Damping RingsLesson 8 e+ e- Circular CollidersS. Guiducci, INFN-LNFSeventh International Accelerator School for Linear Colliders

Hosted by Raja Ramanna Centre for Advanced Technology27 November 8 December 2012

Version 1 16-Nov-12OutlineBasics concepts of circular colliders: luminosity tune shiftsMain design criteria and challenges of the high luminosity and high energy colliders including: different collision schemesluminosity optimizationbeam lifetimesexamples of colliders achievements and design choices for future colliders

23World e+e- colliders luminosityB-FactoriesF-FactoriesFuture Colliders

SuperFactoriesFactoriesLinear collidersSuperBWorld e+e- colliders luminosity plotTwo regions:High luminosity frontierFactories, high precision physics measurementsHigh energy frontierDiscovery measurementsBefore HiggsLEP2 latest circular colliderNext is a linear collider ILC or CLICAfter LHC Higgs discovery at E = 126 GeVMany proposals for a Higgs Factory circular collider (still at brainstorming level)4A Circle?At Snowmass 2001, all options for after-the-LHC were on the table: Linear e+e-Circular e+e-VLHCMuon colliderHigh intensity proton source (aka Proton Driver)In the following years, ICFA played a leading role in making the choice:The next one would be an e+e- colliderIt would be a linear e+e- colliderIt would be a cold linear e+e- colliderAnd the world HEP community followed faithfullyHowever, the debate seemed to come back again after July 4, 2012:The discovery of a Higgs boson may justify a dedicated Higgs FactoryThe low Higgs mass (126 GeV) makes a circular Higgs Factory possibleEven a warm Higgs factory is not bad5Weiren Chou, HF2012, Accelerators for a Higgs Factory, Fermilab, 14-16 November 20126Comparison Table Circular Higgs Factories

Weiren Chou, Accelerators for a Higgs Factory, Fermilab, 14-16 November 2012LuminosityThe Luminosity L is a measure of the probability of particle encounters per unit area per second in a collision processGiven the cross section of a physics process sphys the counting rate of a physics event is

R [s-1] = sphys [cm-2] L [cm-2s-1]

7For head-on collisions, bunched beams of opposite charge, Gaussian charge distributions, L can be written as:

fcoll = nbf0 = collision frequency nb= number of bunches, f0=revolution frequencyN+, N- number of particles/bunch s*x, s*y transverse beam sizes at Interaction Point (IP)4ps*x s*y area of colliding beams

To get high luminosity:Increase the collision frequency Increase the bunch densityLuminosity8

For head-on collisions, bunched beams of opposite charge, Gaussian charge distributions, L can be written as:

fcoll = nbf0 = collision frequency nb= number of bunches, f0=revolution frequencyN+, N- number of particles/bunch s*x, s*y transverse beam sizes at Interaction Point (IP)4ps*x s*y area of colliding beams

To get high luminosity:Increase the collision frequency Increase the bunch density butLuminosity9

Beam-beam effects pose a limitation on the maximum achievable bunch densityBeam-beam effectsBeam-beam effects pose a limitation on the maximum achievable bunch densityParticles in a bunch are strongly affected by the nonlinear field of the counter rotating bunchesIncreasing the bunch density produces beam blow-up and particle lossesA measure of the strength of the beam-beam interaction is given by the linear beam-beam tune shift xx, xyIt exists an empirical upper bound on xx, xy10Achieved beam-beam tune shifts11From ICFA Lepton Colliders Database v8 2005 (M. Biagini)KEKB has achieved xx = 0.127/0.122, xy = 0.129/0.090 and L = 210.8 1032 cm-2/sAchieved peak luminosities12The previous table is not up to date but is useful since it lists many useful parametersHere are the updated numbers for the peak luminositiesM. Zobov, IPAC10

0.8 x 103312Beam-beam tune shift Bassetti - Erskine formulaThe electric field of a gaussian bunch with N particles seen by a test particle in collision can be expressed in terms of the complex error function:

For relativistic particles the electric and magnetic field are equalThese expressions of the fields can be used in simulation programs to evaluate the beam-beam effects with realistic beam distributionsThe beam-beam interaction at large amplitudes is highly nonlinearFor small amplitude particles it is characterized by a quadrupole-like force with focal length:

