable fixed points, so-called alpha buckets, develop where electrons could be stored [2]. We present the first experimental evidence of the existence of these alpha buckets in an electron storage ring and we explore their dependence on the radio frequency system (rf) and lattice parameters. We also demonstrate a potential application of the alpha buckets by creating two-color light beams from an undulator.The longitudinal equations of motion for an electron of energy E in a high energy electron storage ring are given bywhere V rf , v rf ϵ 2ph͞T 0 , and h are the rf voltage, frequency, and harmonic number; E 0 , T 0 , and U 0 are the energy, revolution period, and radiated energy loss per turn of the synchronous electron in the ring. The damping term has been neglected in Eqs.(1) as it does not play a role in the discussion which follows. f and d are the phase deviation and the fractional energy deviation of an electron from the synchronous electron with phase, f s . The momentum compaction factor is expanded to second order in d. The fixed points of the equations of motion are given by the condition that ᠨ f ᠨ d 0. Under normal operating conditions, only the first-order term in the momentum compaction, a 1 , is considered nonzero. In this case, there is one stable and one unstable fixed point at ͑f 0, d 0͒ and ͑p 2 2f s , 0͒, respecti...

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Section: J B Murphy and S L Kramermentioning

confidence: 99%

First Observation of Simultaneous Alpha Buckets in a Quasi-Isochronous Storage Ring

Murphy

Kramer

2000

Phys. Rev. Lett.

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“…Instances are known in astrophysics [1], chemistry [2], hydrodynamics [3], quantum optics [4], etc., where complex escape phenomena can often be well described by a low-dimensional system of differential equations. In most cases, escape is induced by a harmonic (external or parametric) excitation added to the model system [5][6][7], so that, before escape, chaotic transients of unpredictable duration (due to the fractal character of the basin boundary) are usually observed. However, real-world excitations exhibit a great diversity of waveforms as well as many complex transitions from one to another as the system's parameters change.…”

Section: Introductionmentioning

confidence: 99%

Excitation-Reshaping-Induced Chaotic Escape from a Potential Well

Martínez

Chacón

2006

Nonlinear Dyn

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The chaotic escape of a nonlinearly damped oscillator excited by a periodic string of symmetric pulses from a cubic potential well is investigated. Analytical (Melnikov analysis) and numerical results show that chaotic escapes are typically induced over a wide range of parameters by hump-doubling of an external excitation which is initially formed by a periodic string of single-humped symmetric pulses. The role of a nonlinear damping term, proportional to the nth power of the velocity, on the hump-doubling scenario is also discussed.

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“…Because of its potential benefit, interest in the physics of low α c lattice have recently grown [1][2][3][4][5][6][7]. This paper is a review of [8,9]. The aspects of stochastic dynamics of QI system was also studied [10].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics issues for quasi-isochronous storage rings

Jeon

Bai

Chu

et al.

Proceedings of the 1997 Particle Accelerator Conference (Cat. No.97CH36167)

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The synchrotron equation of motion in quasi-isochronous (QI) storage rings was transformed to a universal Weierstrass equation, where solution is given by Jacobian elliptic functions. Scaling properties of QI Hamiltonian were derived. The effects of phase space damping and the sensitivity of particle motion to external harmonic modulation were studied. We found that rf phase modulation is particularly enhanced in QI storage rings. This means that the operators of QI storage rings should pay special attention to rf phase modulation. Exact formula and sum rules for resonance strength coefficients were derived. In the presence of radiation damping and rf phase modulation, QI system exhibits a sequence of period-two bifurcation enroute towards global chaos (instability) in a region of modulation tune. The critical modulation amplitude for the onset of global chaos shows a cusp as a function of modulation tune. This cusp was shown to arise from the transition from the 2:1 to the 1:1 parametric resonances. We also studied the effect of rf voltage modulation and found that the tolerance of rf voltage modulation is much larger than that of rf phase modulation.

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Particle dynamics in quasi-isochronous storage rings

Cited by 21 publications

References 14 publications

First Observation of Simultaneous Alpha Buckets in a Quasi-Isochronous Storage Ring

First Observation of Simultaneous Alpha Buckets in a Quasi-Isochronous Storage Ring

Excitation-Reshaping-Induced Chaotic Escape from a Potential Well

Nonlinear dynamics issues for quasi-isochronous storage rings

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