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

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Tune spectra depends on:Beam-beam strength

Collision pattern

Filling scheme

x ,y = 16.7 mN1= N2 = 1.15 1011 protons/bunchNb= 2808 bunches/beam

Up to 124 beam-beam interactions per turn

Fourfold symmetric filling scheme

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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 interactionsSuper PACMAN bunch: miss head-on collision

Strong effects (high density bunches) Multiple BBI (124 BBIs) Non regular pattern (symmetry breaks)

Strong bch2bch differences

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Tune spreadMultiple Long-range interactions lead to tune shifts

Different tunes into collision

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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

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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)

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QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.One Turn Matrix

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Transfer Matrix:

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• Phase advance

• Linearized HO or LR B-B kick

• Coupling factor

Bunches: Rigid Gaussian distributions

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Beam-Beam Matrix:

I. Analytical Linear Model

B

E

A

M

1B

E

A

M

2

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bunch1

beam1

bunch1

beam2

bch2, …

bch2, …

Solve eigenvalue problem of 1 turn map

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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

QQ

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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

Q1-mode:

all bunches exactly out of phase

Q2,3,4-mode (intermediate modes):

Q-mode: all bunches exactly in phase

Q0Qp1 Qp

2

-mode -mode

-mode -mode

Q1 Q

2 Q3 Q

4 Q

Q2 Q

3

Q3

Q4 Q

Q1

I. ALM: more bunches

Q2

Q4

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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…)

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The eigenvector associated to the Q1 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 Q1

Bunch 1

Bunch 2

Bunch 3

Q1

Q1

Q1

ALM vs RBM: bch to bch differences

QQ

Inputs:• 5 bch trains• 1 HO + 1 LR

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

Symmetry breaking: intensity effects

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Multi Particle Simulations

Between the BBIs: linear transfer (rotation in phase space) and anything else (kickers, collimators, BTF device, etc)

Bunches: Ntot (104-106) macro particles

BB incoherent kick: solving the Poisson equation for any distribution of charged particles (FMM) or Gaussian approximation :

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MPS results (I): Coherent effects: Fourier analysis bunch barycentres turn by turn gives frequency spectra of dipolar modes

Inputs• 4 bunches 105 macroparticles• 2-4 HO collisions• Run of 32000 turns

Effects of:

Landau damping Symmetry breaking in collision scheme and phase advance Intensity fluctuations Bunch to bunch differences Higher order modes

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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)

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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

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• 36 bunches per beam each Ntot=104

• 4 Head-on collisions per turn• 64000 turns run (only 5-6 s of LHC)

Few bunches and only 104 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….

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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)

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Scalability: preliminary results

Computing time:

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

Almost independent of bunch number

Almost independent of the number of interactions

0.7GHz

3 GHz

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RHIC tune spectra with BTFBTF: 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-BeamBTF MEASUREMENT Fill 7915 RHIC pp Run06

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I. Analytical Linear Model (ALM)II. Rigid Bunch Model (RBM)III. Parallel Multi Particle Simulation (MPS) + BTF routine

Simulation tools: COMBI

RHIC configurationProton-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 model:

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Rigid bunch model nominal and SP bunch:

Vertical tune spectrum

Horizontal tune spectrum

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Tune spectra w/o BTF

Landau damping of intermediate coherent modes

Two beams decoupled

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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)

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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)

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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!

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BTF ON: SuperPacman bunch

1) Number of peaks ok (vertical: second peak is present in Blue beam)

2) Location of peaks ok3) H-V coupling not included in model but present in measurements

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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)

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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

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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)

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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

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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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Orbit effectsMultiple Long-range interactions lead to offsets in collision

HV X-ing compensation

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