Report

Introduction to Beam-Beam Effects at the LHC Tatiana Pieloni …with a lot of contributions/help from W. Herr What are beam-beam effects? They occur when two beams collide Two types High energy collisions between two particles (wanted) Distortions of beam by electromagnetic forces (unwanted) Unfortunately: usually both go together… What are beam-beam effects? Beams are made of relativistic charged particles represent an electromagnetic potential for other charges Typically: 0.001% (or less) of particles collide 99.999% (or more) of particles are distorted Beam-beam effects At LHC interactions happen at the IP1 IP2, IP5 and IP8 Many different effects and problems Try to understand some of them Two main questions: 1. What happens to a single particle? 2. What happens to the whole beam? Beam-beam effects Beam is a collection of charges Represent electromagnetic potential for other charges Force on itself (space charge) and opposing beam (beam-beam effects) Main limit in past, present and future colliders Important for high density beams i.e. high intensity and/or small beams: high luminosity Luminosity Beam-beam Force Particle&beam motion distorted Focusing quadrupole Opposite Beam Single particle motion and whole bunch motion • Strongest non linearity when beams collide • Complex time dependent force • LHC number of bunches/crossing angles create new situation Beam-Beam Force Lattice defocusing quadrupole Beam-beam force STRONG AND COMPLEX NON LINEAR FORCE NOT AVOIDABLE Particle distributions Static BB force Self-consistent Beam-beam force time dependent force Perturbative approach is not possible for the LHC, LHC Complications MANY INTERACTIONS Num. of bunches : 3.7 m Long range Head-On For 25ns case 124 BBIs per turn: 4 HO and 120 LR LHC Complications PACMAN and SUPER PACMAN bunches 72 bunches …. Pacman: miss long range BBI (120-40 LR interactions) Super Pacman: miss head-on BBI IP2 and IP8 depending on filling scheme Different bunch families: Pacman and Super Pacman PACMAN and SUPER PACMAN bunches SppS Tevatron RHIC LHC Number Bunches 6 36 109 2808 LR interactions 9 70 0 120/40 Head-on interactions 3 2 2 4 Pacman bunches complexity * ** * *** These effects are already visible in the LHC and single bunch diagnostic is essential to understand the full picture! Beam-beam effects Mathematical derivations Single Particle effects: Detuning with amplitude Dynamic Aperture reduction Multiparticle effects: Orbit Effects Emittance effects Coherent oscillations 1) Intuitive Explanation 2) Observations 3) Cures (…where possible) N.B. All effects occur together with Pacman effects …and with any other noise effect in the collider… Short Beam-beam Mathematics General approach in electromagnetic problems Reference[5] already applied to beam-beam interactions in Reference[3, 4, 1] Derive potential from Poisson equation for beam with distribution r Solution of Poisson equation Then compute the fields From Lorentz force one calculates the force acting on test particle with charge q Assuming round Gaussian distribution and integrating we have radial force Beam-beam Force Linear beam-beam parameter x A test particle will receive a radial kick: Linear beam-beam parameter Quantifies the strength of the force but does NOT reflect the nonlinear nature of the force Beam-beam effects Single Particle effects: Detuning with amplitude Dynamic Aperture reduction Multiparticle effects: Orbit Effects Emittance effects Coherent oscillations Detuning with Amplitude for head-on Instantaneous tune shift of test particle when it crosses the other beam is related to the derivative of the force with respect to the amplitude For small amplitude test particle linear tune shift Detuning with Amplitude for head-on Beam with many particles this results in a tune spread Mathematical derivation in Reference [3] using Hamiltonian formalism and in Reference [4] using Lie Algebra Head-on detuning with amplitude and footprints 1-D plot of detuning with amplitude And in the other plane? THE SAME DERIVATION same tune spread FOOTPRINT 2-D mapping of the detuning with amplitude