Beam echoes in the CERN SPS

Brüning, Oliver; Linnecar, T.; Ruggiero, F.; Scandale, W.; Shaposhnikova, E.; Stellfeld, D.

doi:10.1109/pac.1997.751027

Cited by 11 publications

(15 citation statements)

References 2 publications

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“…[11,12], where it was shown how the echo can be generated and observed for betatron oscillations around an equilibrium orbit of the beam. Experimental observations, however, were initially carried out in the longitudinal direction for a coasting beam [13,14]. In the setup for the longitudinal echo observations the beam energy is modulated by an RF cavity with the frequency ω 1 for a short period of time at some initial time t = 0.…”

Section: Introductionmentioning

confidence: 99%

“…However, as it turns out, after long enough "sleep time" t echo , the beam modulation recoheres for a short period at the frequency mω 1 − kω 2 , where m and k are integer numbers [15]. The experiments [13,14] were carried out using the modulation frequencies in the range from megahertz to hundreds of megahertz. As we will show below, the echo effect can also be implemented at much higher, laser frequencies.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome the low efficacy of the standard approach to modulate the beam, we propose to use a modulation scheme based on the longitudinal echo effect, in a full analogy with the experiments [13,14], albeit extended into the region of optical frequencies. The set up is depicted in Fig.…”

Section: Introductionmentioning

confidence: 99%

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Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation

2009

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We propose to use an echo effect previously observed in hadron accelerators for up-frequency conversion of density modulation in an electron beam. We show that, for generation of high harmonics, this method is much more efficient in comparison with the currently used approach.A one dimensional model of the effect is developed which allows to optimize the amplitude of the modulation for a given harmonic number.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation

2009

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“…The suggested procedure consists in displacing a Gaussian beam, invariant over one turn, with a dipole kick, and to apply a quadrupole kick at time τ ; the echo signal appears at time 2τ in this case. The measurement of echo signals to investigate the longitudinal motion of the beam was also proposed and experimentally achieved [9] [10]. The decay law of the echo amplitude in the presence of noise was established [11].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian dynamics with a weak noise and the echo effect for the rotator model

Turchetti¹,

Bassi²,

Bazzani³

et al. 2006

J. Phys. A: Math. Gen.

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We analyze the effect of a weak noise on the Hamiltonian transport from the analytical and numerical viewpoint. A solvable model, the noisy rotator, is proposed to illustrate the basic phenomena. In the absence of noise, the phase space evolution is a shear flow, whose angular correlations decay following a power law, which depends on the smoothness of the initial action distribution. If the action has a fluctuating component, given by a Wiener process, then the angular correlations decay exponentially according to e − 2 t 3 /6 or faster, where is the noise amplitude. The echo effect is well suited to investigate the competition between the decorrelation due to filamentation and noise. The noisy rotator model allows an exhaustive analytical investigation of the process for a wide class of initial conditions and a generic disturbance. The echo time is proportional to the delay τ of the disturbance and its amplitude is proportional to λτ where λ is the amplitude of the disturbance. The noise reduces the echo amplitude by e −c 2 τ 3 , where c depends on the Fourier components of the initial angular distribution, and of the disturbance applied at time τ . The analytical results, derived in the limit λ → 0, τ → ∞, with λτ finite and sufficiently small to justify a first order expansion, are checked numerically. For more realistic models the analytical procedure would provide qualitative results and scaling laws. Quantitative results are obtained by solving the Fokker-Planck equation with a numerical scheme based on splitting: back propagation and biquadratic interpolation for the integrable part, implicit finite difference scheme for the noise component. The application to a noisy pendulum describing the longitudinal dynamics in a particle accelerator is considered, and we determine the value of the noise amplitude , below which the echo cannot be detected.

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“…Echoes are common in many ar-· eas of physics, including NMR [1] , plasma physics [2--4], nonlinear optics [5], cavity quantum electrodynam-· ics [6 , 7], and cold atoms physics [8][9][10][11] . Echoes were predict ed to occur in proton storage rings [12 , 13], and were observed in high energy hadron b eam experiments [14,15] . Echo-enabled generation of short-wavelength ra-· diation in free-electron lasers [16][17][18] was demonstrat ed (for a recent review, see [19]) .…”

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confidence: 99%

Experimental observation of fractional echoes

et al. 2016

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We report the observation of fractional echoes in a double-pulse excited nonlinear syst em . Unlike standard echoes which appear p eriodically at delays which are integer multiple of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide the first experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of C02 molecules excited by a pair of femtosecond laser pulses . 37.10.Vz, 42. 50. Md Many nonlinear syst ems display the phenomenon of echoes, which is a series of delayed impulsive responses after a pair of short external pulses . These echoes typ-· icany show themselves at times T rv T , 2T, 3T, etc. after the end of the excitation, where T is the delay between the stimulating pulses . Echoes are common in many ar-· eas of physics, including NMR [1] , plasma physics [2--4], nonlinear optics [5], cavity quantum electrodynam-· ics [6 , 7], and cold atoms physics [8][9][10][11] . Echoes were predict ed to occur in proton storage rings [12 , 13], and were observed in high energy hadron b eam experiments [14,15] . Echo-enabled generation of short-wavelength ra-· diation in free-electron lasers [16][17][18] was demonstrat ed (for a recent review, see [19]) .Recently we reported the exist ence of orienta-· tion/ alignment echoes in an ensemble of free classi-· cal rotors stimulat ed by an external impulsive force [20] . We attributed t he echo formation to the kick-· induced filamentation of the rotational ph ase space, and demonstrated the effect experimentally in a gas of C0 2 molecules excited by a pair of femtosecond laser pulses. The time-dependent mean molecular alignment (defined as (cos 2 (B) )(t) , where e is the angle between t he molec-· ular axis and laser polarization) was measured via the laser-induced birefringence signaL The excited syst em exhibited a regular sequence of echo pulses at delays T = T , 2T, 3T, . . . . In addition, our theoretical analysis and numerical simulations [20] also predict ed unusual ad-· ditional recurrences (fractional echoes) at T = (p j q)T, where p and q are mutuany prime numbers. These frac-· tional echoes, however cannot be seen in the alignment signal -t hey require measurement of higher order mo-· ments of the molecular angular distribution.Here we present the first observation of the phe-· nomenon of fractional echoes measured via third-· harmonic generation (THG) in a gas of C0 2 molecules at room t emperature and pressure of 80 mbar. In what follows we introduce the mechanism of the fractional echoes by using a simple 2D classical model, and then describe our experiments in which t he phenomenon of fractional echoes was observed . We also compare the experimental result s to the fun three-dimensional classical and quantum simulations of the echo formation .For a nonresonant laser field interacting with a symmetric linear molecule, such as N 2 , 0 2 or C0 2 , the angular-dependent interaction potent...

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Beam echoes in the CERN SPS

Cited by 11 publications

References 2 publications

Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation

Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation

Hamiltonian dynamics with a weak noise and the echo effect for the rotator model

Experimental observation of fractional echoes

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