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T. Pieloni Laboratory of Particle Accelerators Physics EPFL Lausanne and CERN - AB - ABP

Beam-Beam Tune Spectra in RHIC and LHC. T. Pieloni Laboratory of Particle Accelerators Physics EPFL Lausanne and CERN - AB - ABP. In collaboration with: R.Calaga and W. Fischer for RHIC BTF measurements W.Herr and F. Jones for simulation development. Tune spectra depends on:.

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T. Pieloni Laboratory of Particle Accelerators Physics EPFL Lausanne and CERN - AB - ABP

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  1. Beam-Beam Tune Spectra in RHIC and LHC T. Pieloni Laboratory of Particle Accelerators PhysicsEPFL Lausanne and CERN - AB - ABP In collaboration with: R.Calaga andW. Fischer for RHIC BTF measurements W.Herr and F. Jones for simulation development

  2. Tune spectra depends on: • Beam-beam strength • Collision pattern • Filling scheme x ,y = 16.7 m N1= N2 = 1.15 1011 protons/bunch Nb= 2808 bunches/beam Up to 124 beam-beam interactions per turn Fourfold symmetric filling scheme

  3. Bunch to bunch differences: Time structure of the LHC beam • Collision with crossing angle: • Up to 4 head-on collisions • Up to 120 parasitic interactions PACMAN bunch: miss long range interactions Super PACMAN bunch: miss head-on collision • Strong effects (high density bunches) • Multiple BBI (124 BBIs) • Non regular pattern (symmetry breaks) Strong bch2bch differences

  4. Tune spread Multiple Long-range interactions lead to tune shifts Different tunes into collision

  5. Motivation: Beam-Beam main limiting factor for all past (LEP, SPS collider, HERA) and present (Tevatron, RHIC) colliders: complete theory does not exist for multiple bunches beam • Develop a BB model that CAN: • Riproducemulti bunch beams in train structures and multiple BBIs • Predict bunch to bunch differences (diagnostic & optimization) • Investigate BB effects for different operational scenarios (optimization) • Help understanding the phenomena (can lead to possible cures)

  6. Both beam affected (strong-strong): How do we proceed? • BBIs affect and change both beams • Examples: LEP, RHIC, LHC … • Numerical Simulations (COherent Multi Bunch multi Interactions code COMBI): • Analytical Linear Matrix formalism (ALM) • Rigid Bunch Model (RBM) • Multi Particle Simulations (MPS)

  7. I. Analytical Linear Model Beam-Beam Matrix: B E A M 1 bunch1 beam1 bch2, … B E A M 2 bunch1 beam2 bch2, … • Phase advance • Linearized HO or LR B-B kick • Coupling factor Transfer Matrix: Solve eigenvalue problem of 1 turn map Bunches:Rigid Gaussian distributions One Turn Matrix

  8. Eigenvalues:give the system dipolar mode eigen-frequencies (tune): Mode frequencies calculations for bunches Stability studies I. Analytical linear model Solving the eigenvalue problem, like for a system of coupled oscillators: Q Q • Eigenvectorsgive the system oscillating patterns modes: • To understand bunches oscillation patterns • With other simulations to understand bunch to bunch differences

  9. Inputs: Beam 1 = 4 equispaced bunches Beam 2 = 4 equispaced bunches HO collision in IP1-2 and LT I. ALM: more bunches Q1 Q2 Q3 Q4 Q Qp1 Qp2 Q0 Q1 Q2 -mode -mode 5 different Eigen-values 8 differentEigen-vectors Q3 Q2 Q1-mode: all bunches exactly out of phase Q2,3,4-mode (intermediate modes): Q-mode: all bunches exactly in phase Q3 Q4 -mode -mode Q4 Q

  10. II. Rigid Bunch Model • Bunches: rigid objects assumed Gaussian • At BBI: coherent bb kick from the opposite bunch (analytically calculated by • Between BBI: linear transfer (rotation in phase space) and anything else (transverse kick from collimators, kickers…) • Fourier analysis of the bunch barycentres turn by turn gives the tune spectra of the dipole modes

  11. ALM vs RBM: bch to bch differences Inputs: • 5 bch trains • 1 HO + 1 LR Q Q Example Q1 Bunch 1 Q1 Bunch 2 Q1 The eigenvector associated to the Q1 shows that the total effect on the bunches varies from bunch to bunch depending on direct and indirect coupling to a PACMAN bunch Bunch 3 • We can predict bunch to bunch differences in the tune spectra Q1

  12. Symmetry breaking: intensity effects • Inputs: • 4 bch vs 4 bch • HO in IP1, 3, 5 and 7 • intensity variation of b4 • ALM: • All modes visible • Degeneracy break due to symmetry breaking • RBM: • Evidence of direct and indirect coupling to b4 • Degeneracy breaking of coherent modes due to missing bunch b4

  13. Multi Particle Simulations • Bunches: Ntot (104-106) macro particles • BB incoherent kick:solving the Poisson equation for any distribution of charged particles (FMM) or Gaussian approximation : • Between the BBIs:linear transfer (rotation in phase space) and anything else (kickers, collimators, BTF device, etc)

  14. MPS results (I): • Coherent effects: Fourier analysis bunch barycentres turn by turn gives frequency spectra of dipolar modes Effects of: • Landau damping • Symmetry breaking in collision scheme and phase advance • Intensity fluctuations • Bunch to bunch differences • Higher order modes Inputs • 4 bunches 105 macroparticles • 2-4 HO collisions • Run of 32000 turns

