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Introduction to Beam -Beam Effects at the LHC

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)

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Introduction to Beam -Beam Effects at the LHC

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  1. Introduction to Beam-Beam Effects at the LHC Tatiana Pieloni …with a lot of contributions/help from W. Herr

  2. 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…

  3. 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

  4. 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: What happens to a single particle? What happens to the whole beam?

  5. 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

  6. Particle&beam motion distorted Focusing quadrupole Opposite Beam Single particle motion andwhole bunch motiondistorted • Strongest non linearity when beams collide • Complex time dependent force • LHC number of bunches/crossing angles create new situation

  7. Beam-Beam Force Lattice defocusing quadrupole Beam-beam force STRONG AND COMPLEX NON LINEAR FORCE NOT AVOIDABLE

  8. Particle distributions Static BB force Self-consistent Beam-beamforce time dependent force Perturbative approach is not possible for the LHC,

  9. LHC Complications MANY INTERACTIONS Num. of bunches : 3.7 m r Long range Head-On For 25ns case124 BBIs per turn: 4 HO and 120 LR

  10. 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

  11. PACMAN and SUPER PACMAN bunches These effects are already visible in the LHC and single bunch diagnostic is essential to understand the full picture!

  12. 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…

  13. 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

  14. Beam-beam Force

  15. Linear beam-beam parameter x Linear beam-beam parameter A test particle will receive a radial kick: Quantifies the strength of the force but does NOT reflect the nonlinear nature of the force

  16. Beam-beam effects • Single Particle effects: • Detuning with amplitude • Dynamic Aperture reduction • Multiparticle effects: • Orbit Effects • Emittance effects • Coherent oscillations

  17. 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

  18. 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

  19. 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

  20. 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

  21. Long-range footprints DQy 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 The picture is more complicated now the LARGE amplitude particles see the second beam and have larger tune shift

  22. 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

  23. 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

  24. 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

  25. 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

  26. Beam-beam effects • Single Particle effects: • Detuning with amplitude • Dynamic Aperture reduction • Multiparticle effects: • Orbit Effects • Emittance effects • Coherent oscillations

  27. 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

  28. 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

  29. Dynamic Aperture • Dynamic Aperture depends on beta at the IP Reference [6] • Interplay of different parameters to reduce losses as for not reducing DA

  30. Dynamic aperture reduction vs tune • Dynamic Aperture depends on the working point Reference [8] Working point optimization can help reducing effects

  31. Beam-beam effects • Single Particle effects: • Detuning with amplitude • Dynamic Aperture reduction • Multiparticle effects: • Orbit Effects • Emittance effects • Coherent oscillations

  32. 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

  33. LHC orbit effects 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 d = 0 - 0.4 units of beam size Moreover can lead to emittance growths Reference [7]

  34. HV crossing as passive compensation IP1 and IP5 alternating crossing is a passive compensation for pacman effects VER offset IP5 Reference [7] • Two low beta experiments (LR effects stronger) • Opposite Azimuth (same pairs colliding) • Bunch to bunch fluctuations small • Similar Optics (strength depends on sep) HV crossing passive compensation

  35. 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

  36. Beam-beam effects • Single Particle effects: • Detuning with amplitude • Dynamic Aperture reduction • Multiparticle effects: • Orbit Effects • Emittance effects • Coherent oscillations

  37. 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 • Transverse Noise • …IBS and more of them

  38. 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 Working tune point optimization to reduce effect for the LHC 13th and 16th order could give same effects

  39. Emittance growth due to offsets in collision Offsets at collision Maximum LHC expects 0.4 s offsets at IPs due to long-rang Ds/s0(per turn) A clear dependency on the offset amplitude has been demonstrated

  40. Emittance growth due to offset Smaller beams have stronger effect Intense beams have stronger effect Ds / s0 LHC nominal Ds / s0 LHC nominal (a.u.) (a.u.) And strong tune dependency stay away from 3rd order resonance Reduce orbit effects with passive compensation, interplay with parameters to not enter threshold values and working point optimization to avoid enhancement

  41. Emittance growthvs 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 • BAD Working Point • Offset in collision • Transverse Noise Cures: 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)

  42. Beam-beam effects • Single Particle effects: • Detuning with amplitude • Dynamic Aperture reduction • Multiparticle effects: • Orbit Effects • Emittance effects • Coherent modes

  43. 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 behaviourof all particles of a bunch • Coherent motion requires an organized behaviourof all particles of the bunch • Coherent beam-beam force • Beam distributionsY1 and Y2mutually 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

  44. 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!

  45. Simple case: one bunch per beam 0-mode p-mode 0-mode Turn n p-mode 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 Q0 Tune xbb • 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)

  46. Simple case:one bunch per beam and Landau damping 0-mode p-mode Tune spread Qp Q0 Tune xbb • 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

  47. Coherent modes at RHIC Tune spectra before collision and in collision two modes visible

  48. If we have 2 Head-on collisions? Rigid Bunch Simulation 4bch vs 4 bch, 2 Head-on collisions IP1 and IP2 Q Q Q Q Multi Particle Simulation Q Q Q Q Many modes appear not all are Landau damped! Modes out of Landau damping range can become unstable

  49. And if we add long-range interactions? 5bch train 1Head-on and 1 long-range Q Q All possible modes Bunch 1 • Long-range introduce sidebands to main head-on modes • NO Landau damping of LR modes

  50. And Pacman effects? Bunch 1 Bunch 3 • Each bunch will have different number of modes and tune spectra Single bunch diagnostic so important

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