The beam-beam tune shift is the first order approximation to the betatron tune change given by: xx,y = b*x,y Kx,y /(4p)

13

M. Bassetti, G. A. Erskine CERN-ISR-TH/80-06

Beam-beam tune shiftThe beam-beam tune shift is given by:

Inserting in the luminosity formula we get

For flat beams and14

Beam-beam tune shiftAssume both tune shifts equal to the limit value i.e. kb=k

At the b-b limit to further increase luminosity we can: Increase the current and the emittance keeping the tune shift constantCurrent is limited by the RF power available, vacuum system limits and beam instabilitiesEmittance is limited by vacuum chamber aperture and dynamic apertureReduce by with challenges on the IR design and dynamic apertureMinimum by is limited by the hourglass effect

15

In the drift near the IP: by(s) = by* + s2/by* To squeeze the vertical beam size, and increase Luminosity, by* at IP must be decreasedThis is efficient only if at the same time the bunch length is shortened to sz by otherwise particles in the head and tail of the bunches will collide at a larger by

16Hourglass effect: why short bunches?Bunch length by*00,020,040,060,080,1-0,02-0,0100,010,02s (m) 1 mm 5 mm 2 cmLow by insertion17L* is the length of the drift between the IP and the first QD quadrupole focusing in the vertical planeb(s) = b* + s2/b* bmax L*2/b*DAFNEL*=0.3 mb*= 6 mmbmax 15 m

QD quadrupolegradient = 26 T/mlength = 0.25 m

SuperBL*=0.52 mb*= 0.21 mmbmax 1700 m

QD quadrupolegradient = 100 T/mlength = 0.3 m DAFNE - Siddharta IRSuperconductingPermanent Magnet18SuperB Final Focus sectionsSpin rotator optics is replaced with a simpler matching section

IPY-sextX-sextMatchCrabHERMatching section is shorter than HER to provide space for SR optics

IPY-sextX-sextMatch & Spin RotatorCrabLERb* = 26 / 0.25 mm b* = 32 / 0.21 mm P. RaimondiL. Malisheva18Different collision schemesSingle ring, few bunches, few IPs, head-on collisions (Aco, Adone, VEPPII, Spear, Petra, PEP, LEP, BEPC?)Exotic schemes (DCI (4 beams), Doris (first attempt with a vertical crossing angle), VEPP2000 (round beams), CESR (pretzel orbit))Double rings, multibunch, 1 IP, crossing angleSmall Piwinski angle (Factories: PEPII, KEKB, DAFNE, BEPCII)Large Piwinski angle and crab waist (present DAFNE, SuperB, SuperKEKB, BINP t/charm proposal) 1919Single ring - head-on collisionThe number of IPs is 2nb, twice the number of bunchesBeam-beam sets a limit on the maximum tune shift in the ring: more IPs less luminosity per IPTherefore the number of bunches is small, ~18, and the collision frequency is of the order of the revolution frequencyBelow beam-beam limit luminosity is proportional to the square of the particles per bunch N2/byAbove beam-beam limit, luminosity increases linearly with N/byDue to hourglass effect sz byBunch peak current is pushed to the maximum 20Single ring - head-on collisionAt low energy main limitations aresingle bunch instabilities due to the interaction of the bunch e.m. fields with the vacuum chamber (HOM heating, bunch lenghtening, )Large beam emittances requiring large magnetic apertures and large dynamic aperturesAt high energy main limitations come from RF power available and issues related to high synchrotron radiation powerHOM heating and stability issues related to high bunch charge and short bunches 21Double rings crossing angleThe bunches are stored in 2 separate rings crossing at 1 IP with a crossing angleThey travel in the same vacuum chamber in a short region near the IPIn this region the bunches see each other with an offset at a number of parasitic points, at distances from the IP equal to half the bunch distance The tune shift due to the parasitic crossings is inversely proportional to the square of the bunch separation22Double rings crossing angleLuminosity is proportional to the number of bunches L nbBelow bb limit L N2Above bb limit L NTherefore it is convenient to increase number of bunches instead of the particles per bunch N, i.e. increase the average current I = enbN/T0 at constant bunch peak current Ipeak = eN/(2psl) decreasing the impact of single bunch instabilitiesThe limit on maximum nb is the tune shift due to the parasitic crossingsThe limit to the maximum ring current is again RF power, and issues related to high synchrotron radiation At Factories very large currents have been stored with collision frequencies of the order 100 350 MHz

