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KEKB and Superkekb Design*) Low emi(ance rings: Colliders mainly based on experiences of KEKB and SuperKEKB design*) Y. Funakoshi KEK *) Based on the works done by KEK/SuperKEKB opcs group members: K. Oide, H. Koiso, Y. Ohnishi, A. Morita, H. Sugimoto Comparison of emi(ances of colliders Comparison of emi(ances of colliders Future colliders LEP3 Exisng colliders TLEP-H From Beam Dynamics Newsle(er No. 31 Courtesy of F. Zimmermann, H. Burkhardt and Q. Qin F. Zimmmerman Comparison of emi(ances of colliders [cont’d] Future colliders Exisng colliders LEP3 TLEP-H Necessity of low emi(ance in colliers Importance of verFcal emi(ance • In many high luminosity colliders such as KEKB and PEP-II, the machines were operated well above the beam-beam limit. Usually the verFcal beam-beam limit is lower than the horizontal one. • Even above the beam-beam limit, the luminosity increases linearly as funcFon of the beam currents. • In this situaon, it is commonly considered that the verFcal emi(ance in single beam is not important for the luminosity, since the verFcal emi(ance is determined by the beam-beam blowup. • However, the beam-beam simulaon predicts that the smaller verFcal emi(ance in single beam is important for a higher luminosity. • In some machines such as SuperKEKB, SuperB and TLEP, a very low verFcal emi(ance is necessary to achieve the design beam-beam parameter. Simulaon: KEKB Luminosity vs. VerFcal emi(ance (single beam) KEKB Achieved: 0.24nm, σy = 1.18µm (LER) Simulaon by K. Ohmi εy(nm) • Smaller verFcal emi(ance always gives be(er performance. SuperKEKB beam-beam simulaon 1.2e+36 0.25x SuperKEKB design 0.5x 1e+36 1.25x LER HER 2x 1xy εx [nm] 3.2 4.6 8e+35 ) εy [pm] 8.64 11.5 -1 s -2 6e+35 L (cm SuperKEKB design luminosity 4e+35 Strong-strong method (PIC) 2e+35 For the long-rage force, the gaussian distribuFon was assumed. 0 0 1000 2000 3000 4000 5000 turn Smaller verFcal emi(ance gives higher luminosity. Much lower verFcal emi(ance than the design will be needed to K. Ohmi achieve the design luminosity. Methods for low emi(ances Horizontal emi(ance • Suppress radiaon excitaon – Photon spectrum (longer bending magnets) – Reduce the integral of H • Low emi(ance lace – phase advance of FODO cell, special lace • Enhance radiaon damping – Damping wiggler – Damping parFFon number • Ex. TRISTAN(ΔfRF = +3kHz -> εx = 165nm -> 80nm ) Cγ 2 H ds ε = γ ds/ 2 2 x ∫ 3 ∫ 2 H = γ xηx + 2αxηxη!x + βxη!x Jx ρ ρ € 2.5 π cell lace (KEKB, SuperKEKB) • Five π/2(90°) cells are merged. Ten dipole magnets are reduced to four. • 13 quadruple magnets/cell. • Emi(ance and α (momentum compacFon) are tunable by changing the paern of dispersion in wide range. • Non-interleaved sextupole scheme was adopted. A -I’ sextuple pair is connected # −1 0 0 0 & by –I’ transformer. % ( % m21 −1 0 0 ( −I" = % 0 0 −1 0 ( % ( % 0 0 m 1 ( $ 42 − ' Tunability of 2.5 π cell lace • Tunability of emi(ance and α εx = 10nm HER KEKB LER LER εxand α: tunability (SuperKEKB) ●In SuperKEKB, emi(ance is minimized by making use of this tunability. εx = 36nm KEKB LER ●α can be negave 1 η α = ds C ∫ ρ VerFcal emi(ance • VerFcal emi(ance (single beam, zero current) ε = κε + (η ) + ε coupling dispersion