of particles And for long-range interactions? Second beam centered at d (i.e. 6s) •Small amplitude particles positive tune shifts •Large amplitude can go to negative tune shifts Long range tune shift scaling for distances Long-range footprints DQy The picture is more complicated now the LARGE amplitude particles see the second beam and have larger tune shift Separation in vertical plane! And in horizontal plane? The test particle is centered with the opposite beam tune spread more like for head-on at large amplitudes Beam-beam tune shift HO + LR IP5 Head-on + LR with HORIZONTAL separation HO tune footprint + In the horizontal plane long range tune shift In the vertical plane head-on tune shift IP1 Head-on + VERTICAL separation The opposite of IP5 PASSIVE COMPENSATION Qy Qx Footprints Pacman bunches and passive compensation with HV crossing 75 ns spacing 25 ns spacing Reference [7] PASSIVE COMPENSATION to reduce space on tune diagram and avoid resonances When long-range effects become important footprint wings appear and alternating crossing important Tune shift passive compensation HV crossing IP1 and IP5 Reference [7] PASSIVE COMPENSATION reduces Pacman effect Alternating crossing of IP1 and IP5 is a trick to compensate beam-beam long range tune shifts Tevatron Footprints Antiproton bunches footprint (blue) Proton bunches footprint (orange) Working point optimization 15-20% reduced emittance growth over first 15min HEP stores in Tevatron RUN II away from 5th and 12th order resonance Beam-beam effects Single Particle effects: Detuning with amplitude Dynamic Aperture reduction Multiparticle effects: Orbit Effects Emittance effects Coherent oscillations Dynamic Aperture Dynamic Aperture: area in amplitude space with stable motion Reference [6] Stable area reduced by beam-beam resulting in losses and bad lifetime Dynamic Aperture Dynamic Aperture depends on beam intensity and crossing angle Reference [6] Stable area depends on beam-beam parameters choice of parameters is the result of careful study of different effects Dynamic Aperture Dynamic Aperture depends on beta at the IP Reference [6] Interplay of different parameters to reduce losses as for not reducing DA e b a Np As small as possible Not too small As large as possible Defined Dynamic aperture reduction vs tune Dynamic Aperture depends on the working point Reference [8] Working point optimization can help reducing effects Beam-beam effects Single Particle effects: Detuning with amplitude Dynamic Aperture reduction Multiparticle effects: Orbit Effects Emittance effects Coherent oscillations Orbit Effects Long Range Beam-beam interactions lead to orbit effects Long range kick For well separated beams The force has an amplitude independent contribution: ORBIT KICK Orbit can be corrected but we should remember PACMAN effects LHC orbit effects d = 0 - 0.4 units of beam size Orbit effects different due to pacman effects and the many long-range add up giving a non negligible effect Can be measured and calculated very well Reference [7] Moreover can lead to emittance growths HV crossing as passive compensation IP1 and IP5 alternating crossing is a passive compensation for pacman effects VER offset IP5 Reference [7] HV crossing passive compensation •Two low beta experiments (LR effects stronger) •Opposite Azimuth (same pairs colliding) •Bunch to bunch fluctuations small •Similar Optics (strength depends on sep) Tevatron orbit effects Beam-beam single bunch orbit can be well reproduced and measured also in LEP Effects can become important (1 s offset not impossible) LUMINOSITY Deterioration Reference [2] Passive compensations reduces effects and equal beam parameters helps keeping compensation effective Beam-beam effects Single Particle effects: Detuning with amplitude Dynamic Aperture reduction Multiparticle effects: Orbit Effects Emittance effects Coherent oscillations Emittance effects/growth? Emittance growth occurs when small amplitude particles move to larger values (the core of a bunch) and one observes bad lifetimes and bad luminosity lifetime Driving mechanisms BAD Working