2324M. Zobov, IPAC10Crossing angle and Piwinski angle25q/2

Small Piwinski angle to reduce strength of synchro-betatron resonancesSince generally sx 30 min it is needed Ec/E0 < 0.1h This condition sets a limit on N/(sxsz)45From V. Telnov, arXiv:1203.6563

BeamstrahlungN/(sxsz) < 0.1ha/(3gre2)Lifetime limitationL fcoll N2/(sxsy)LuminosityP fcoll N g4/rD Beam power rD= magnets bending radius

To increase beam lifetime: Reduce N and increase fcoll keeping P constant Reduces L as wellIncrease sx and reduce sy keeping luminosity constant Increases xy (ok if you are below the tune shift limit)Increase the ring energy acceptance High RF voltage Large off energy dynamic aperture: a challange to achieve with the large chromaticity of the low b insertion 46

Lifetime>4h h=3%Simulate and track O(108) macroparticles and check the energy spread spectrum Lifetime computed from the fraction of particles beyond a given momentum acceptance (h)Exponential dependence on h

BS lifetime47TLEP-HBS lifetime for nominal parameters (assuming h=0.04): LEP3: >~ 30 min TLEP-H: ~day >4h for h=0.03, ~4 min for h=0.02

M. Zanetti, HF2012SuperB beam lifetime estimationLifetime (seconds)HER LERRadiative Bhabha290* / 280+380* / 420+Touschek1320420Coulomb Beam-gas30401420Bremsstrahlung72 hrs77 hrs* 1% momentum acceptance assumed+ momentum acceptance calculated with trackingDominated by luminosity itself- all other contributions are much smaller but for the Touschek effect in the LER.Dynamic aperture and momentum acceptance are crucial for the Touschek lifetimededicated Monte Carlo simulation (for all the effects contributing to particle losses) necessary for:lifetime evaluation careful study of backgrounds, horizontal/vertical collimation system design and shieldingswith collimators inserted and IBS included (momentum acceptance calculated with tracking)

-150Position H Collim.Position H Collim.Position secondary H Collim.IPbx, by Dx0Touschek trajectories Total Lifetime220 s(3.7 min) 180 s (3.0 min)M. BoscoloContinuous injectionTo keep the luminosity nearly constant continuous injection at high repetition rate is neededPEP-II had the most powerful injector!49

SuperB Injection system layout

At a luminosity of 1036 cm-2s-1 beam lifetime is limited by Bhabha scattering at IP to ~ 5 minTo keep nearly constant such a high luminosity continuous injection in the two rings of the collider, with high efficiency ~ 99%, is needed:~ 3 1011 e- and e+ per secondBeams from the sources are alternatively stored in a damping ring (DR) reducing the emittances to the very low values requiredPolarized gun (SLAC type) for e-Positron converter Positron linacInjection tracking with beam-beam for SuperB

No beam-beam Crab = 1 Crab = 0.5 Crab = 0

Average over (30001 30100) turns (6 damping times)Average over (1 100) turnsNo beam-beam Crab = 1 Crab = 0.5 Crab = 0Contour plots of the injected beam distribution in the plane of normalized betatron amplitudes. 105 particles were tracked, and their coordinates over 100 consecutive turns were collected to build the distribution. 51D.Shatilov

No BBCW offCW onQuale delle due?

51SuperKEKB Injection system layout52M.Yoshida, T. Higo IPAC12LEP3/TLEP: double ring w. top-up injectionsupports short lifetime & high luminosity

a first ring accelerates electrons and positrons up to operating energy (120 GeV) and injects them at a few minutes interval into the low-emittance collider ring, which includes high luminosity 1034 cm-2 s-1 interaction pointsA. BlondelF. Zimmermann HF2012 SuperB - ultra high luminositySuperB is an asymmetric lepton collider aiming at a luminosity of 1036 cm-2 s-1 at the Y(4S) center of mass energy 10.6 GeVThe target luminosity is ~ two orders of magnitude larger than that achieved by PEP-II (SLAC, USA) and KEKB (KEK, Japan)The leptons are stored in two rings (e+@6.7 GeV, e-@4.2 GeV) intersecting with a crossing angle at the interaction pointInteraction region design is based on crab waist scheme 54Layout @ Tor Vergata University campus55LER Spin RotatorsInjection & RF sectionIP3 ID cells3 ID cellsLinac complex

