Low emiance 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 emiances of colliders Comparison of emiances of colliders

Future colliders LEP3

Exisng colliders TLEP-H

From Beam Dynamics Newsleer No. 31 Courtesy of F. Zimmermann, H. Burkhardt and Q. Qin F. Zimmmerman

Comparison of emiances of colliders [cont’d]

Future colliders

Exisng colliders

LEP3

TLEP-H Necessity of low emiance in colliers Importance of vercal emiance • In many high luminosity colliders such as KEKB and PEP-II, the machines were operated well above the beam-beam limit. Usually the vercal beam-beam limit is lower than the horizontal one. • Even above the beam-beam limit, the luminosity increases linearly as funcon of the beam currents. • In this situaon, it is commonly considered that the vercal emiance in single beam is not important for the luminosity, since the vercal emiance is determined by the beam-beam blowup. • However, the beam-beam simulaon predicts that the smaller vercal emiance in single beam is important for a higher luminosity. • In some machines such as SuperKEKB, SuperB and TLEP, a very low vercal emiance is necessary to achieve the design beam-beam parameter. Simulaon: KEKB Luminosity vs. Vercal emiance (single beam)

KEKB Achieved: 0.24nm, σy = 1.18µm (LER)

Simulaon by K. Ohmi

εy(nm) • Smaller vercal emiance always gives beer 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 distribuon was assumed. 0 0 1000 2000 3000 4000 5000 turn Smaller vercal emiance gives higher luminosity. Much lower vercal emiance than the design will be needed to K. Ohmi achieve the design luminosity. Methods for low emiances Horizontal emiance • Suppress radiaon excitaon – Photon spectrum (longer bending magnets) – Reduce the integral of H • Low emiance lace – phase advance of FODO cell, special lace • Enhance radiaon damping – Damping wiggler – Damping paron 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. • Emiance and α (momentum compacon) 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 emiance and α

εx = 10nm HER KEKB LER LER

εxand α: tunability (SuperKEKB)

●In SuperKEKB, emiance is minimized by making use of this tunability. εx = 36nm KEKB LER ●α can be negave

1 η α = ds C ∫ ρ Vercal emiance

• Vercal emiance (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 correcon can reduce residual coupling value. – Vercal dispersion • Machine errors (such as mis-alignment of Q or SX mganets. ) – The dispersion correcon can reduce residual dispersions. • Vercal dispersion in design – Fringe field of detector solenoid, vercal bending magnets – Opening angle of radiaon • Usually negligible ( or ulmate limit of vercal dispersion)

– εy ~ 1 fm (LEP3) Issues Issues of low emiance colliders

• Vercal emiance in design • Machine errors – Opcs correcon (Low emiance tuning) – Opcs correcon with large energy saw-tooth -> skip • Beam-beam blowup -> skip • Intra-beam scaering -> skip • Instabilies -> skip – Blowup due to electron clouds • Touschek lifeme -> skip • Maintenance of beam collision -> skip Issue 1 Vercal emiance in design Vercal Emiance originated from Solenoid Fringe (SuperKEKB) • The vercal kick by fringe field of detector solenoid could create a large vercal emiance. H 1 1 1 ε ∝ ds ∝ Bx ≅ − xBz$ ≅ − sφBz$ y ∫ ρ3 ρ 2 2 • Efforts to decrease vercal emiance 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 vercal emiance(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. Vercal Emiance originated from Solenoid Fringe

Crossing angle = LER angle + HER angle = 83 mrad

proporonal 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 • Magnec 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 emiance 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 distribuon Emiance values are average of 100 random samples.

