2.24 Collision Schemes of Circular Electron-Positron Factories

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1 Collision Schemes of Circular Electron-Positron Factories Mikhail Zobov INFN, Laboratori Nazionali di Frascati, Italy Mail to: Present Generation Electron-Positron Factories Present generation lepton factories have been very successful. Both B-factories, KEKB in Japan and PEPII in USA, have largely exceeded their design goals. A collection of articles summarizing their performances can be found in [1]. The Italian Φ-factory DAΦNE has exceeded the phase-i design luminosity in 2004 [2] and obtained a luminosity increase by a factor 3 after implementation of the novel crab waist collision scheme [3]. In the beginning of this year also the Tau-Charm factory in Beijing, BEPCII, has reached its design luminosity [4]. All the present generation factories relied, at least at the beginning of their operation, on the standard strategy in choosing beam parameters in order to achieve high luminosity. The strategy can be understood by considering the well-known expressions for the luminosity L and beam-beam tune shifts. For simplicity we start with the case of head-on collisions of short bunches having equal beam parameters at the Interaction Point (IP) (1) where ξ x, y are the space charge parameters whose maximum values are limited by the beam-beam effects, ε x is the horizontal emittance of the beams, s x, y are their rms sizes at the IP, β y is the vertical beta function at the IP, N the number of particles per bunch, Nb is the number of bunches and f0 the revolution frequency. Neglecting beam dynamics aspects, the luminosity increase in a collider at a given energy requires (according to Eq. (1)) - higher number of particles per bunch, - more colliding bunches, - larger beam emittance, - smaller beta functions at the IP, - round beams, - higher tune shift parameters. The present factories have obtained their good luminosity performances trying to fulfill almost all the above conditions as much as possible except that - it was chosen to collide flat bunches s << since it is rather difficult to provide a y s x good dynamic aperture for the round beam case with both vertical and horizontal beta functions low at the IP;

2 257 - besides, in order to eliminate parasitic collisions in multibunch operation a small horizontal crossing angle was necessary. In the factories a relatively small s Piwinski angle Φ = z θ tg 1 was mandatory to avoid excessive geometric s x 2 luminosity reduction and to diminish the strength of synchrobetatron resonances arising from beam-beam interaction with the crossing angle. However, a further substantial luminosity increase based on the standard collision scheme is hardly possible due to several limitations imposed by beam dynamics requirements: - in order to minimize the luminosity reduction due to the hour-glass effect (the dependence of the vertical beam size on the longitudinal position along the crossing region) the vertical beta function at the IP can not be much smaller than the bunch length β s ; y z - a drastic bunch length reduction is impossible without incurring into single bunch instabilities: bunch lengthening and microwave instabilities due to the beam interaction with the surrounding vacuum chamber. Besides, too short bunches tend to produce Coherent Synchrotron Radiation (CSR) affecting beam quality and leading to a dramatic increase of the power losses; - a further multibunch current increase would result in different kinds of coupled bunch beam instabilities, excessive power loss due to interactions with parasitic Higher Order Modes (HOM) and increase of the required wall plug power; - higher emittances conflict with stay-clear and dynamic aperture limitations, require again higher currents to exploit the emittance increase for the luminosity enhancement; - tune shifts saturate and beam lifetime drops due to a strong nonlinear beam-beam interaction Novel Concepts In order to overcome these limitations several novel collisions concepts and new collision schemes were proposed. The most known are the following - round beam collision preserving an additional integral of motion; - crab crossing; - collision with large Piwinski angle ( superbunch in hadron colliders); - crab waist collision; - collision with travelling waist; - longitudinal strong RF focusing. Recently some of these ideas, such as round beam collisions, crab crossing and crab waist have been experimentally tested. The idea of round beams collisions preserving one of the integrals of motion was proposed by A.Ruggiero in 1982 [5] and then developed by the Novosibirsk Team for the Φ-factory design [6]. It requires equal emittances, equal small and positive fractional tunes, equal beta functions at the IP, no betatron coupling in the arcs. A 90 rotation at each passage of the transverse oscillation plane by means of solenoids in the interaction regions (IR) provides conservation of the longitudinal component of the angular moment