SuperB project has been approved by the Italian Government as part of the National Research Plan

Will be built by the Cabibbo Lab in the Tor Vergata University campus, just 5 Km away from the INFN Frascati National Laboratories. SuperB-Factory design in a nutshellLow emittance, large Piwinski angleLongitudinal overlap area related to horizontal beam size not to bunch length, so it can be greatly reduced allowing a reduction of:Vertical beta, beam size, hourglass and tune shiftHorizontal tune shift (1D beam-beam)Crab-waist sextupoles at a proper phase with respect to the IP:suppress most of XY resonances tunes area for operation is largerSame Luminosity with lower currents:lower HOM heating less power consumption56Design requirements & challenges (some!)Extremely small emittances, both H and V, comparable to those achieved in the last generation SR sources or planned for linear colliders Damping RingsStrong IP doublets:SC quads in a restricted spaceseparated beams control of background ratesphysical apertureCoupling & chromaticity correction in the IRDynamic aperture with crab sextupoles Control of vibrations at IP Sensitivity to magnets alignment errors Low Emittance TuningTouschek lifetime and IBS emittance growth57Super B-Factories main parametersParameterSuperBSuperKEKBHER (e+)LER (e-)HER (e-)LER (e+)Luminosity (cm-2s-1)10368x1035C (m)1200 3016E (GeV)6.74.187.0074Crossing angle (mrad)6083Piwinski angle20.816.919.324.6I (mA)1900244026003600ex/y (nm/pm) (with IBS)2/52.5/6.24.6/11.53.2/8.6IP sx/y (mm/nm)7.2/368.9/3610.7/6210.1/48sl (mm)5556N. bunches9782500Part/bunch (x1010)5.16.66.59.04sE/E (x10-4)6.47.36.58.14bb tune shift (x/y)0.0026/0.1070.004/0.1070.0012/0.0810.0028/0.088Beam losses (MeV)2.10.862.41.9Total beam lifetime (s)254269332346Polarization (%)08000RF (MHz)476508.9M. E. Biagini IPAC12

AcknowledgementsIn this lesson is described the work of many accelerator physicists since AdA; Ill try to give the references but its impossible to reference allA useful source of information on circular colliders is the ICFA BD Newsletter 48Very interesting and updated material on the new Higgs Factories can be found at the workshop HF2012, Accelerators for a Higgs Factory, Fermilab, 14-16 November 2012Other data and references can be found in the proceedings of the IPAC (and PAC, EPAC, APAC) conferencesThanks to all the contributors and in particular to my colleagues Marica Biagini, Mikhail Zobov and Manuela Boscolo who borrowed me their slides and to Mario Bassetti who introduced me in the field59Thanks to all60This presentation is based on the work of many physicists over many years and on fruitful discussions with many colleaguesSorry for not mentioning everybody in the slides or in the referencesTop level parametersTop Level ParametersCircular e+e- colliderMuon collidergg colliderLEP3TLEPSuper-FermilabIHEP RingSLAC/LBNLMuon-Low LMuon-High LILC-basedCLIC-basedRecirculatingSLC-basedTRISTANSite-fillerRinglinac-basedIHEP-50kmIHEP-80kmILC (x=4.46)ILC (x=1.97)CLIC (x=4.46)CLIC (x=4.46)

Energy (center of mass)GeV240240 (375)240240240240240126126126 (lum. peak)126 (lum.peak)126126132 (max gg)130Luminosity (per IP) 1034 cm-2 s-11510.522.53.8510.0010.010.03 (gg > 125 GeV)0.12 (gg > 125GeV)0.36 (gg > 0.6ECM)0.65 (gg > 0.6ECM)0.06 (gg > 125 GeV)1No. of IP2 (4 )2 (4) 1121122111111No. of Higgs per year (per IP)20k100k13k100k200k5k50k~5k~10k10k to 20k5000 /1e7secSize (length or circumference) km26.781401649.7869.8826.70.30.3~14?~16?912P(wall)MW200200100200300300200100125~100?~100?150?300?100150Polarization e-00080%80%80%80%90%80% e+000 +, -10%10-20% g93% (lum. peak)86% (lum. peak)100%100%90%Energy upgrade limit240100 TeV (pp)24025025024010 TeV10 TeV0.8Ee- (typical)0.8Ee- (typical)?260Technical readiness (no. of years from now)35> 20unknownunknown10151010610

