BeamBeam energy luminosity headon beambeam effects longrange beambeam

Beam-Beam • energy & luminosity • head-on beam-beam effects • long-range beam-beam effects • beam-beam diagnostics • beam-beam compensation 06/25/15 BCM 9

why high(er) energy? • quantum mechanics: de Broglie wavelength l=h/p → examining matter at smaller distance requires higher momentum particles • many of the particles of interest to particle physics are heavy → high-energy collisions are needed to create these particles 06/25/15 BCM 9

colliding beams centre-of-mass energy: beam hits a “fixed target” two beams collide colliding two beams against each other can provide much higher centre-of-mass energies than fixed target! 06/25/15 BCM 9

evolution of beam energy over 70 years new technologies: Nb-Ti SC magnets colliders repeated jumps from saturating to emerging technologies storage rings have been the frontrunner technology for the last ~50 years P. Lebrun 06/25/15 BCM 9

1 st cyclotron, ~1930 E. O. Lawrence 11 -cm diameter 1. 1 Me. V protons LHC, 2008 9 -km diameter 7 Te. V protons after ~80 years ~107 x more energy ~105 x larger 06/25/15 BCM 9

luminosity R= s L luminosity reaction rate cross section C. Amsler et al. , Physics Letters B 667, 1 (2008) stot~ from cosmic rays LHC s. Higgs ~ 30 pb 06/25/15 BCM 9 100 mbarn ~ 10 -25 cm 2 sinelastic~ 60 mbarn~ 6 x 10 -26 cm 2 → with 300 fb-1 LHC produces ~ 10 million Higgs

Luminosity N Number of particles per bunch nb Number of bunches f Revolution frequency σ* Beam size at interaction point F Reduction factor due to crossing angle ε Emittance εn Normalized emittance β* Beta function at IP Round beams, beam 1 = beam 2 06/25/15 BCM 9 7 M. Lamont

hadron-collider peak luminosity vs. year Courtesy W. Fischer LHC run 1 (2012 -13) accumulated more integrated luminosity than all previous hadron colliders together! 06/25/15 BCM 9

Beam-Beam Effects • head-on effects – tune spread & dynamic beta function – drop in beam lifetime, emittance growth – beam-beam limit • beam sizes must be matched at IP • sensitivity to tune modulation – coherent and incoherent effects, coupled modes – beamstrahlung, spin precession & depolarization • long-range effects – bunch-to-bunch orbit & tune differences • beam-beam diagnostics (deflection, v. d. Meer scans) • various compensation techniques – collisions scheme (alt. crossing, crab cavity, crab waist) – Tevatron & RHIC Electron Lenses – wire compensation (LHC, DAFNE, SPS tests) 06/25/15 BCM 9

head-on beam-beam effect head-on beam-beam collision in the LHC 06/25/15 BCM 9

(nonlinear) beam-beam force center of opposing beam at small amplitude similar to effect of defocusing quadrupole for pure head-on collision 06/25/15 BCM 9 for single collision (nominal LHC ~0. 0033

vertical tune Qy beam-beam tune spread from head-on collisio particles in the transverse tail tune spread DQy maximum acceptable tune spread is limited by resonances n. Qx+m. Qy=p tune footprint particles at the center of the bunch tune spread DQx up to resonance order |n|+|m|~13 06/25/15 BCM 9 horizontal tune Qx

vertical tune Qy particles in the transverse tail tune spread DQy 1 collision / turn particles at the center of the bunch 2 collisions / turn 06/25/15 BCM 9 horizontal tune Qx

beam-beam limit in e+e- colliders J. Seeman luminosity and vertical tune-shift parameter versus beam current for various electron-positron colliders; the tune shift saturates at some current value, above which the luminosity grows linearly 06/25/15 BCM 9

beam-beam limit in e+e- colliders with strong radiation damping R. Assmann 06/25/15 BCM 9 damping decrement per IP