  15. MPS results (II): • Incoherent effects: studies of “emittance” (beam sizes) behaviour: Effects of: • Different crossing planes • Noise due to equipment • Offsets in collision • 3 independent studies • 3 different codes (J.Qiang,W.Herr-F.Jones, COMBI)

  16. RBM vs MPS: Super-pacman bunches Inputs: • 4 bch vs 4 bch • HO in IP1, 3, 5 and 7 • intensity variation of b4 RBM: • Evidence of direct and indirect coupling to b4 different tune spectra • Different frequencies and sliding of coherent modes with b4 intensity variations • Landau damping of bunch modes inside their different incoherent spread

  17. 36 bunches per beam each Ntot=104 • 4 Head-on collisions per turn • 64000 turns run (only 5-6 s of LHC) The LHC… More than 10 days CPU time and still…. • Few bunches and only 104 macroparticles • No parasitic interactions included • Only 5-6 sec of LHC (not enough for emittance studies)

  18. COMBI in Parallel mode • Supervisor: • Controls propagation of the bunches • Controls the calculation for the interactions of bunches • Workers: • Store the macro-particle parameters and perform calculation : • Single bunch action • Double bunch action • MPI-protocol • Master/Slave Architecture • Clusters: EPFL MIZAR (448 CPUs) and EPFL BlueGene (8000 CPUs)

  19. Scalability: preliminary results • Very good results up to 64 bunches per beam each of 104 macroparticles, undergoing up to 64 BBIs and 16 rotations, 124+1 CPUs for runs of 64000 turns • Scalability studies on-going 0.7GHz Computing time: • Almost independent of bunch number • Almost independent of the number of interactions 3 GHz

  20. RHIC tune spectra with BTF BTF: tune distributions of colliding beams, amplitude response of the beams as a function of exciting frequency • Beam set of oscillators with transverse tune distribution • External driving force

  21. BTF during store: Beam-Beam BTF MEASUREMENT Fill 7915 RHIC pp Run06

  22. Analytical Linear Model (ALM) Rigid Bunch Model (RBM) Parallel Multi Particle Simulation (MPS) + BTF routine Simulation model: RHIC configuration Proton-Proton run 06 • 2 IPs (6 and 8) • 111 bunches over 360 buckets • 9 SuperPacman bunches (1HO) • 102 Nominal bunches (2 HO) • Different working points for the two beams • Blue: Hor=0.6897 Ver=0.6865 • Yellow: Hor=0.693 Ver=0.697 Simulation tools: COMBI

  23. Rigid bunch model nominal and SP bunch: Horizontal tune spectrum Vertical tune spectrum

  24. Tune spectra w/o BTF • Landau damping of intermediate coherent modes • Two beams decoupled

  25. MPS BTF ON: Nominal Bunch • Number of peaks NOT ok (missing intermediate peak in Horizontal) • Total tune spread ok (model shifted to smaller tunes, in vertical)

  26. MPS BTF ON: SuperPacman bunch • Number of peaks ok, (Hor intermediate mode signature of 1 HOcoll) • Location of peaks ok, (tune distribution shift to higher freq)

  27. Why SuperPacman bunches? • BTF is stripline pickup: single bunch measurement, takes signal from bunch with highest intensity • SuperPacman bunches are the most intense!

  28. BTF ON: SuperPacman bunch • Number of peaks ok (vertical: second peak is present in Blue beam) • Location of peaks ok • H-V coupling not included in model but present in measurements

  29. The LHC tune spectra Beam filling scheme: Run parameters: Collision pattern: • Other action codes: • 4 only long range interactions • 5 excitation (white noise, defined kicks) • 8 BPMs • 9 AC excitation (for BTFs)

  30. The LHC tune spectra: Beam filling scheme: 64 bunches per beam (in train structures) Collision pattern: 4 Head on collisisons 20 LR interactions Simulation code complete! Studies on-going for LHC scenarios

  31. Different beam-beam models were developed to reproduce the effects for the LHC but can be applied to any circular collider We are able to predict bunch to bunch differences We now have a better understanding of multi bunch beam-beam effects COMBI parallel code benchmarked with experimental data, good agreement for RHIC (only 2 HO collisions) Conclusions I

  32. Conclusions II • RHIC BTF measurements are now reproduced and understood (number and location of peaks): • BTF measurements excite coherent modes which are Landau damped • BTF distribution depends on bunch measured: we need to know which bunch is measured and its collision pattern • Only codes which allow multi-bunch beam structures and multiple beam-beam interactions can reproduce the correct picture • Chromaticity and linear H-V coupling effects under study • Simulation campaign for a more “realistic” LHC scenario (124 BBIs and 72 bunch trains up to 2808 bunches) • Study tolerances on fluctuations & beam parameters • Emittance studies of offsets in collision • Effects of impedances, noise, feedback system and measurements devices

  33. CERN: Werner Herr and LHC Commissioning and Upgrade studies TRIUMF: Fred Jones Brookhaven NL: M.Blaskiewicy, R.Calaga, P.Cameron, W.Fischer EPFL: Professors A. Bay, L. Rivkin and A. Wrulich EPFL MIZAR and BG Teams: J. Menu, J.C. Leballeur and C. Clemonce People and laboratories:

  34. Orbit effects Multiple Long-range interactions lead to offsets in collision HV X-ing compensation

  35. BTF during store: Beam-Beam BTF MEASUREMENT Fill 7915 RHIC pp Run06

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