Specific issues requiring further R&DIRTunnelRFunknownunknownRF in B-fieldOprical cavityOptical cavityIRSCRF e- pol gunSR shieldingIRVacuum Muon beam coolingSeed laserSeed laserLaser/FELTapered UV FELRF couplerSR shielding(not extensive)4 MW proton sourceSpreaderRF couplerBunched beam capture/recombinationPolarization energy measurement

Linear e+e-Linear e+e- colliderILCCLIC

CLIC-500CLIC-3000Top Level ParametersEnergy (center of mass)GeV2505003000Luminosity (per IP) 1034 cm-2 s-10.752.35.9No. of IP111No. of Higgs per year (per IP)Size (length or circumference) km3113.248.3P(wall)MW160272589Polarization e-80%80%80% e+30%30%Energy upgrade limit 3TeVTechnical readiness (no. of years from now)20162016Specific issues requiring further R&DCryomodule costPositron targetFFS test at ATF2

Other Important ParametersGeometric luminosity 1034 cm-2 s-1Pinch enhanced luminosity 1034 cm-2 s-10.752.35.9Linac EaccMV/m31.580100Ne (no. of particles per bunch)10^1020.680.372nb (number of bunches per pulse)1312354312Bunch distances0.5540.00050.0005I(beam)mA0.0210Pulse repetition rateHz55050P(beam)MW2.63ex,nmm-mrad102.40.66ey,nmm-mrad0.0350.020.02beta_x IPmm1384beta_y IPmm0.410.10.07sx, IPnm729200~40sy, IPnm7.662.3~1sz, IPmm0.30.0720.044sigma_E IP%0.30.3Energy spread%0.19(e-), 0.15(e+)Full crossing anglemrad1418.620Average number of photons1.1761.32.1dB beam-beam%0.953728Upsilon (max)0.0487Upsilon (average)0.0203

Circular e+e-Circular e+e- colliderLEP3TLEPSuper-FermilabIHEP RingSLAC/LBNLTRISTANSite-fillerRingIHEP-50kmIHEP-80kmTop Level ParametersEnergy (center of mass)GeV240240 (375)240240240240240Luminosity (per IP) 1034 cm-2 s-11510.522.53.851No. of IP2 (4 )2 (4) 11211No. of Higgs per year (per IP)20k100k13k100k200kSize (length or circumference) km26.781401649.7869.8826.7P(wall)MW200200100200300300200Polarization e-000 e+000Energy upgrade limit240100 TeV (pp)240250250240Technical readiness (no. of years from now)35> 20unknownunknownSpecific issues requiring further R&DIRTunnelRFunknownunknownSR shieldingIRVacuum RF couplerSR shielding(not extensive)RF coupler

Other Important ParametersBending radiuskm2.695.41.7536.27.82625Ne1010 per bunch10050 (75)678070608nb (number of bunches)580 (12)8 / beam2265250I(beam)mA7.224.3 (5.4)6.5517.521.37.2E(synch)GeV/turn6.992.1 (9.3)3.510.532.356.99P(synch) per beamMW505022.55051.85050ex,nmm-mrad58702210 (6850)940053213052.83757338553358.12133072410ey,nmm-mrad2312 (34)9.42721.135029354216.67318982390.00beta_x IPmm20020020020028020050beta_y IPmm1112111sx, IPnm7100043000 (63000)890067319600005347918.97sy, IPnm320220 (320)634763002662.64sz, IPmm3.11.7 (2.5)1.22.851.611.5sigma_E, IP%0.230.15 (0.22)0.142.80E-010.130.12Full crossing anglemrad000000Beam lifetime due to radiative Bhabhasec10801920 (3240)1080960600b-b tune shift x0.090.10 (0.05)0.0320.0670.1020.080.036b-b tune shift y0.080.10 (0.05)0.0830.0950.0730.080.07Damping partition number1.511, 1, 21.5, 1, 1.51, 1, 21, 1, 22 (longi.)Longitudinal damping timeturns2657 (13)4511415115RF Voltage GV126 (12)8.31291212Synchrotron oscillation tune0.190.12 (0.12)0.230.1920.3920.3640.135Average number of photons0.60.50 (0.51)3.20.360.50.480.24dB beam-beam%0.030.035 (0.035)0.02 / crossing1.50E-020.0380.0578.74E-05Upsilon0.00090.00150.0138.77E-047.70E-04