beam-beam limit in hadron colliders “Regarding the HO tune shift limit, it is not possible to extract a general rule since it depends strongly on the observable chosen to define it (experiment background, luminosity lifetime) and on the noise and tune stability of the single machine…” O. Brüning LHC and Tevatron have reached total beam-beam tune shifts of n. IP x x ~0. 02 -0. 03 with acceptable lifetimes and emittance behavior Simulations by K. Ohmi (IPAC 12) suggest a hurdle at n. IP x x ~0. 05 if there is a crossing angle or transverse offset, and values up to 0. 2 without the latter two 06/25/15 BCM 9

dynamic beta function & dynamic emittance IP beta function in collision (single IP) dynamic emittance in e+e- storage ring correction computed by A. V. Otboyev and E. A. Perevedentsev, PRST-AB 1999 → dynamic beam size s~(b*e)1/2 tune slightly above 0. 5 is preferred smaller beam size exploited, e. g. , at KEKB e/e 0 σ/σ0 x 0=0. 05 β/β 0. M. Furman 06/25/15 BCM 9 Q

beam-beam effects in linear colliders 06/25/15 BCM 9

beam-beam disruption at the SLC at highest luminosity more than 100% luminosity increase 06/25/15 BCM 9

beamstrahlung synchrotron radiation emitted during the collision in the strong field of the opposing beam 06/25/15 BCM 9

beamstrahlung effects for a highest-energy e+e- storage ring two effects: (1) increased energy spread and bunch lengthening due to the additional synchrotron radiation with large quantum fluctuation (2) reduction of the beam lifetime due to (rare) emission of hard photons 06/25/15 BCM 9

beam-beam depolarization storage-ring collider: experiments at LEP x/IP=0. 04 x/IP=0. 015 beam-beam depolarization does not scale with the linear beam-beam tune shift; other parameters like spin tune and synchrotron tune also important linear collider: spin precession in the magnetic field of the opposing beam and beamstrahlung spin-flip radiation during the collision 06/25/15 BCM 9

long-range collisions crossing angle avoids parasitic collisions; long-range collisions on either side of IP; 06/25/15 BCM 9

beam-beam deflection vs. offset head-on collision long-range collision (30 of these for each head-on!) 06/25/15 BCM 9

LHC: 4 primary IPs and 30 long-range collisions per IP 120 in total partial mitigation by alternating planes of crossing at IP 1 & 5 etc.

Long-Range Beam-Beam Collisions • perturb motion at large betatron amplitudes, where particles come close to opposing beam • cause ‘diffusive aperture’ (Irwin), high background, poor beam lifetime • increasing problem for SPS, Tevatron, LHC, . . . that is for operation with larger # of bunches SPS Tevatron Run-II LHC #LR encounters 9 70 120

experience from Tevatron Run-II “long-range beam-beam interactions in Run II at the Tevatron are the dominant sources of beam loss and lifetime limitations of anti-protons …” (T. Sen, PAC 2003) LR collisions reduce the dynamic aperture by about 3 s to a value of 3 -4 s; little correlation between tune footprint and dynamic aperture drop in ey for first 4 pbar bunches after injection; asymptotic emittance is measure of their dynamic aperture

LR vertical crossing head-on LR horizontal crossing LHC tune “footprint” due to head-on & long-range collisions in IP 1 & IP 5 (Courtesy H. Grote)

total LHC tune “footprint” for regular and “PACMAN” bunch (Courtesy H. Grote) LR collisions ‘fold’ the footprint!

residual long-range effects – bunch-by-bunch orbit differences LHC example: Luminous centroid position in ATLAS detector. Top (bottom) Figure shows the vertical (horizontal) luminous region position and a zoom over the first four trains of 36 bunches. M. Schaumann, R. Alemany

residual long-range effects – bunch-by-bunch tune differences A. Jansson Tevatron example: The individual pbar tunes at collisions measured by the 1. 7 GHz Schottky shows (a) first/last bunch of each train has a significantly different vertical/horizontal tune than those in the middle of the train (b) 3 -fold symmetry.

luminosity loss due to crossing angle Piwinski angle Geometric luminosity loss as a function of the Piwinski angle.

crab crossing “Crab-crossing” configuration in the crossing plane

HL-LHC compact crab-cavity prototypes LARP-BNL LARP-ODUJLAB Uni. Lancaster-CICERN

crab-waist crossing for flat beams regular crossing M. Zobov, P. Raimondi, et al. crab waist vertical waist position in s varies with horizontal position x • allows for small by* • and avoids synchrobetatron resonances

generation and effect of crab waist CW sextupoles on CW sextupoles off simulated luminosity performance crab waist was invented for Italian Super. B now option for FCC -ee

luminosity levelling - LHC Luminosity decay in ATLAS and CMS and levelled luminosity at LHCb – typical example from LHC run 1 (Courtesy C. Gaspar).

