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 op cs 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
Exis ng 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
Exis ng colliders
LEP3
TLEP-H Necessity of low emi ance in colliers Importance of ver cal 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 ver cal beam-beam limit is lower than the horizontal one. • Even above the beam-beam limit, the luminosity increases linearly as func on of the beam currents. • In this situa on, it is commonly considered that the ver cal emi ance in single beam is not important for the luminosity, since the ver cal emi ance is determined by the beam-beam blowup. • However, the beam-beam simula on predicts that the smaller ver cal emi ance in single beam is important for a higher luminosity. • In some machines such as SuperKEKB, SuperB and TLEP, a very low ver cal emi ance is necessary to achieve the design beam-beam parameter. Simula on: KEKB Luminosity vs. Ver cal emi ance (single beam)
KEKB Achieved: 0.24nm, σy = 1.18µm (LER)
Simula on by K. Ohmi
εy(nm) • Smaller ver cal emi ance always gives be er performance. SuperKEKB beam-beam simula on 1.2e+36 0.25x SuperKEKB design 0.5x 1e+36 1.25x LER HER 2x
1x y 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 distribu on was assumed. 0 0 1000 2000 3000 4000 5000 turn Smaller ver cal emi ance gives higher luminosity. Much lower ver cal emi ance than the design will be needed to K. Ohmi achieve the design luminosity. Methods for low emi ances Horizontal emi ance • Suppress radia on excita on – Photon spectrum (longer bending magnets) – Reduce the integral of H • Low emi ance la ce – phase advance of FODO cell, special la ce • Enhance radia on damping – Damping wiggler – Damping par on 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 la ce (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 compac on) are tunable by changing the pa ern 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 la ce
• 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 nega ve
1 η α = ds C ∫ ρ Ver cal emi ance
• Ver cal 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 correc on can reduce residual coupling value. – Ver cal dispersion • Machine errors (such as mis-alignment of Q or SX mganets. ) – The dispersion correc on can reduce residual dispersions. • Ver cal dispersion in design – Fringe field of detector solenoid, ver cal bending magnets – Opening angle of radia on • Usually negligible ( or ul mate limit of ver cal dispersion)
– εy ~ 1 fm (LEP3) Issues Issues of low emi ance colliders
• Ver cal emi ance in design • Machine errors – Op cs correc on (Low emi ance tuning) – Op cs correc on with large energy saw-tooth -> skip • Beam-beam blowup -> skip • Intra-beam sca ering -> skip • Instabili es -> skip – Blowup due to electron clouds • Touschek life me -> skip • Maintenance of beam collision -> skip Issue 1 Ver cal emi ance in design Ver cal Emi ance originated from Solenoid Fringe (SuperKEKB) • The ver cal kick by fringe field of detector solenoid could create a large ver cal emi ance. H 1 1 1 ε ∝ ds ∝ Bx ≅ − xBz$ ≅ − sφBz$ y ∫ ρ3 ρ 2 2 • Efforts to decrease ver cal emi ance from this process – Adjustment of solenoid axis -> rota on of Belle detector – Effort to avoid steep slope of solenoid by careful design of compensa on solenoid magnets – Iron shield at the tail part of solenoid field – Improvement of modeling of solenoid field • Latest design values of ver cal 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. Ver cal Emi ance originated from Solenoid Fringe
Crossing angle = LER angle + HER angle = 83 mrad
propor onal to φ4
Solenoid axis = angle bisector Energy ra o 4/(4+7)
We choose 41.5 mrad and the contribution of solenoid fringe is ~4 pm.
2010.3.31 18 Compensa on Solenoids • Magne c design of compensa on 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 Op cs correc on (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 simula on
€ νx ~0.53 Random errors with gaussian
νy ~0.57 target distribu on Emi ance values are average of 100 random samples.
Typical value of mis-alignment: ~ 100µm -> We need correc on. -> 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 simula on
€ νx ~0.53 Random errors with gaussian νy ~0.57 distribu on Emi ance values are average of 100 random samples.
