Crab crossing scheme is an essential collision scheme to achieve high luminosity for the future colliders with large crossing angles. However, when bunch length of one or both colliding beams is comparable with the wavelength of the crab cavity voltage, the nonlinear dependence of the crabbing kick may present a challenge to the beam dynamics of the colliding beams and impact the beam quality as well as the luminosity lifetime. In this paper, the results of nonlinear dynamics in the crab crossing scheme are presented, using both analytical and numerical studies. The result indicates that higher-order synchro-betatron resonances may be excited in the crab crossing scheme with large crossing angle, which causes the beam quality deterioration and luminosity degradation. The studies also reveal possible countermeasures to suppress the synchro-beta resonance, hence mitigate the degradation of beam quality and luminosity.
We applied Frequency Map Analysis (FMA) - a method that is widely used to explore dynamics of Hamiltonian systems - to beam-beam effects study. The method turned out to be rather informative and illustrative in the case of a novel Crab Waist collision approach, when "crab" focusing of colliding beams results in significant suppression of betatron coupling resonances. Application of FMA provides visible information about all working resonances, their widths and locations in the planes of betatron tunes and betatron amplitudes, so the process of resonances suppression due to the beams crabbing i…
We analyze the stop-band due to crab cavities for horizontal tunes that are either close to integers or close to half integers. The latter case is relevant for today's electron/positron colliders. We compare this stop-band to that created by dispersion in an accelerating cavity and show that a single typical crab cavity creates larger stop-bands than a typical dispersion at an accelerating cavity. We furthermore analyze whether it is beneficial to place the crab cavity at a position where the dispersion and its slope vanish. We find that this choice is worth while if the horizontal tune is clo…
The diffusion process near low order synchro-betatron resonances driven by beam-beam interactions at a crossing angle is investigated. Macroscopic observables such as beam emittance, lifetime and beam profiles are calculated. These are followed with detailed studies of microscopic quantities such as the evolution of the variance at several initial transverse amplitudes and single particle probability distribution functions. We present evidence to show that the observed diffusion is anomalous and the dynamics follows a non-Markovian continuous time random walk process. We derive a modified mast…
Numerical simulations have shown that a recently proposed 'crabbed waist' scheme of beam-beam collisions can substantially increase the luminosity of a collider. In this paper we give a qualitative explanation why this scheme works. For this purpose we use simple geometrical considerations and analyze peculiar properties of vertical motion modulations by synchrotron and horizontal betatron oscillations. It is shown that in the 'crabbed waist' scheme these modulations, which are the main sources of beam-beam resonances excitation, are significantly suppressed. Some numerical examples demonstrat…
Beam collisions with a crossing angle at the interaction point have been applied in high intensity colliders to reduce the effects of parasitic collisions which induce emittance growth and beam lifetime deterioration. The crossing angle causes the geometrical reduction of the luminosity. Crab cavity can be one of the most promising ways to compensate the crossing angle and to realize effective head-on collisions. Moreover, the crab crossing mitigates the synchro-betatron resonances due to the crossing angle. Crab cavity experiment in SPS is proposed for deciding on a full crab-cavity implement…
In a lepton storage ring of very high energy (e.g. in the $e^+e^-$ Higgs factory) synchrotron radiation from quadrupoles constrains transverse dynamic aperture even in the absence of any magnetic nonlinearities. This was observed in tracking for LEP and the Future Circular $e^+e^-$ Collider (FCC-ee). Here we describe a new mechanism of instability created by modulation of the particle energy at the double betatron frequency by synchrotron radiation in the quadrupoles. Energy modulation varies transverse focusing strength at the same frequency and creates a parametric resonance of the betatron …
Indus-2 is a synchrotron radiation source which is operational at RRCAT, Indore; India. It is essentially pertinent in any synchrotron radiation facility to store the electron beam without beam loss. During the day to day operation of Indus-2 storage ring difficulty was being faced in accumulating higher beam current. After examining, it was found that the working point was shifting from its desired value during accumulation. For smooth beam accumulation, a fixed desired tune in both horizontal and vertical plane plays a great role in avoiding the beam loss via resonance process. This demanded…
One of the main advantages of proposed by P. Raimondi "Crab Waist" collision scheme is a strong suppression of betatron resonances excited by beam-beam interaction. Some qualitative explanations with numerical examples, describing beam-beam resonances for different collision schemes, were given in arXiv:physics/0702033. This paper can be considered as an "appendix" (additional illustration) to that one. We performed a number of full 2D betatron tune scans (beam-beam simulations) for different collision schemes, so one can easily see how the beam-beam resonances appear and disappear, depending …
In an ideal accelerator, the single-particle dynamics can be decoupled into transverse motion -- the betatron oscillations -- and longitudinal motion -- the synchrotron oscillations. Chromatic and dispersive effects introduce a coupling between these dynamics, the so-called synchro-betatron coupling. We present an analysis of the fully coupled dynamics over a single synchrotron oscillation that leads to an averaged invariant with synchro-betatron coupling in a generic lattice. We apply this analysis to two problems: first, a toy lattice where the computations are analytically tractable, then a…