LHC event pile up in 2012 detector design value Recorded luminosity versus the mean number of interactions per crossing at the CMS detector during the 2012 LHC run.

luminosity levelling – HL-LHC upgraded ATLAS & CMS detectors can handle up to 140 -200 events per crossing (but not more)

beam-beam diagnostics • beam-beam deflection scans • van-der-Meer scans • beamstrahlung • …

luminosity optimization – van-der-Meer scans S. White bump calibration! Calibration scan performed in the horizontal plane for IP 5 (LHC 2010) Same horizontal scan in IP 5 shown in logarithmic scale with pure Gaussian fits.

beam-beam deflection - formulae single-particle deflection for round Gaussian beams: single-particle deflection for flat Gaussian beams (sx>sy): V. Ziemann, “Beyond Bassetti and Erskine: Beam-beam deflections for non-Gaussian beams”, 1991

beam-beam deflection scan at SLC Observation of beam-beam deflections at the interaction point of the SLAC Linear Collider; P. Bambade, R. Erickson, W. A. Koska, W. Kozanecki, N. Phinney, and S. R. Wagner; Phys. Rev. Lett. 62, 2949 – Published 19 June 1989

beam-beam deflection with flat beams SLC vertical beam-beam deflection scan at low current, demonstrating a single-beam size of about 410 nm (1994/95)

beam-beam deflection scans at LEP Beam-beam deflection scan for a beam energy of 65. 1 Ge. V. Beam-beam deflection scan at a beam energy of 68. 1 Ge. V. The bunch currents are more than twice as large/ Luminosities predicted with beam sizes extracted from the fits agreed well with direct measurements by the experiments.

beamstrahlung diagnostics detected on beamstrahlung monitors inferred from downstream BPM signal number of beamstrahlung photons & average energy loss; sensitive to individual sx and sz L. Hendrickson knob radiative Bhabha a schematic cut away drawing of the SLC beamstrahlung detector. Pelectron beam pipe, C-converter, M 1, 2, 3 - mirrors, PMT-photomultipliers (Bonvicini, Field, Minten) beamstrahlung signal dithering process for SLC luminosity optimization

beam-beam compensation • nonlinear magnets (octupoles etc. ) • 4 -beam collisions • wire compensation • electron lenses

b-b compensation with octupole resonance 10 Qy=96 in amplitude plane for (a) zero machine nonlinearity (b) positive nonlinearity (c) negative nonlinearity VEPP-4 e+e- collider 1980’s A. Zholents positron loss rate and specific luminosity during scan across the resonance 10 Qy=96 with (a) positive and (b) negative nonlinearity Octupole magnets were used for compensating, or adding to, the cubic nonlinearity in the beam-beam force at the VEPP-4 e+e- collider (Novosibirsk, Russia). A severalfold reduction of electron halo loss rate was demonstrated at optimal octupole current. Compensation efficiency was strongly dependent on the machine tune.

Long-Range Beam-Beam Compensation for the LHC • To correct all non-linear effects correction must be local. • Layout: 41 m upstream of D 2, both sides of IP 1/IP 5 current-carrying wires Phase difference between BBLRC & average LR collision is 2. 6 o (Jean-Pierre Koutchouk)

all 30 LR collisions around one IP occur at nearly same betatron phase (spread<2 o) one current-carrying wire parallel to beam can compensate their effect, field at large distance is ~1/r like the LR beam field distance wire-beam ~ average LR beam-beam separation wire current x length: Iw lw = Nb n. LR e c

simulated LHC tune footprint with & w/o wire correction • . 16 s • . 005 s • . 016 s Beam separation at IP (Jean-Pierre Koutchouk, LHC Project Note 223, 2000)

wire compensator prototype at CERN SPS

DAFNE wire compensator C. Milardi, et al, Proc. EPAC’ 06 (2006), p. 2808 DAFNE e+ beam current and lifetime as a function of time: wires on (red) and wires off (cyan); the non-local wire correction led to a significant increase of the beam and luminosity lifetimes (>30%)

