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

T. Pielonip.2 Tune spectra depends on:  Beam-beam strength  Collision pattern  Filling scheme  x,  y = 16.7  m N 1 = N 2 = protons/bunch N b = 2808 bunches/beam Up to 124 beam-beam interactions per turn Fourfold symmetric filling scheme

T. Pielonip.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

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

T. Pielonip.5 Motivation: Develop a BB model that CAN:  Riproduce multi 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) 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

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

T. Pielonip.7 One Turn Matrix Transfer Matrix: Phase advance Linearized HO or LR B-B kick Coupling factor Bunches: Rigid Gaussian distributions Beam-Beam Matrix: I.Analytical Linear Model BEAM1BEAM1 BEAM2BEAM2 bunch1 beam1 bunch1 beam2 bch2, … Solve eigenvalue problem of 1 turn map

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

T. Pielonip.9 5 different Eigen-values 8 different Eigen-vectors Inputs: Beam 1 = 4 equispaced bunches Beam 2 = 4 equispaced bunches HO collision in IP1-2 and LT Q  1 -mode: all bunches exactly out of phase Q  2,3,4 -mode (intermediate modes): Q  -mode: all bunches exactly in phase Q0Q0 Qp1Qp1 Qp2Qp2  -mode   -mode  -mode Q1Q1 Q2Q2 Q3Q3 Q4Q4 QQ Q2Q2 Q3Q3 Q3Q3 Q4Q4 QQ Q1Q1 I.ALM: more bunches Q2Q2 Q4Q4

T. Pielonip.10 II.Rigid Bunch Model  Fourier analysis of the bunch barycentres turn by turn gives the tune spectra of the dipole modes  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…)

T. Pielonip.11 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 We can predict bunch to bunch differences in the tune spectra Example Q  1 Bunch 1 Bunch 2 Bunch 3 Q1Q1 Q1Q1 Q1Q1 ALM vs RBM: bch to bch differences QQ QQ Inputs: 5 bch trains 1 HO + 1 LR

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

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

T. Pielonip.14 MPS results (I):  Coherent effects: Fourier analysis bunch barycentres turn by turn gives frequency spectra of dipolar modes Inputs 4 bunches 10 5 macroparticles 2-4 HO collisions Run of turns Effects of:  Landau damping  Symmetry breaking in collision scheme and phase advance  Intensity fluctuations  Bunch to bunch differences  Higher order modes

T. Pielonip.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)

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

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

T. Pielonip.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)

T. Pielonip.19 Scalability: preliminary results Computing time: Very good results up to 64 bunches per beam each of 10 4 macroparticles, undergoing up to 64 BBIs and 16 rotations, CPUs for runs of turns Scalability studies on-going  Almost independent of bunch number  Almost independent of the number of interactions 0.7GHz 3 GHz

T. Pielonip.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

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

T. Pielonip.22 I.Analytical Linear Model (ALM) II.Rigid Bunch Model (RBM) III.Parallel Multi Particle Simulation (MPS) + BTF routine Simulation tools: COMBI 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= Ver=  Yellow: Hor=0.693 Ver=0.697 Simulation model:

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

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

T. Pielonip.25 MPS BTF ON: Nominal Bunch 1)Number of peaks NOT ok (missing intermediate peak in Horizontal) 2)Total tune spread ok (model shifted to smaller tunes, in vertical)

T. Pielonip.26 MPS BTF ON: SuperPacman bunch 1)Number of peaks ok, (Hor intermediate mode signature of 1 HOcoll) 2)Location of peaks ok, (tune distribution shift to higher freq)

T. Pielonip.27 Why SuperPacman bunches? 1) BTF is stripline pickup: single bunch measurement, takes signal from bunch with highest intensity 2) SuperPacman bunches are the most intense!

T. Pielonip.28 BTF ON: SuperPacman bunch 1)Number of peaks ok (vertical: second peak is present in Blue beam) 2)Location of peaks ok 3)H-V coupling not included in model but present in measurements

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

T. Pielonip.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

T. Pielonip.31 Conclusions I  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)

T. Pielonip.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

T. Pielonip.33 People and laboratories: 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

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T. Pielonip.35 Orbit effects Multiple Long-range interactions lead to offsets in collision HV X-ing compensation

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