3 258 M z = ypx xpy [7]. Thus the transverse motion becomes one-dimensional. In addition to the obvious advantages coming from Eq. (1), the round beam scheme helps to eliminate all betatron coupling resonances that are of crucial importance for tune shift saturation and lifetime degradation. The synchrobetatron resonances are also weakened since the transverse tune shift is almost independent of particle s longitudinal position. The round beam concept was successfully tested at the electron-positron collider VEPP2000 in 2007 at the energy of 510 MeV [8]. Despite the low energy a high single bunch luminosity of 1.2x10 31 cm -2 s -1 was achieved together with the maximum tune shift as high as [9]. Another round beam collisions scheme, Mobius accelerator, was proposed in [10] and tested at CESR providing a tune shift of 0.09 in agreement with simulations [11]. The crab crossing collision scheme was proposed by R. Palmer in 1988 [12] and further developed in [13]. This idea makes it possible to collide bunches at a large crossing angle without luminosity loss and excitation of synchrobetatron resonances. In the crab crossing scheme both bunches are tilted before collision by half the crossing angleθ / 2, providing head-on collision at the IP. The tilt is created by a transverse RF deflector (crab cavity) giving opposite transverse kicks to the bunch head and tail. The RF deflector is placed at a point where the betatron phase in the crossing plane is p / 2 from the IP. In the classic crab crossing scheme another RF deflector after the collision point is used to restore the tilt. The crab crossing collisions with a single crab cavity per ring were successfully performed at the KEK B-factory [14]. A world record luminosity of 2.1x10 34 cm -2 s -1 has been obtained in this configuration. However, the achieved luminosity is still lower than that predicted by numerical simulation and work is in progress to find out the reasons of the disagreement. The idea of colliding with a large Piwinski angle is not a new one as well. In 1995, discussing beam-beam interactions with a large crossing angle, K.Hirata suggested that a large angle might have several merits for future high-luminosity colliders [15]. It has been also proposed for hadron colliders to increase the bunch length and the crossing angle [16, 17] for luminosity optimization. The advantages of a large Φ can be understood by writing down the formulae for the luminosity and tune shifts with a horizontal crossing angle. Neglecting the hour-glass effect, the expressions can be obtained from Eq. (1) simply by substituting the horizontal beam size by the effective transverse size 2 s x s x 1+ Φ. Then, for large Piwinski angle, Φ >> 1, the luminosity and the tune shifts scale as [18] Nξ y N β y / ε y ; ξ y ; β y s zθ N L ξ (2) x ( s θ ) 2 Clearly, in such a case, if it were possible to increase N proportionally tos z θ, the vertical tune shift ξ y would remain constant, while the luminosity would grow proportionally tos z θ. Moreover, the horizontal tune shift would drop 1/( s z θ ). The idea of using a travelling waist (focus) to compensate the luminosity reduction due to the hour-glass effect in circular colliders came from linear colliders [19]. In the travelling waist collision scheme, the optical focal point depends on the longitudinal position of a particle within the bunch. In other words, particles with different longitudinal coordinates in collision see the same and minimal beta functions. In circular colliders the travelling waist can be realized by a combination of accelerator components that provides a transformation z

4 described by a Hamiltonian H = H0 zp y relating the longitudinal position z and the 2 vertical momentum p y. For example, as proposed in [20], the travelling waist with the crab crossing can be obtained by using together crab cavities and sextupole magnets. The longitudinal strong RF focusing is an alternative way to obtain short bunches at the IP [21]. It consists in realizing a large momentum compaction of the lattice together with a strong RF gradient. In this regime the bunch length is no longer constant, but it is modulated along the ring and can be minimized at the IP. In turn, if the main impedance generating elements of the ring are located where the bunch remains long, it is possible to minimize the strength of wake fields. This helps to avoid microwave instabilities and excessive bunch lengthening due to the potential well distortion [22]. This concept was proposed as one of the possible options for the DAΦNE upgrade [23] Crab Waist Collision Scheme Contrary to the conventional strategy, the crab waist collision scheme requires small emittance and large crossing angle; there is no need to decrease the bunch length and push beam currents beyond the values already achieved in the present factories. This scheme can greatly enhance the luminosity of a collider since it combines several potentially advantageous ideas [24] - the first step is to provide a large Piwinski angle by decreasing the horizontal beam size s x and increasing the crossing angle θ. In this way, in addition to the advantages of the large Piwinski angle scheme, the length of the collision region, proportional to s x / θ can be substantially decreased for low emittance beams. Besides, the problem of Parasitic Crossings (PC) is automatically solved due to the larger crossing angle and a beam separation in terms of at the PC positions. - the vertical beta at the IP can be made very low, comparable to the small length of the collision region, without significant luminosity loss due the hour-glass effect. In addition to the obvious geometric luminosity increase, the micro-beta scheme provides several advantages in beams dynamics: a) possibility of bunch current increase (if it is limited byξ y ), thus resulting in further luminosity gain; b) suppression of vertical synchrobetatron resonances [25]; c) reduction of the vertical tune shift with longitudinal oscillation amplitude [25]. - a further luminosity boost is given by the crab waist transformation described by 1 2 the Hamiltonian H = H0 + xp y that provides a vertical beta function rotation in θ such a way that the beta function waist of one beam is oriented along the central trajectory of the other one. In practice the waist rotation (that is why it is called crab waist ) is provided by sextupole magnets placed on both sides of the IP in phase with the IP in the horizontal plane and at p/2 in the vertical one. The integrated crab sextupole strength should satisfy the following condition depending on the crossing angle and the beta function at the IP and the sextupole locations