4 -beam collisions DCI (late 1970’s): 3 -beam configuration: a factor of 5 of the beam-beam limit but no improvement of performance in 4 -beam configuration - excitaiton of nonlinear beam-beam resonances together with coherent signalsin qualitative agreement with a prediction [Derbenev, . 1973] that the coherent beam-beam limit is not improved by the 4 -beam system, due to the cancellation of the beam driven Landau damping. Scheme of four beam collisions (e+e-) in the DCI storage ring J. E. Augustin et al, Vol. 2, Proc. 7 th Int. Conf. High Energy Accelerators (1969), p. 113 ; Orsay Storage Ring Group, Proc. IEEE PAC’ 79 (San Francisco, 1979) ; Ya. Derbenev, SLAC TRANS-151,

Tevatron electron lens (TEL) Layout of the Tevatron Electron Lens (TEL) E. Tsyganov et al. , SSCL-519, (1993); Phys. Part. Nuclei 27 (1996), p. 279 V. Shiltsev et al. , Phys. Rev. Lett. 99 (2007), 244801; V. Shiltsev et al. , New Journ. Phys. 10 (2008), 043042.

TEL in operation TEL was used to correct the primary beam-beam limitation of the Tevatron performance related to a tune spread along the bunch train. By using the lenses as pulsed bunch-bybunch focusing elements, the tunes of the normal and Pacman bunches can be equalized, leading to a noticeable gain in lifetime. Intensity lifetime of proton bunch 12 when the TEL is consequently switched off and on during the Tevatron highenergy physics collision store. V. Shiltsev et al. , Phys. Rev. Lett. 99 (2007), 244801; V. Shiltsev et al. , New Journ. Phys. 10 (2008), 043042.

RHIC b-b compensation w e-lenses Basic idea: • beam-beam collisions with positively charged beam • add collision with a negatively charged beam – with matched intensity and same amplitude dependence Compensation of nonlinear effects: • e-beam current and shape => reduces tune spread • ∆ψx, y = kπ between p-p and p-e collision => reduces resonance driving terms Expect up to 2 x more luminosity I. Ben Zvi, W. Fischer

RHIC electron lenses Layout of the two electron lenses in RHIC’s IR 10. There are three beams in each lens - the two proton beams and the electron beam acting on one of the proton beams. The proton beams are vertically separated.

RHIC electron lenses – set up w beam alignment of the electron and proton beams using electron backscattering detector (e. BSD) beam transfer function (BTF) measurements as a function of tune for various e-beam currents. X. Gu BTF measurements for various ebeam sizes.

RHIC electron lenses at work - 2 V. Schoefer previous limit strong emittance growth at ξ/IP= 0. 006. with electron lenses ξ/IP= 0. 011; achieved routinely without large emittance growth average and peak luminosity doubled! Peak and average luminosity for RHIC stores as a function of bunch intensity. Peak luminosity in Run 12 saturated at 50 × 1030 cm− 1 s− 1 due to beam-beam induced emittance blowup. Electron lens compensation allowed higher luminosity in Run 15

integrable optics with e-lenses electron lenses may provide a way to implement nonlinear integrable lattices in accelerators; experiments to verify these concepts are planned in the Fermilab Integrable Optics Test Accelerator nonlinear Mc. Millan kick (1967)) layout of the electron lens in the IOTA ring G. Stancari

summary • beam-beam effects constrain collider design parameters and limit collider performance • new effects, like beamstrahlung and disruption, appear at high energy or smaller spot sizes – important as energy and luminosity of colliders are increasing • various mitigation and compensation schemes are pursued (crab cavities and wires at HL-LHC, e-lenses for Tevatron and RHIC, crab waist for FCC-ee)

all course material will be posted on the web site http: // web. cern. ch/be-abp-frankz-uspas 15