Luminosity at 160 GeV CoM 1034 cm-2 s-1525Luminosyt at 91 GeV CoM 1034 cm-2 s-120100Gamma_Lorentz234835exnm-rad4.3eynm-rad2.15E-02Emittance aspect ratio200sigma_E, s.r.%0.2sigma_E, IP (needed acceptance)%2.5Beam lifetime due to beamstrahlungsec900# of cells in arcs800Peak in arcsm55Peak dispersion in arcsm Peak horiz beam size in arcsmm Momentum compaction0.000024RF FrequencyMHz700RF energy acceptance%10

Muon colliderMuon colliderMuon-Low LMuon-High LTop Level ParametersEnergy (center of mass)GeV126126Luminosity (per IP) 1034 cm-2 s-10.0010.01No. of IP22No. of Higgs per year (per IP)5k50kSize (length or circumference) km0.30.3P(wall)MW100125Polarization +, -10%10-20%Energy upgrade limit10 TeV10 TeVTechnical readiness (no. of years from now)1015Specific issues requiring further R&DRF in B-fieldMuon beam cooling4 MW proton sourceBunched beam capture/recombinationPolarization energy measurement

Other Important ParametersBending radiuskm0.040.04Nmu 1010 per bunch200500nb (number of bunches)11ex,nmm-mrad400200ey,nmm-mrad400200beta_x IPmm6040beta_y IPmm6040sx, IPnm200000120000sy, IPnm200000120000sz, IPmm6040sigma_E, IP%0.0030.003Luminosity life timesec0.000660.00066Repetition rateHz1515

gg collidergg colliderILC-basedCLIC-basedRecirculatingSLC-basedlinac-basedILC (x=4.46)ILC (x=1.97)CLIC (x=4.46)CLIC (x=4.46)Top Level ParametersEnergy (center of mass)GeV126 (lum. peak)126 (lum.peak)126126132 (max gg)130Luminosity (per IP) 1034 cm-2 s-10.03 (gg > 125 GeV)0.12 (gg > 125GeV)0.36 (gg > 0.6ECM)0.65 (gg > 0.6ECM)0.06 (gg > 125 GeV)1No. of IP111111No. of Higgs per year (per IP)~5k~10k10k to 20k5000 /1e7secSize (length or circumference) km~14?~16?912P(wall)MW~100?~100?150?300?100150Polarization e-80%80%80%80%90%80% g93% (lum. peak)86% (lum. peak)100%100%90%Energy upgrade limit0.8Ee- (typical)0.8Ee- (typical)?260Technical readiness (no. of years from now)1010610Specific issues requiring further R&DOprical cavityOptical cavityIRSeed laserSeed laserLaser/FELSCRF e- pol gunSpreaderTapered UV FEL

Other Important ParametersDrive electron energyGeV8311080?80?8080Ne1010 per bunch220.40.6815nb (number of bunches per pulse)2860286016942124CW1000bunch distances0.330.330.5(154) x 4(11)0.5(354) x 24(6)51electron I(beam)mA0.0450.0450.110.310Pulse repetition rateHz5510050CW10electron P(beam)MW3.85.08.6508Electron beam ex,nmm-mrad10101.41.456 ey,nmm-mrad0.030.030.050.050.55 beta_x CPmm4.54.565 beta_y CPmm5.36.0100 beta_x IP50.5 beta_y IP0.10.5 sx, CPnm535460400140 sy, CPnm32290.30.3440125 sz, CPmm0.350.350.03200 sigma_E IP%0.22 in ML0.22 in ML0.3510.351