Typical value of mis-alignment: ~ 100µm -> We need correcon. -> low emiance 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 distribuon Emiance 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 vercal misalignment) Coupling .044995709319378976 Dispersion .0045765442050508375 Dispersion and coupling correcons SuperKEKB simulaon • Machine errors – Quadruples: rotaonal errors, random rms: 100µrad – Sextupoles: vercal offset, random rms: 100µm – BPM roll: random rms:10mrad, 20mrad, 30mrad • Method of correcon – X-y coupling correcon • Measurement: vercal leaked orbit by kicks with horizontal DC correctors • Minimize leaked orbit by using skew-Q windings of sextupole magnets – Vercal dispersion • Measurement: Orbit change with RF frequency shis • Minimize vercal 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 realisc simulaon SuperKEKB HER • Correcons: 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, resoluon:2µm • Correctors: DC correctors(H,V), skew-windings of sextuples, Strength of Quadrupoles, horizontal movers of sextupoles

Residuals of opcs funcons (average of 100 samples) - horizontal dispersion: rms 1.4mm - vercal dispersion: rms 2.0mm - horizontal beta-beat: 1% - vercal beta-beat: 2% - vercal emiance 2pm +/- 0.3pm

Example of opcs correcons (aer correcons)

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 jier 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 Opcs Correcon

IP

37 Effects of Tunnel deformaon at SuperKEKB HER Target (7.8pm) Vercal posions of quadrupoles

Vercal emiance -If the alignment error around the V-LCC (vercal local chromacity correcon) area Tunnel deformaon observed at KEKB is excluded, the vercal emiance can be - A large subsidence has been observed: preserved well below the target value with ~ 2mm/year and sll in progress. opcs correcons. - In the construcon 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 correcon 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 vercal emiance of LEP was residual vercal dispersion.

Limit of vercal dispersion in LEP came from vercal dispersion generated by separaon bumps and from the measurement noise.

Phys. Rev. ST Accel. Beams 3, 121001 (2000) Vercal emiance in collision (from luminosity) R. Assmann, P. Raimondi, G. Roy, J.Wenninger Low Emiance Tuning algorism developed for SuperB Correcon with skew-Q followed by vercal correcon + BPM • Method roll esmaon – simultaneous correcon 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) Correcon with vercal correctors

Beam sizes -σy = 16 +/- 0.5 µm (before corrcon) -> 7 +/- 0.5 µm (vercal 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) Esmated BPM roll Difference between SR ring and high energy colliders • IR – Detector solenoid and its compensaon – Low beta inseron – Local chromacity correcon • Size of rings – In larger rings, orbit dri tends to be large. • Accuracy of opcs measurement with orbit dris • Beam-beam interacon – Restricon on choice of working point Summary • Emiances of colliders are compared. • Emiances of proposed ring Higgs factories are somewhat lower than exisng colliders. • Emiance of SuperB and SuperKEKB are much lower in both horizontal and vercal direcon. • In the SuperKEKB design, we found that the fringe field of detector solenoid can be a source of vercal emiance. We succeeded to avoid this problem by design efforts around IP. • The major sources of the vercal emiance are mis-alignments of the magnets. • The key issue is to compensate those machine errors by opcs correcon (low emiance tuning). • The KEKB/SuperKEKB method for opcs correcon is shown. • In the simulaons of SupeKEKB, we will be able to achieve the design vercal emiance (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 simulaon and experiment. • Other methods of correcon, DFS developed at CERN and Low Emiance Tuning algorism developed for SuperB, are shown. • In the future ring colliders, the low emiance will be much more important. To achieve the design vercal emiance of SuperKEKB and SuperB, maybe we need a lot of efforts to compensate machine errors. • Design vercal emiance of ring Higgs factories seems reachable based on experience of SuperKEKB and SuperB. In addion, experiences in low-emiance SR rings and ATF are also important. Spare slides Effect of mis-alignment of SX and Q

• HER(Quad rotaon) – Coupling term: .0010816287630558967 – Dispersion term: 3.748599954860665e-05

• HER(Sextu vercal misalignment) – Coupling term: .044995709319378976 – Dispersion term: .0045765442050508375 SuperKEKB IR opcs Machine Parameters of the KEKB (June 17 2009)

ν s

ν x /ν y * * β x / βy

µ * σ y ξx / ξy

Machine Parameters

2011/July/20 LER HER unit E 4.000 7.007 GeV I 3.6 2.6 A Number of bunches 2,500 Bunch Current 1.44 1.04 mA Circumference 3,016.315 m

