An R&D program to establish a road map for the installation of crab cavities in the LHC is rapidly advancing. Both local and global crab schemes are under investigation to develop cavities that will be compatible with the LHC optics and meet the aperture requirements. Space and aperture constraints to accommodate a prototype crab cavity in the LHC along with related optics issues are presented. The design of a prototype $TM_{110}$ cavity and pertinent RF requirements including impedance estimates and damping are discussed

Calaga, R

Sun, Y

Tomás, R

Zimmermann, F

CERN Document Server

LHC-PROJECT-REPORT-113604Sep2008R. Calaga1), Y. Sun, R. Tomás, F. ZimmermannEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsCRAB COMPENSATION FOR LHC BEAMSAn R&D program to establish a road map for the installation of crab cavities in the LHC is rapidlyadvancing. Both local and global crab schemes are under investigation to develop cavities that will becompatible with the LHC optics and meet the aperture requirements. Space and aperture constraints toaccommodate a prototype crab cavity in the LHC along with related optics issues are presented. The designof a prototype TM110 cavity and pertinent RF requirements including impedance estimates and damping arediscussed.Large Hadron Collider ProjectAbstractLHC Project Report 1136CERN,CH-1211 Geneva 23Switzerland1) BNL, NY, USACERN, Geneva, SwitzerlandPresented atEPAC'08, 11th European Particle Accelerator Conference, Genoa, Italy - June 23-27, 2008CRAB COMPENSATION FOR LHC BEAMS ∗R. Calaga, BNL, NY 11973, USAY. Sun, R. Toma´s, F. Zimmermann CERN, GenevaAbstractAn R&D program to establish a road map for the in-stallation of crab cavities in the LHC is rapidly advancing.Both local and global crab schemes are under investigationto develop cavities that will be compatible with the LHCoptics and meet the aperture requirements. Space and aper-ture constraints to accommodate a prototype crab cavityin the LHC along with related optics issues are presented.The design of a prototype TM110 cavity and pertinent RFrequirements including impedance estimates and dampingare discussed.INTRODUCTIONA small angle (∼ 0.3-0.5 mrad) crab scheme has beendefined as the first step to realize a full crab crossingscheme for the LHC IR upgrade [1, 2]. The luminosityincrease solely from crab cavities is expected to be 12-18%for the nominal LHC with β∗ = 55 cm and 43-62% forthe upgrade with β∗ = 25 cm for cavity frequecies of 400-800 MHz respectively. Due to space constraints and tech-nical ease, a global scheme at the LHC is considered as thebest choice for the first experimental test of crab cavities inhadron colliders. In this scheme the cavities are placed inthe accelerating RF section (IR4) to provide head-on col-lision at one of the interaction points in the LHC. A firstmini-workshop (LHC-CC08) took place in February 2008to discuss several beam dynamics and RF issues and builda global collaboration to establish a road map for the R&Dprototype. A large collaboration spanning three continentsis now in place to develop an optimized cryomodule com-patible with the LHC and IR4 requirements. A tWiki pageis set up to maintain a central repository and coordinate theproject at an international level [3]. The objective of therepository is to provide easy access to latest developmentsrelated to LHC crab cavities and to share information withcrab cavity developments from the ILC and light sourcesfor mutual benefit. Regular meetings over the web enablediscussions about the latest progress of the cryomodule. Inthis paper the installation issues at IR4, nominal cavity de-sign, impedance and damping requirements are discussed.APERTURE & COLLIMATIONThe tight aperture constraints imposed by the LHC col-limation system for machine protection and quench pre-vention leaves very little or no margin for additional aper-ture [4]. A global crab scheme would approximately re-∗This work was partially performed under the auspices of the US De-partment of Energy, We also acknowledge the support of the EuropeanCommunity-Research Infrastructure Activity under the FP6 ”Structuringthe European Research Area” programme (CARE, contract number RII3-CT-2003-506395)quire an additional 0.5σ of aperture (see orbits in Fig. 1) toaccommodate the tilted bunch. The horizontal retraction 0 0.2 0.4 0.6 0.8 1 0  5  10  15  20  25δx Orbit: [σ units]Two Global Cavities (IP4, IP7)Longitudinal Position [km]Crab Cavityδp/p=1x10-4Figure 1: Orbit deviation of a 1σz particle for a globallycrabbed beam compared to deviation of a particle at 1σ δp/p.of the collimators would