opening angle – x-y coupling • Machine errors (such as mis-alignment of Q or SX mganets. ) – The coupling correcFon can reduce residual coupling value. – VerFcal dispersion • Machine errors (such as mis-alignment of Q or SX mganets. ) – The dispersion correcFon can reduce residual dispersions. • VerFcal dispersion in design – Fringe field of detector solenoid, verFcal bending magnets – Opening angle of radiaon • Usually negligible ( or ulFmate limit of verFcal dispersion) – εy ~ 1 fm (LEP3) Issues Issues of low emi(ance colliders • VerFcal emi(ance in design • Machine errors – Opcs correcon (Low emi(ance tuning) – OpFcs correcFon with large energy saw-tooth -> skip • Beam-beam blowup -> skip • Intra-beam scaering -> skip • InstabiliFes -> skip – Blowup due to electron clouds • Touschek lifeFme -> skip • Maintenance of beam collision -> skip Issue 1 VerFcal emi(ance in design VerFcal Emi(ance originated from Solenoid Fringe (SuperKEKB) • The verFcal kick by fringe field of detector solenoid could create a large verFcal emi(ance. H 1 1 1 ε ∝ ds ∝ Bx ≅ − xBz$ ≅ − sφBz$ y ∫ ρ3 ρ 2 2 • Efforts to decrease verFcal emi(ance from this process – Adjustment of solenoid axis -> rotaon of Belle detector – Effort to avoid steep slope of solenoid by careful design of compensaon solenoid magnets – Iron shield at the tail part of solenoid field – Improvement of modeling of solenoid field • Latest design values of verFcal emi(ance(zero current) – εy ~ 0.77pm (LER), εy ~1.5pm (HER) 19 Layout of final focus Quads (KEKB/SuperKEKB) QC2 QC1 QC2 KEKB e- e+ Finite-crossing 22 mrad (KEKB) Both beams QCS QCS pass through QCSs. QC2 QC2 IP QC1 SuperKEKB(NBS) Finite-crossing 83 mrad (KEKB-NBS) e+ QC2 e- QC2 QC1 QC1 Synchrotron light QC2 IP can be mitigated. QC1 QC1 QC2 Each beam passes through centers of20 quadrupoles. VerFcal Emi(ance originated from Solenoid Fringe Crossing angle = LER angle + HER angle = 83 mrad proporFonal to φ4 Solenoid axis = angle bisector Energy rao 4/(4+7) We choose 41.5 mrad and the contribution of solenoid fringe is ~4 pm. 2010.3.31 18 Compensaon Solenoids • MagneFc design of compensaon solenoids with iron components – By introducing iron components on the beam lines, the solenoid profile was changed. Without iron components (the model in the last meeting) With iron components 2012/03/14 Issue 2 Opcs correcon (Low emi(ance tuning) Sextuple mis-alingnment Δεy J 1− cos 2πν x cos 2πν y 2 ≅ x ε β β k L 2 2 x ∑ x y ( 2 ) coupling Δy Jy sext 4(cos 2πν x − cos 2πν y ) sext 2 σδ 2 2 + Jz ηx βy (k2L) dispersion 4 sin2 πν ∑ x sext SuperKEKB HER simulaon € νx ~0.53 Random errors with gaussian νy ~0.57 target distribuFon Emi(ance values are average of 100 random samples. Typical value of mis-alignment: ~ 100µm -> We need correcFon. -> low emi(ance tuning Quadruple mis-alingnment Δε y Jx 1− cos 2πν x cos 2πν y 2 ≅ ε β β k L 2 2 x ∑ x y ( 1 ) coupling Δθ Jy quad (cos 2πν x − cos 2πν y ) quad 2 σδ 2 2 + Jz ηx βy (k1L) dispersion sin2 πν ∑ x quad SuperKEKB HER simulaon € νx ~0.53 Random errors with gaussian νy ~0.57 distribuFon Emi(ance values are average of 100 random samples. Typical value of mis-alignment: ~ 100µrad -> Quadrupole rotaonal errors are less serious than the sextuple mis-alignments. Comparison