Point Offset in collision Bad Working point Emittance growth due to small amplitude particles crossing resonances Tevatron experienced some bunches with 15-20% emittance increase over first 15 minutes of HEP stores during RUN II due to some bunches crossing 5th and 12th order Emittance growth due to offsets in collision Offsets at collision Maximum LHC expects 0.4 s offsets at IPs due to long-rang A clear dependency on the offset amplitude has been demonstrated Emittance growth due to offset LHC nominal Intense beams have stronger effect (a.u.) LHC nominal (a.u.) Smaller beams have stronger effect And strong tune dependency stay away from 3rd order resonance Emittance growth vs cures Emittance growth occurs when small amplitude particles move to larger values (the core of a bunch) and one observes reduction of luminosity and bad lifetimes Driving mechanisms Cures: BAD Working Point WP optimization stay away from 13th and 16th order resonance in LHC Reduce LR orbit effects (large d and HV crossing) and WP optimization (away from 3rd order) Try to reduce at minimum any transverse excitation when beams in collision (reduced damper gains) Offset in collision Transverse Noise Beam-beam effects Single Particle effects: Detuning with amplitude Dynamic Aperture reduction Multiparticle effects: Orbit Effects Emittance effects Coherent modes Coherent dipolar beam-beam modes Coherent beam-beam effects arise from the forces which an exciting bunch exerts on a whole test bunch during collision We study the collective behaviour of all particles of a bunch Coherent motion requires an organized behaviour of all particles of the bunch Coherent beam-beam force •Beam distributions Y1 and Y2 mutually changed by interaction •Interaction depends on distributions •Beam 1 Y1 solution depends on beam 2 Y2 •Beam 2 Y2 solution depends on beam 1 Y1 •Need a self-consistent solution Coherent beam-beam effects •Whole bunch sees a kick as an entity (coherent kick) • Coherent kick seen by full bunch different from single particle kick •Requires integration of individual kick over particle distribution •Coherent kick of separated beams can excite coherent dipolar oscillations •All bunches couple because each bunch “sees” many opposing bunches(LR): many coherent modes possible! Simple case: one bunch per beam 0-mode p-mode 0-mode p-mode Turn n Turn n+1 0-mode at unperturbed tune Q0 Tune spread p-mode is shifted at Qp =1.1-1.3 xbb Incoherent tune spread range [0,-x] Qp xbb Q0 Tune • Coherent mode: two bunches are “locked” in a coherent oscillation • 0-mode is stable (mode with NO tune shift) • p-mode can become unstable (mode with largest tune shift) Simple case: one bunch per beam and Landau damping 0-mode p-mode Tune spread Qp xbb Q0 Tune Incoherent tune spread is the Landau damping region any mode with frequency laying in this range should not develop • p-mode has frequency out of tune spread • No Landau damping possible Coherent modes at RHIC Tune spectra before collision and in collision two modes visible If we have 2 Head-on collisions? 4bch vs 4 bch, 2 Head-on collisions IP1 and IP2 Rigid Bunch Simulation Q Multi Particle Simulation Q Q Q Q Q Q Q Many modes appear not all are Landau damped! Modes out of Landau damping range can become unstable And if we add long-range interactions? 5bch train 1Head-on and 1 long-range All possible modes Qp Qs Bunch 1 • Long-range introduce sidebands to main head-on modes • NO Landau damping of LR modes And Pacman effects? Bunch 1 Bunch 3 •Each bunch will have different number of modes and tune spectra Single bunch diagnostic so important What can we done to avoid problems? • Coherent motion requires organized motion of many particles • This possible with high degree of symmetry (avoid equal parameters for two beams) • Possible countermeasures: symmetry breaking Different tunes for two beams Different bunch Intensities Many collisions and coupling with different bunches Different emittances, longitudinal motion… Different Tunes p-mode 0-mode Q-Q0/x Tune split breaks symmetry and coherent modes disappear Analytical calculations