5 β K = x (3) θ β β yβ y x The crab waist transformation yields a small geometric luminosity gain due to the vertical beta function redistribution along the collision region, while the dominating effect comes from the suppression of betatron (and synchrobetatron) resonances arising in the conventional collision scheme due to the vertical motion modulation by the horizontal betatron oscillations [26]. The effect of the resonance suppression is clearly demonstrated by using frequency map analysis technique [27] (see Fig.1). Figure 1: DA -beam NE beam footprint with crab sextupoles off (left) and on (right) obtained by frequency map analysis techniques [27]. The crab waist collision scheme has been successfully tested at the electron-positron collider Φ-factory DAΦNE providing luminosity increase by a factor 3 [3]. The achieved peak luminosity of 4.5x10 32 cm -2 s -1 is close (within 10%) to the design value, in a good agreement with numerical simulations [28]. The successful test provided the opportunity to continue the DAΦNE physics program with the upgraded detector of the KLOE-2 experiment [29, 30]. The advantages of the crab waist collision scheme have triggered several collider projects exploiting its potential. At present this scheme is considered to be most attractive for the next generation lepton factories since it holds the promise of increasing the luminosity of the storage-ring colliders by 1-2 orders of magnitude beyond the current state-of-art, without any significant increase in beam current and without reducing the bunch length. Several new collider projects seek to exploit the potential of the crab waist collision scheme. In particular, physics and accelerator communities are discussing and developing new projects which make use of the CW collision scheme: SuperB-factory in Japan (SuperKEKB [31]), SuperC- Tau factory in Novosibirsk [32], two Higgs-factories FCC-ee at CERN [33] and CEPC in China [34]. The SuperKEKB is a natural upgrade of the very successful KEKB, Japanese B-factory at KEK (Tsukuba). The design luminosity goal of the project is 0.8x10 36 cm -2 s -1, i.e. by a factor of 40 higher than the world record luminosity of 2.1x10 34 cm -2 s -1 achieved at KEKB.

6 261 The commissioning of SuperKEKB has successfully started in the very beginning of 2016 [35]. The Budker Institute of Nuclear Physics (Novosibirsk, Russia) is promoting the project of a new generation SuperC-Tau factory. The crab waist concept should allow reaching the project luminosity of (1-2)x10 35 cm -2 s -1 that by more than 2 orders of magnitude higher than the luminosity of 1.0x10 33 cm -2 s -1 presently achieved at the operating τ-charm factory BEPCII in Beijing [4]. SuperC-Tau has entered in the list of 6 most important Russian mega-science projects. In December 2015 the injection complex of the new collider has been successfully commissioned. In 2014 CERN launched the Future Circular Collider (FCC) study aimed at the design of a 100-km proton-proton collider with the collision energy of 100 TeV. As an intermediate step, the electron-positron collider (FCC-ee) hosted in the same tunnel and covering the energy range between 90 GeV and 350 GeV is also under consideration and its intensive design study is ongoing. The CW scheme has been proposed [36] and recently chosen as the baseline option for the FCC-ee design. This scheme provides a substantially higher luminosity with respect to the traditional head-on collisions at low energies and approximately the same luminosity at higher energies (> 240 GeV) at much relaxed beam optics parameters. A CW lattice solution with twice higher vertical beta function at the interaction point, good dynamic aperture and energy acceptance and manageable photon energies has been found. Presently China is considering building a 54-km long Higgs factory CEPC (Circular Electron Positron Collider). Along with the head-on collision option the collider design team has started seriously evaluating a possibility to build a local double ring option with the Crab Waist interaction region [37]. In order to complete the picture, we should mention other collider projects that were considering an application of the CW scheme such as SuperB [38] and SuperTau- Charm [39] factories in Italy, a 500 GeV e+e- collider in a 233-km tunnel [40] in USA, and an upgrade option of the LHC based on collisions of very flat bunches [41, 42] References 1. ICFA Beam Dynamics Newsletter48, April M.Zobov et al., DAΦNE Operations and Plans for DAΦNE2, Proc. of PAC2005, pp , 2005 (SLAB-PUB-11655). 3. M. Zobov et al., Test of Crab Waist Collisions at DAΦNE Φ-Factory, Phys. Rev. Lett , C.H.Yu et al., BEPCII Performance and Beam Dynamics Studies on Luminosity, Proc. of IPAC2016, pp , A.G.Ruggiero, Integrability of the Two-Dimensional Beam-Beam Interaction in a Special Case, Particle Accelerators 12, pp , L.M.Barkov et al., Phi Factory Project in Novosibirsk, Proc. of the KEK Topical Conference on e+e- Collision Physics, p , V.V. Danilov et al., The Concept of Round Colliding Beams, Proc. of EPAC96, p D. Berkaev et al., Status and Progress VEPP-2000, Proc. of RuPAC 2008, p A.Romanov et al., Status the of Electron-Positron Collider VEPP-2000, Proc. PAC2013, pp , R. Talman, A Proposed Mobius Accelerator, Phys.Rev.Lett. 74, pp ,