εx/εy 3.2(1.9)/8.64(2.8) 4.6(4.4)/11.5(1.5) nm/pm ():zero current

Coupling 0.27 0.28 includes beam-beam

βx*/βy* 32/0.27 25/0.30 mm Crossing angle 83 mrad

-4 -4 αp 3.25x10 4.55x10

-4 -4 σδ 8.08(7.73)x10 6.37(6.31)x10 ():zero current

Vc 9.4 15.0 MV

σz 6.0(5.0) 5(4.9) mm ():zero current

νs -0.0247 -0.0280

νx/νy 44.53/44.57 45.53/43.57

U0 1.87 2.43 MeV

τx,y/τs 43.1/21.6 58.0/29.0 msec

ξx/ξy 0.0028/0.0881 0.0012/0.0807 Luminosity 8x1035 cm-2s-1 SuperKEKB LER Crab waist

NX 12.5 NX 13.0 NY 12.25 NY 12.25 K2 5.95 K2 5.95

IR: lerfqlc_Oide_1137.sad H. Koiso Dynamic aperture with sextupoles for crab waist

0% 50% 100%

with opmizaon with opmizaon

50% 100% before opmizaon before opmizaon

Crab Waist schemeは、SuperKEKBではdynamic aperture減少のため 成り立たないと考えられている。 H. Koiso Importance of low emiance in colliders • Luminosity formula used for usual colliders does not contain emiances directly. $ * ' γ σ y I ξy R L = ± &1 + ) ± ± L 2er σ * β * R e % x ( y± ξ y

* re βy± N ξy± = Rξ± 2πγ σ * σ * +σ * € ± y ( x y ) Luminosity Formula

Beam-Beam parameter Lorentz factor Beam current

Geometrical * reducon factors $ ' (crossing angle, γ σ y I±ξy± R L = ± &1 + ) L hourglass effect) 2er σ * β * R e % x ( y± ξ y

Vercal beta funcon at IP Beam aspect rao at IP

Minimum value is limited by hourglass effect € Importance of low emiance in colliders [cont’d] • Low emiances are directly connected to higher luminosity in some situaons. – The machines which do not reach the beam-beam limit such as TRISTAN or LEP. – Ring Higgs factory like LEP3 demands an extremely small vercal emiance. – To realize “Nano-beam scheme” in SuperKEKB and SuperB, an extremely low (horizontal) emiance is necessary. • Also, an extremely low vercal emiance is demanded to reach the beam-beam limit. – Even in convenonal ring colliders, a smaller vercal emiance brings a higher luminosity. NanoBeam scheme

Head-on collision

σs * hourglass condition: βy >~ σs NanoBeam collision

L

* hourglass condition: βy >~ L In the present design, we do not employ the crab waist scheme. Luminosity and beam-beam parameter with NanoBeam collision Luminosity 1 N N L= p e f R 2 2 col L 2 2π σ zφc σ ye + σ yp Beam-beam parameter

* N * re βyp e re βyeNp ξyp = Rξyp ξye = Rξye 2πγ p σ zφcσ ye 2πγ e σ zφcσ yp

φc effecve effecve σz = σx / sinφc σx = σz sinφc SuperKEKB Machine Parameters

KEKB SuperKEKB (LER) (LER) N− N+

Crossing angle 11mrad 41.5mrad L = * fRL * βx 1.2m 32mm 4πσ z sinφcσ y * βy 5.9mm 0.27mm

εx 18nm 3.2nm

εy 169pm 8.64pm * re βy± N εy / εx 0.94%5 0.27% ξ = R y± 2πγ * sin * ξ± σx* 147 µm 10.1 µm ± σ y (σ z φc +σ y ) σx* effecve - 249 µm

σz ~7mm 6mm

σz effecve - 0.24mm

σy ~1µm 48nm

Very low emiances both in horizontal and vercal direcons. F.Zimmermann

Higgs Factory LEP3 Vercal emiance in LEP3

r β * N ξ = e x±  x± 2 * * * πγ± σ x (σ x +σ y )

* * * εy r β N βy = βx ξy± = ξx± ξ = e y±  ε y± 2 * * * x πγ± σ y (σ x +σ y )

* * re βy± N Hourglass condion β ≥ σ ξy = R y z ± 2 * * * ξ± πγ± σ y (σ x +σ y )

A small vercal emiance (εy/εx) is needed to achieve the target ξy with a small βy*. Specific luminosity of KEKB w/ crab cavies

KEKB was operated well above the beam-beam limit.