be reduced with the consequenceof even tighter tolerances and perhaps larger losses [6]. Theimpact of the global crab scheme on LHC collimation isunder study to define the exact retraction and associatedtolerances. Fig. 2 shows the additional beta-beat for a glob-ally crabbed beam with nominal LHC parameters which iscompared to the off-momentum β-beat. The crabbed beamβ-beat is approximately a factor of 10 less and is not fore-seen to be an issue. However, the tolerance imposed by-0.3-0.2-0.1 0 0.1 0.2 0.3 0  5  10  15  20  25Δβx,y/βx,y [%]Particle at 1 σzTwo Global Cavities (IP4, IP7)βxβy-4-3-2-1 0 1 2 3 4 0  5  10  15  20  25Δβx,y/βx,y [%]Particle at 1 σδp/pβxβyLongitudinal Position [km]Figure 2: Top: β-beat of a 1σz particle for a globallycrabbed beam compared to a particle at the center of thebunch. Beta beat of particle with momentum deviation of1σδp/p compared to synchronous a particle.large off-momentum β-beat is very severe. Mitigation ofthis β-beat with appropriate optics solution is essential forany IR upgrade scenario. A solution which significantly re-duces the off-momentum beta beat at the collimators (downto β∗ ∼ 0.2 m) has been recently been developed by spe-cial powering of all arc sextupoles and optimizing phaseadvances between the arcs [5].IR4 INSTALLATION & ISSUESThe nominal beam line separation between the twobeams in the LHC is 19 cm for the most part of the ring.This makes it difficult to transversely accommodate con-ventional RF cavities with a frequency of 800 MHz orsmaller. The IR4 region, currently hosting the LHC mainRF, has a special dog-leg to horizontally separate the twobeam lines to 42 cm which removes this constraint. Two 0 100 200 300 400 500 9.7  9.8  9.9  10  10.1  10.2  10.3-0.4-0.2 0 0.2 0.4 0.6 0.8 1β x,y [m]Dx [m]Longitudinal Position [km]IP4Potential Location (Global CC)βxβyDxFigure 3: Nominal optics and magnetic elements in the IR4region of the LHC. The two green blocks represent the po-tential locations (∼10 m) for cavities in the global scheme.locations of 5m length as depicted in Fig. 3 have beenidentified as potential locations that can be used unless theequipment originally foreseen for these points become es-sential for LHC operation [7]. IR4 also provides anothersignificant advantage as the existing RF infrastructure canbe adapted to the crab cavities including the cryostat de-sign, waveguides, power sources and controls while con-forming to LHC technical and mechanical specifications. 0.23 0.235 0.24 0.245 0.25 0.255 0.26 0.265 0.27 0.23  0.235  0.24  0.245  0.25  0.255  0.26  0.265  0.27μ yμxCell45 CORmax=0.004, dpmax=0.0015n1<6.8n1>6.8n1,QF>7.1Figure 4: Tuning range of the LHC betatron phase advance.The horizontal and vertical axes of the plot are the horizon-tal and vertical phase advances per arc cell with the LHCoperating point marked in a square.Fig. 4 presents the tuning range of the betatron phaseadvance in the nominal LHC. The figure shows the hor-izontal and vertical phase advances per arc cell, respec-tively. The red line delimits the accessible values of thephase advances as constrained by aperture limitations andthe nominal closed orbit and aperture assumptions for theLHC within the cell. A tighter aperture cut would yieldthe area within the blue line. A wide range for phase ad-vance tunability is available when using the usual aper-ture assumptions for the LHC thus providing margin foroperation and the cavity voltage. Small changes in IR4quadrupole strengths can provide additional margin via lo-cal β-function modification.CAVITY DESIGNThe cavity geometry first originated from an initial 400MHz design via a geometrical parameter scan to reachsome semi-optimal RF charateristics. After scaling to 800MHz, an additional optimization was performed on the 800MHz cavity to arrive at the two designs shown in Fig. 5.The optimized geometric and the corresponding RF param-eters are shown in Table 1 and Table 2 respectively. The-30-20-10 0 10 20 30 0  10  20  30  40  50  60  70r [cm]z [cm](Emax, Bmax)λ/2 = 37.5 cmCavity Radius = 24 cmIris = 14 cmBNL Ver 2.1SLAC VerFigure 5: 800 MHz two-cell cavity from crab crossing forthe LHC. An alternate version optimized by SLAC group(blue, geomterical parameters courtesy L. Xiao, Z. Li)achieves lower surface fields.two geometries shown differ mainly in the wall angle of thecavity which subsequently affects the final optimum set ofgeometrical parameters. Typically, a finite wall angle of 6◦or larger is preferred for cavity treatment. Fine tuning maybe required to meet the final requirements related to surfacefields, multipacting and coupler