Synchrotron radiation of relativistic electrons in storage rings naturally leads to the process of damping of betatron oscillations. Damping time and transverse beam emittance can be reduced by wigglers or undulators while the beam parameters are still well defined by the common radiation integrals, based on the properties of synchrotron radiation. However, the quantum excitation of betatron oscillations in principle can be considerably reduced if an electron radiation occurs due to the Thomson scattering in the periodic electromagnetic field. After a brief introduction we compare radiation pr…
Robust Betatron-Tune Measurement from Schottky Spectra: Complementary Classical and Deep-Learning Paradigms
Shanghai Institute of Applied Physics, Chinese Academy of Sciences（中国科学院上海应用物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高级研究院）
We report on extensive measurements at the Cornell Electron-positron Storage Ring of electron-cloud-induced betatron tune shifts for trains of positron bunches at 2.1 and 5.3 GeV with bunch populations ranging between 0.64x10^10 and 9.6x10^10. Measurements using a witness bunch with variable distance from the end of the train and variable bunch population provide information on cloud decay and cloud pinching during the bunch passage. We employ Monte Carlo simulations of the reflection and absorption of synchrotron radiation photons to determine the pattern of absorption sites around the circum…
We show that electron betatron resonance acceleration by an ultra-intense ultra-short laser pulse in a near critical density plasma works as a high-brightness gamma-ray source. Compared with laser plasma X-ray sources in under-dense plasma, near critical density plasma provides three benefits for electron radiation: more radiation electrons, larger transverse amplitude, and higher betatron oscillation frequency. Three-dimensional particle-in-cell simulations show that, by using a 7.4J laser pulse, 8.3mJ radiation with critical photon energy 1MeV is emitted. The critical photon energy $E_c$ inc…
Beam-beam simulations predict that PEP-II luminosity can be increased by operating the horizontal betatron tune near and above a half-integer resonance. However, effects of the resonance and its synchrotron sidebands significantly enhance betatron and chromatic perturbations which tend to reduce dynamic aperture. In the study, chromatic variation of horizontal tune near the resonance was minimized by optimizing local sextupoles in the Interaction Region. Dynamic aperture was calculated using tracking simulations in LEGO code. Dependence of dynamic aperture on the residual orbit, dispersion and…
An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam motion in a synchrotron. By observing this coherent motion, the optical parameters can be directly measured at the beam position monitor locations. The driven oscillation induced by an AC dipole will generate a phase space ellipse which differs from that of the free oscillation. If not properly accounted for, this difference can lead to a misinterpretation of the actual optical parameters, for instance, of 6% or more in the cases of the Tevatron, RHIC, or LHC. The effect of an A…
Development of x-ray phase contrast imaging applications with a laboratory scale source have been limited by the long exposure time needed to obtain one image. We demonstrate, using the Betatron x-ray radiation produced when electrons are accelerated and wiggled in the laser-wakefield cavity, that a high quality phase contrast image of a complex object (here, a bee), located in air, can be obtained with a single laser shot. The Betatron x-ray source used in this proof of principle experiment has a source diameter of 1.7 microns and produces a synchrotron spectrum with critical energy E_c=12.3 …
A new scheme for the two-dimensional cooling of ion beams in storage rings is suggested in which ions interact with a counterpropagating broad-band laser beam. The interaction region in the direction of the ion movement is much less then the wavelength of the ion betatron oscillations. The laser beam in the orbit plane has sharp flat edge directed to the ion beam and the width of the laser beam of the order of the ion beam width. Laser beam radial position is being displaced with some velocity at first from inside and then from outside to the ion beam and decreases both betatron and synchrotro…
In DAΦNE, the Frascati e+/e- collider, the crab waist collision scheme has been successfully implemented in 2008 and 2009. During the collision operations for Siddharta experiment, an unusual synchrotron damping effect has been observed. Indeed, with the longitudinal feedback switched off, the positron beam becomes unstable with beam currents in the order of 200-300 mA. The longitudinal instability is damped by bringing the positron beam in collision with a high current electron beam (~2A). Besides, we have observed a shift of \approx 600Hz in the residual synchrotron sidebands. Precise measur…
Petawatt-class lasers can produce multi-GeV electron beams through laser wakefield electron acceleration. As a by-product, the accelerated electron beams can generate broad synchrotron-like radiation known as betatron radiation. In the present work, we measure the properties of the radiation produced from 2 GeV, 215 pC electron beams, which shows a broad radiation spectrum with a critical energy of 515 keV, extending up to MeV photon energies and 10 mrad divergence. Due to its high energy and flux, such radiation is an ideal candidate for gamma-ray radiography of dense objects. We employed a c…
In DAFNE, the Frascati $e^+e^-$ collider operating since 1998, an innovative collision scheme, the crab waist, has been successfully implemented during the years 2008-09. During operations for the Siddharta experiment an unusual synchrotron oscillation damping effect induced by beam-beam collisions has been observed. Indeed, when the longitudinal feedback is off, the positron beam becomes unstable with currents above 200-300 mA due to coupled bunch instability. The longitudinal instability is damped by colliding the positron beam with a high current electron beam (of the order of 2 A). A shift…