in Reference [8] Different bunch intensities For two bunches colliding head-on in one IP the coherent mode disappears if intensity ratio between bunches is 55% Reference[8] We assumed: • equal emittances • equal tunes • NO PACMAN effects (bunches will have different tunes) The LHC will be a very “dirty” collider at nominal configuration! Coherent modes can be visible for few bunches in symmetric configurations!! LHC example 8 fold symmetry Nominal bunch 8 fold symmetry Superpacman bunch For a simplified LHC case: •4 head-on collisions at IP1, IP2, IP5 and IP8 • 4 long-range interactions per IP • Full 8-fold symmetry to enhance coherent modes We should not expect coherent modes for the LHC full configuration! An example: RHIC running with mirrored tunes Proton-Proton Configuration 2 Experiments (IPs 6 and 8) 111 bch/beam with abort gap 9 empty slots (2 different bunch families) 9 SuperPacman bunches (1HO collision) 102 Nominal bunches (2 HO collisions) 2 Bunch Families 2 Frequency spectra What should we expect ? RHIC working points are mirrored respect to diagonal: Beam 1 (Q1,Q2) Beam 2 (Q2,Q1) Same effect than a tune split but both beams have same space on tune diagram Beam Loss and Bad Lifetime: Beam Losses and background: Why? •DA reduction due to beam-beam •Long-range effects •Noise to the beam •Unmatched beams Reference[10] Bad lifetime and Lumi reduction: •Bad working point •Offsets in collision •Transverse noise Beam-beam Limits Beam-beam effects come from two different type of interactions! Pushing the collider performances means reaching beam-beam limits. Limits can come from Head-on interaction or from Long-range and the cures to apply are different and could make worse one or the other! Parameter Head-on Long-range Emittances Larger Smaller Intensity Smaller Smaller b* - Larger WP optimization Find the best Find the best Summary I Single Particle effects: Cures?! Detuning with amplitude WP optimization and HV crossing, beam parameters as equal as possible and filling schemes to equalize collisions Dynamic Aperture reduction Increase LR d, bigger crossing angle, Intensity moderation and careful choice of WP Multiparticle effects: Orbit Effects HV crossing, parameters equal, filling schemes, increase LR separations Emittance effects Avoid bad tunes, increase LR separations, reduce transverse noise Coherent modes Many tricks, but filling schemes many collisions, parameter fluctuations …some comments Beam-beam effects are very important for a collider Past experience and studies explain many features and observations but the LHC will still reserve some surprises (PACMAN effects) Single bunch diagnostic is at the basis of a correct interpretation of the collider performances Beam-beam has many effects and they depend on different parameters. Improving one can make others worse. That’s way a one solution to the problem does NOT always exist! Careful choice of beam parameters if we know the limits will define the best operating scenario Optimization of the machine working point is a first step to control many beam-beam effects Some references: [1] http://cern.ch/Werner.Herr/CAS2009/proceedings/bb_proc.pdf [2]V. Shiltsev et al, “Beam beam effects in the Tevatron”, Phys. Rev. ST Accel. Beams 8, 101001 (2005) [3] Lyn Evans “The beam-beam interaction”, CERN 84-15 (1984) [4] Alex Chao “Lie Algebra Techniques for Nonlinear Dynamics” SLAC-PUB-9574 (2002) [5] J. D. Jackson, “Classical Electrodynamics”, John Wiley & Sons, NY, 1962. [6] H. Grote, F. Schmidt, L. H. A. Leunissen,”LHC Dynamic Aperture at Collision”, LHCProject-Note 197, (1999). [7] W. Herr,”Features and implications of different LHC crossing schemes”, LHC-Project-Note 628, (2003). [8] A. Hofmann,”Beam-beam modes for two beams with unequal tunes”, CERN-SL-99-039 (AP) (1999) p. 56. [9]Y. Alexahin,”On the Landau damping and decoherence of transverse dipole oscillations in colliding beams ”, Part. Acc. 59, 43 (1996). [10] K. Cornelis BB workshop 1999 [11] D. Kaltchev and W. Herr, Dynamic Aperture studies [12] Beam-beam webpage http://lhc-beam-beam.web.cern.ch/lhc-beam-beam/