of coupling term and dispersion term νx ~0.53 νy ~0.57 HER(Quad rotaon) Coupling .0010816287630558967 Dispersion 3.748599954860665e-05 HER(Sext verFcal misalignment) Coupling .044995709319378976 Dispersion .0045765442050508375 Dispersion and coupling correcFons SuperKEKB simulaon • Machine errors – Quadruples: rotaonal errors, random rms: 100µrad – Sextupoles: verFcal offset, random rms: 100µm – BPM roll: random rms:10mrad, 20mrad, 30mrad • Method of correcFon – X-y coupling correcFon • Measurement: verFcal leaked orbit by kicks with horizontal DC correctors • Minimize leaked orbit by using skew-Q windings of sextupole magnets – VerFcal dispersion • Measurement: Orbit change with RF frequency shiss • Minimize verFcal dispersion by using skew-Q windings of sextupole magnets Design Target 0.5 10 mrad 0.4 20 mrad 30 mrad 0.3 Demands for roll errors of BPM 0.2 -> less than 20mrad 0.1 Number of entries [arb. unit] 0 2 4 6 8 10 Vertical emittance [pm] More realisFc simulaon SuperKEKB HER • CorrecFons: Closed orbit, x-y coupling, dispersion, beta-beat • Machine errors (random) (except for IR magnets) – Quadrupoles: offset:100µm(H,V), rotaon: 100µrad, strength: 2.5 x 10-4 – Sextuples: offset:100µm(H,V) – BPM: roll:10mrad, resoluFon:2µm • Correctors: DC correctors(H,V), skew-windings of sextuples, Strength of Quadrupoles, horizontal movers of sextupoles Residuals of opFcs funcFons (average of 100 samples) - horizontal dispersion: rms 1.4mm - verFcal dispersion: rms 2.0mm - horizontal beta-beat: 1% - verFcal beta-beat: 2% - verFcal emi(ance 2pm +/- 0.3pm Example of opFcs correcFons (aer correcFons) Comparison of simulaon and measurement (KEKB) #samples = 100 • Machine errors (random) σΔx,rms σΔy,rms (µm) σΔθ,rms σΔK/K,rms (µm) (mrad) Quad 100 meas.*2 meas.*2 1x10-4 Skew Quad 100 meas.*2 meas.*2 1x10-4 HER Sextupole 100 interpolaon 0.1 1x10-4 +100 * σy ~1.2µm BPM*1 100 interpolaon 0.1 (real machine) +100 Δy,rms ~15-18 µm (real machine) *1) BPM ji(er error : = 2 m σΔx, Δy,rms µ ε /ε ~ 1.0% (ε ~24nm) *2) Measured by MG group y x x • Opcs correcons Real machine: – Beta-beat Δηy,rms ~8 mm – X-y coupling – dispersions νx 44.5138 νy 41.5900 Real machine: Δηx,rms ~10 mm KEKB HER Machine Error and OpFcs CorrecFon IP 37 Effects of Tunnel deformaon at SuperKEKB HER Target (7.8pm) VerFcal posiFons of quadrupoles VerFcal emi(ance -If the alignment error around the V-LCC (verFcal local chromacity correcFon) area Tunnel deformaon observed at KEKB is excluded, the verFcal emi(ance can be - A large subsidence has been observed: preserved well below the target value with ~ 2mm/year and sFll in progress. opcs correcons. - In the construcFon period of KEKB (1998), - As for the alignment error of V-LCC, we all magnets were aligned on the same plane. will need a special care. This is a remaining problem. Dispersion Free Steering (DFS) method developed at CERN for LEP • Method – simultaneous correcFon of closed orbit and dispersion MICADO – SVD inversion of response matrix – Correctors: dc corrector magnets DFS Qx = 98.35 E = 100GeV Qy = 96.18 beam εx = 44nm ΔQ = 0.17 DFS Minimum κ ~0.6% (εx =25 nm) The main source of verFcal emi(ance of LEP was residual verFcal dispersion.
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