Typical value of mis-alignment: ~ 100µrad -> Quadrupole rota onal errors are less serious than the sextuple mis-alignments. Comparison of coupling term and dispersion term
νx ~0.53 νy ~0.57 HER(Quad rota on) Coupling .0010816287630558967 Dispersion 3.748599954860665e-05
HER(Sext ver cal misalignment) Coupling .044995709319378976 Dispersion .0045765442050508375 Dispersion and coupling correc ons SuperKEKB simula on • Machine errors – Quadruples: rota onal errors, random rms: 100µrad – Sextupoles: ver cal offset, random rms: 100µm – BPM roll: random rms:10mrad, 20mrad, 30mrad • Method of correc on – X-y coupling correc on • Measurement: ver cal leaked orbit by kicks with horizontal DC correctors • Minimize leaked orbit by using skew-Q windings of sextupole magnets – Ver cal dispersion • Measurement: Orbit change with RF frequency shi s • Minimize ver cal 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 realis c simula on SuperKEKB HER • Correc ons: Closed orbit, x-y coupling, dispersion, beta-beat • Machine errors (random) (except for IR magnets) – Quadrupoles: offset:100µm(H,V), rota on: 100µrad, strength: 2.5 x 10-4 – Sextuples: offset:100µm(H,V) – BPM: roll:10mrad, resolu on:2µm • Correctors: DC correctors(H,V), skew-windings of sextuples, Strength of Quadrupoles, horizontal movers of sextupoles
Residuals of op cs func ons (average of 100 samples) - horizontal dispersion: rms 1.4mm - ver cal dispersion: rms 2.0mm - horizontal beta-beat: 1% - ver cal beta-beat: 2% - ver cal emi ance 2pm +/- 0.3pm
Example of op cs correc ons (a er correc ons)
Comparison of simula on 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 interpola on 0.1 1x10-4 +100 * σy ~1.2µm BPM*1 100 interpola on 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
• Op cs correc ons 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 Op cs Correc on
IP
37 Effects of Tunnel deforma on at SuperKEKB HER Target (7.8pm) Ver cal posi ons of quadrupoles
Ver cal emi ance -If the alignment error around the V-LCC (ver cal local chroma city correc on) area Tunnel deforma on observed at KEKB is excluded, the ver cal emi ance can be - A large subsidence has been observed: preserved well below the target value with ~ 2mm/year and s ll in progress. op cs correc ons. - In the construc on 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 correc on 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 ver cal emi ance of LEP was residual ver cal dispersion.
Limit of ver cal dispersion in LEP came from ver cal dispersion generated by separa on bumps and from the measurement noise.
Phys. Rev. ST Accel. Beams 3, 121001 (2000) Ver cal emi ance in collision (from luminosity) R. Assmann, P. Raimondi, G. Roy, J.Wenninger Low Emi ance Tuning algorism developed for SuperB Correc on with skew-Q followed by ver cal correc on + BPM • Method roll es ma on – simultaneous correc on of closed orbit, dispersion and x-y coupling (expansion of DFS) – SVD inversion of response matrix – Correctors: corrector magnets, skew-Q, BPM roll
Tested at SLS (PSI) Correc on with ver cal correctors
Beam sizes -σy = 16 +/- 0.5 µm (before corrc on) -> 7 +/- 0.5 µm (ver cal correctors) -> 4.4 +/- 0.4(stat) +/- 0.5 (stat) µm à εy ~ 1.3pm
IPAC2012, TUOAA03 S.M. Liuzzo, M.E. Biagini, P. Raimondi, INFN/LNF, Frasca (Roma) M. Aiba, M. Boge, PSI (Villigen) Es mated BPM roll Difference between SR ring and high energy colliders • IR – Detector solenoid and its compensa on – Low beta inser on – Local chroma city correc on • Size of rings – In larger rings, orbit dri tends to be large. • Accuracy of op cs measurement with orbit dri s • Beam-beam interac on – Restric on on choice of working point Summary • Emi ances of colliders are compared. • Emi ances of proposed ring Higgs factories are somewhat lower than exis ng colliders. • Emi ance of SuperB and SuperKEKB are much lower in both horizontal and ver cal direc on. • In the SuperKEKB design, we found that the fringe field of detector solenoid can be a source of ver cal emi ance. We succeeded to avoid this problem by design efforts around IP. • The major sources of the ver cal emi ance are mis-alignments of the magnets. • The key issue is to compensate those machine errors by op cs correc on (low emi ance tuning). • The KEKB/SuperKEKB method for op cs correc on is shown. • In the simula ons of SupeKEKB, we will be able to achieve the design ver cal emi ance (except for IR magnet alignment errors). We haven’t found any showstopper so far. However, we have to note that there is some discrepancy between simula on and experiment. • Other methods of correc on, DFS developed at CERN and Low Emi ance Tuning algorism developed for SuperB, are shown. • In the future ring colliders, the low emi ance will be much more important. To achieve the design ver cal emi ance of SuperKEKB and SuperB, maybe we need a lot of efforts to compensate machine errors. • Design ver cal emi ance of ring Higgs factories seems reachable based on experience of SuperKEKB and SuperB. In addi on, experiences in low-emi ance SR rings and ATF are also important. Spare slides Effect of mis-alignment of SX and Q
• HER(Quad rota on) – Coupling term: .0010816287630558967 – Dispersion term: 3.748599954860665e-05
• HER(Sextu ver cal misalignment) – Coupling term: .044995709319378976 – Dispersion term: .0045765442050508375 SuperKEKB IR op cs Machine Parameters of the KEKB (June 17 2009)