geometries.Table 1: Two optimized geometries for 800 MHz LHC-CCParameter Crab CavityBNL v2.2 SLACIris Radius, Riris [cm] 7.0 7.0Wall Angle, α [deg] 6.0 0.0Iris/Eq. Ellipse, r = ba /R =BA 2.0/0.8 0.8/1.0Cav. wall to iris, d [cm] 1.0 3.37512 Cell, L =λβ4 [cm] 9.375 9.375Eq. Height, D [cm] 23.8 23.3Cavity Beta, β = v/c 1.0 1.0Table 2: RF characteristics of the two geometries for a kickgardient of Bkick = 6.6 MV/m (Lactive ∼Parameter Unit Crab CavityBNL v2.2 SLACEpeak MV/m 30Bpeak mTR/Q⊥ Ω 112 118k|| V/pC 0.54 0.43k⊥ V/pC/m 2.635 2.16437.5cm)103 8722IMPEDANCE REQUIREMENTSThe impedance spectrum of BNL v2.2 cavity was calcu-lated with ABCI [8]; see Fig. 6. A comparison between an8cm and 6cm beam pipe radius is shown to roughly identifyany trapped modes and the corresponding frequency shiftswith aperture. The exact aperture will be chosen based onthe optimum coupling-damping scheme while minimizingthe number of trapped modes below the cut-off frequenciesof the beam pipe. 0 5 10 15 20 25 0  0.5  1  1.5  2  2.5  3  3.5  4Longitudinal Imp [kΩ]Above 2 GHz, Landau Damped< 200 kΩMon Imp (8cm BP)Mon Imp (6cm BP) 0 0.1 0.2 0.3 0  0.5  1  1.5  2  2.5  3  3.5  4Transverse Imp [MΩ/m]<< 2 MΩAbove 2 GHz, Landau DampedFrequency [GHz]Dip Imp (8cm BP)Dip Imp (6cm BP)Figure 6: Longitudinal and transverse impedance spectrumof an 800 MHz two-cell from ABCI. A comparison be-tween 8cm (red) and 6cm (blue) is shown.It is estimated that single and coupled-bunch longitudi-nal modes above 2 GHz will be Landau-damped due to thefrequency spread of synchrotron oscillations. Tolerancescan be set by estimating the impedance requirements givenby [9, 10, 11],Rsh,L <ηEeI0β2(ΔE)2 ΔωsωsFf0τG(frτ) (1)Im(Zn)<ηEeIbβ2(ΔE)2 Δωsωsf0τ. (2)In the transverse plane the natural frequency spread,chromaticity, bunch-by-bunch transverse damper and Lan-dau octupoles should also damp potentially unstable modesabove 2 GHz. The stability limit from Landau octupoles at7 TeV can be formulated in terms of a maximum limit ontune shifts (Re{ΔQ} < 3× 10−4, Im{ΔQ} < 1× 10−4).Pessimistically assuming that the sampling frequency fallson the resonance,Rsh,T  Z0Cγr0MNbβ|Im{ΔQ}|max (3)Table 3 lists the corresponding tolerances.Table 3: Impedance tolerances estimatesParameter Unit Longitudinal TransInj TopCoup bunch, Rsh kΩ 137 196 2 MΩ/mCoup bunch, Qext < 200 -Broadband, Im{Z/n} Ω 0.24 0.15 -COUPLER GEOMETRIESVery strong damping of lower and higher order modesare required to stay well below the LHC instability thresh-olds. In addition a robust design is paramount for stableoperation and tuning. With these constraints and in view ofthe KEK-B operational experience four designs shown inFig. 7 are presently under study. These designs and otherideas will be compared on a common basis to evaluate theireffectiveness and ease of fabrication to reach the final de-sign that will comply with LHC specifications.Figure 7: Potential coupler geometries to achieve strongdamping with a robust design. Top: Coax-to-coax andwaveguide-to-coax (courtesy X. Liling, Z. Li), bottom:multiple waveguides and coax-to-hook (courtesy G. Burt)CONCLUSIONSA low angle global crab compensation scheme locatedin IR4 is defined as the best option for a first experimentaldemonstration of crab cavities in hadron colliders and alsofor the phase I upgrade of the LHC to recover the geomet-ric reduction of luminosity. A globally crabbed beam inthe LHC requires an additional aperture of approximately0.5σ. The associated collimator retraction and its impacton the collimation efficiency is under investigation. Opticsscans indicate ample margin for tuning the phase advanceand beta functions during machine operation. Two designsof a prototype TM110 cavity and pertinent RF requirementsincluding impedance estimates and damping requirementswere presented.ACKNOWLEDGMENTSWe would like to thank all the members of LHC-CC col-laboration for valuable discussions and their contribution.REFERENCES[1] R. Calaga et. al, C-AD 308, LARP-doc 707, CARE-08-002.[2] R. Calaga et al., proceedings of IR07, Frascati, Italy (2007).[3] https://twiki.cern.ch/twiki/bin/view/Main/LHCCrabCavities.[4] R. Assmann et al., LHC project note 277.[5] S. Fartoukh, presented at LIUWG meeting, 2008.[6] R. Assmann, presentation at the LHC-CC08.[7] J. Tuckmantel, Private communication.[8] Y. Chin, User’s Guide Ver 9.4, CERN SL/94-02.[9] E. Shaposhnikova, LHC Project Note 242 (2000).[10] F. Sacherer, IEEE Tr. Nucl.Sci. NS-20 , 825 (1973).[11] V. Balbekov et al., IHEP Preprint 91-14, Protvino (1991).

Crab Compensation for LHC Beams

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