How to increase the physics output per MW.h for FCC-ee?

The efficiency of colliders for physics is largely determined by their luminosity, while most of the energy consumed by high-energy $e^+e^-$ colliders is proportional to the total beam current. Thus, the energy efficiency is mainly determined by the specific luminosity that needs to be maximized. One of the most effective ways to achieve this is by using the Crab waist collision scheme, which implies a large Piwinski angle (LPA). A distinctive feature of the FCC-ee is the great influence of beamstrahlung (radiation in the field of an opposite bunch) on beam dynamics. At low energies, this manifests itself in a significant increase in the energy spread and bunch length, at high energies, in a limitation of the beam lifetime. The collision of intense bunches with LPA and beamstrahlung can also lead to various kinds of instabilities limiting the luminosity. Here, we discuss the main aspects to consider when optimizing the parameters of the FCC-ee collider at different energies and explain the choice of basic parameters such as RF voltage, lattice functions at IP, bunch intensity, etc. We will also pay attention to open issues requiring further study and identify some key points for the next phase of this project.Comment: 6 pages, 3 figure

Synchrotron oscillation damping due to beam-beam collisions

In DA{\Phi}NE, 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 measurements have been performed by using both a commercial spectrum analyzer and the diagnostics capabilities of the DA{\Phi}NE longitudinal bunch-by-bunch feedback. This damping effect has been observed in DA{\Phi}NE for the first time during collisions with the crab waist scheme. Our explanation is that beam collisions with a large crossing angle produce a longitudinal tune shift and a longitudinal tune spread, providing Landau damping of synchrotron oscillations.Comment: 3 pages, 5 figures, talk presented to IPAC'10 - Kyoto - May 24-28 201

Aplication of Frequency Map Analysis to Beam-Beam Effects Study in Crab Waist Collision Scheme

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 is clearly seen.Comment: 11 pages, 10 figure

Suppression of the longitudinal coupled bunch instability in DAΦ{\Phi}NE in collisions with a crossing angle

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 of about -600 Hz in the residual synchrotron sidebands is observed. Precise measurements have been performed by using both a commercial spectrum analyzer and the diagnostic capabilities of the longitudinal bunch-by-bunch feedback. The damping effect has been observed in DAFNE for the first time during collisions with the crab waist scheme. Our explanation, based both on theoretical consideration and modeling simulation, is that beam collisions with a large crossing angle produce longitudinal tune shift and spread, providing Landau damping of synchrotron oscillations.Comment: 6 pages, 9 figures, ICFA mini-Workshop on "Mitigation of Coherent Beam Instabilities in particle accelerators" MCBI 2019, 23-27 Sep 2019, Zermatt, CH. arXiv admin note: substantial text overlap with arXiv:1006.178

Recent Beam-Beam Effects at VEPP-2000 and VEPP-4M

Budker INP hosts two e+e- colliders, VEPP-4M operating in the beam energy range of 1-5.5 GeV and the low-energy machine VEPP-2000, collecting data at 160-1000 MeV per beam. The latter uses a novel concept of round colliding beams. The paper presents an overview of observed beam-beam effects and obtained luminosities.Comment: Presented at the ICFA Mini-Workshop on Beam-Beam in Hadron Colliders, CERN, Geneva, Switzerland, 18-22 March 201

Beam-beam simulations for particle factories with crabbed waist

The recently proposed "crabbed waist" scheme for beam-beam collisions can substantially increase luminosity since it combines several potentially advantageous ideas. Large crossing angle together with small horizontal beam size allow having very small beta- functions at the interaction point (IP) and ordinary bunch length without incurring in the "hourglass" effect. The other main feature of such a collision scheme is the "crabbed waist" transformation, which is realized by two sextupoles placed in proper betatron phases around the IP. Such a transformation can strongly suppress the beam- beam betatron resonances induced in collisions with large Piwinski angle, thus providing significant luminosity increase and opening much more room for choices of the working point. In this paper we present the results of beam-beam simulations performed in order to optimize the parameters of two currently proposed projects with the crabbed waist: the DAPhiNE upgrade and the Super B- factory project

Study of IR Design for the LHC Upgrade

A conceptual novel optics was developed for a future upgrade of the LHC interaction regions (IR). Applying the collision scheme with a large Piwinski angle and crab waist, originating from e+e- colliders, to an existing pp collider requires fairly unequal IP beta functions, while the transverse proton emittances are naturally equal. The extremely small vertical IP beta function calls for a novel final magnetic focusing element, a so-called double half quadrupole. At least a partial local chromatic correction is mandatory. Similar, simpler optics designs were explored for the LHeC electron beam. Possible benefits were also studied for higher-energy proton collisions at the HE-LHC, for which the proposed scheme appears quite attractive. Pertinent beam experiments were performed, analysed and prepared at DAFNE and LHC