7 E. Young et al., Collisions of resonantly coupled Beams at the Cornell Electron- Positron Ring (CESR), Proc. of PAC97, p R.B. Palmer, Energy Scaling, Crab Crossing and the Pair Problem, SLAC-PUB- 4707, December K. Oide and K. Yokoya, Beam-Beam Collision Scheme for Storage-Ring Colliders, Phys.Rev. A40, pp , Y. Funakoshi et al., Recent Progress of KEKB, Proc.of PAC09, pp K. Hirata, Analysis of Beam-Beam Interactions with a Large Crossing Angle, Phys.Rev.Lett. 74, pp , K. Takayama et al., Superbunch Hadron Colliders, Phys.Rev.Lett , F. Ruggiero and F. Zimmermann, Luminosity Optimization Near the Beam-Beam Limit by Increasing Bunch Length or Crossing Angle, Phys.Rev.ST Accel.Beams , For example, D. Shatilov and M. Zobov, Beam-Beam Collisions with an Arbitrary Crossing Angle: Analytical Tune Shifts, Tracking Algorithm without Lorentz Boost, Crab-Crossing, ICFA Beam Dyn.Newslett. 37, pp , V. Balakin, in Proc. of the Int. Workshop on Final Focus and Interaction Regions of next Generation Linear Colliders, Stanford, CA, May 2-6, SLAC Y. Ohnishi, Recent Report on Design of SuperKEKB, ICFA Beam Dynamics Newsletter 48, pp , A. Gallo, P. Raimondi and M. Zobov, Strong RF Focusing for Luminosity Increase: Short bunches at the IP, Proceedings of Workshop on e+ e- in the 1-GeV to 2-GeV Range: Physics and Accelerator Prospects, Alghero, Sardinia, Italy, Sep 2003, e-print: physics/ L. Falbo, D. Alesini and M. Migliorati, Longitudinal Beam Dynamics Simulation in Electron Rings in Strong RF Focusing Regime, Phys.Rev.ST Accel.Beams , A. Gallo et al., Proposal of a Strong RF Focusing Experiment at DAΦNE, Proc. of EPAC2004, p.683, P. Raimondi, D. Shatilov and M. Zobov, Beam-Beam Issues for Colliding Schemes with Large Piwinski Angle and Crabbed Waist, LNF IR, Feb p. e- Print: physics/ D.V. Pestrikov, Vertical Synchrobetatron Resonances Due to Beam-Beam Interaction with Horizontal Crossing, Nucl.Instrum.Meth. A336, pp , P. Raimondi, D. Shatilov and M. Zobov, Suppression of Beam-Beam Resonances in Crab Waist Collisions, Proc. of EPAC08, p.2620, D. Shatilov, E. Levichev, E.Simonov and M. Zobov, Application of Frequency Map Analysis to Beam-Beam Effects Study in Crab Waist Collision Scheme, Phys. Rev. ST Accel. Beams M. Zobov et al., Beam Dynamics in Crab Waist Collisions at DAΦNE, ICFA Beam Dyn.Newslett. 48, pp , C. Milardi C et al., DAΦNE Consolidation Program and Operation with KLOE-2 Detector, ICFA Beam Dyn. Newslett. 67 pp. 9-27, M. Zobov et al., Simulations of Crab Waist Collisions in DAΦNE with KLOE-2 Interaction Region, IEEE Trans.Nucl.Sci. 63, no.2, pp , Y.Ohnishi et al., Accelerator design at SuperKEKB, Prog. Theor. Exp. Phys. 2013

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