Beam-Beam Tune Spectra in RHIC and LHC

Transcription

1 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

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

3 T. Pieloni p.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 T. Pieloni p.4 Different tunes into collision

5 Motivation: T. Pieloni p.5 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: 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)

6 T. Pieloni p.6 How do we proceed? Both beam affected (strong-strong): 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 QuickTime and a Photo - JPEG decompressor are needed to see this picture. T. Pieloni p.7 QuickTime and a Photo - JPEG decompressor are needed to see this picture. QuickTime and a Photo - JPEG decompressor are needed to see this picture. I. Analytical Linear Model Solve eigenvalue problem of 1 turn map Beam-Beam Matrix: B E A M 1 bunch1 beam1 bch2, QuickTime and a Photo - JPEG decompressor are needed to see this picture. QuickTime and a Photo - JPEG decompressor are needed to see this picture. B E A M 2 bunch1 beam2 bch2, Transfer Matrix: Bunches: Rigid Gaussian distributions QuickTime and a Photo - JPEG decompressor are needed to see this picture. Phase advance Linearized HO or LR B-B kick Coupling factor One Turn Matrix QuickTime and a Photo - JPEG decompressor are needed to see this picture.

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

9 I. ALM: more bunches T. Pieloni p.9 Inputs: Beam 1 = 4 equispaced bunches Beam 2 = 4 equispaced bunches HO collision in IP1-2 and LT 5 different Eigen-values Q π 1 Q π 2 Q π 3 Q π 4 Q σ Q p 1 Q p 2 Q π 1 π-mode Q 0 π 2 -mode Q π 2 8 different Eigen-vectors Q π 2 Q π 3 Q π1 -mode: all bunches exactly out of phase Q π 2,3,4 -mode (intermediate modes): Q σ -mode: all bunches exactly in phase Q π 3 π 2 -mode Q π 4 σ-mode Q π 4 Q σ

10 T. Pieloni p.10 II. Bunches: rigid objects assumed Gaussian Rigid Bunch Model 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 T. Pieloni p.11 ALM vs RBM: bch to bch differences Inputs: 5 bch trains 1 HO + 1 LR Example Q σ 1 Q π Q σ Bunch 1 Q σ 1 Bunch 2 The eigenvector associated to the Q σ1 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 Q σ 1 Q σ 1 Bunch 3

12 Symmetry breaking: intensity effects 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

13 T. Pieloni p.13 Multi Particle Simulations Bunches: N tot ( ) 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 T. Pieloni p.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 10 5 macroparticles 2-4 HO collisions Run of turns

15 T. Pieloni p.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 T. Pieloni p.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

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

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

19 T. Pieloni p.19 Scalability: preliminary results 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 Computing time: Almost independent of bunch number Almost independent of the number of interactions 0.7GHz 3 GHz

20 T. Pieloni p.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 T. Pieloni p.22 RHIC configuration Proton-Proton run 06 Simulation model: 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 tools: COMBI I. Analytical Linear Model (ALM) II. Rigid Bunch Model (RBM) III. Parallel Multi Particle Simulation (MPS) + BTF routine

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

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

25 T. Pieloni p.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)

26 T. Pieloni p.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)

27 T. Pieloni p.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!

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. Pieloni p.28

29 T. Pieloni p.29 The LHC tune spectra Run parameters: Beam filling scheme: 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: T. Pieloni p.30 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 T. Pieloni p.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)

32 T. Pieloni p.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 T. Pieloni p.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

34 T. Pieloni p.34

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

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