LHC optics measurement & correction procedures M. Aiba, R. - - PowerPoint PPT Presentation

LHC optics measurement & correction procedures

• M. Aiba, R. Calaga, A. Morita, R. Tomás &
• G. Vanbavinckhove

Thanks to: I. Agapov, M. Bai, A. Franchi,

• M. Giovannozzi, V. Kain, G. Kruk, J. Netzel,
• S. Redaelli, F. Schmidt, J. Wenninger and
• F. Zimmermann

Extended LTC - March 2008

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Contents

• Calibration independent measurements:

+ Phase measurements:

• from FT or SVD of turn-by-turn BPM data
• from Closed Orbit Distortion

+ Betas from phases + Normalized Dispersion + Coupling from FT of turn-by-turn BPM data

• Correction

+ Response matrix inversion + Simulations + RHIC tests and future SPS tests

• Controls application

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Turn-by-turn BPM data

• 4
• 3
• 2
• 1

1 2 3 4 100 200 300 400 500 600 700 800 900 1000 x [mm] Turn number Fake LHC BPM data (pilot bunch) σbpm=0.2mm Decoherence due to ∆Q 3mm kick

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FFT of BPM data

50 100 150 200 250 300 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Amplitude [arb. units] Frequency [tune units] Fake LHC BPM FFT Qx

• 2Qx

Qy Qs, 2Qs, ...

∆φx between BPM1 and BPM2 = φbpm2

Qx -φbpm1 Qx

Coupling inferred from the amplitude of Qy

• AbpmN

Qy

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FFT versus SUSSIX

0.5 1 1.5 2 2.5 3 100 200 300 400 500 600 700 800 900 1000 Phase error [deg] Number of turns 3mm oscillation + 0.2mm Gaussian error (no decoherence) ∝ N-1/2 SUSSIX FFT

In presence of noise SUSSIX reduces the phase error by a factor 2-3 showing same scaling with N.

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Closed Orbit Distortion

The xCO change at location s produced by a corrector c is given by: ∆xCO(s) ∝

• βs cos(|φs − φc| − Qπ)

A collection of orbits using different correctors allows to fit βs and φs at all BPMs yielding:

• calibration dependent βs
• calibration independent φs
• A. Morita, PRSTAB 10, 072801
• perational in KEK-B

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LHC COD performance simulation

0.00 0.05 0.10 0.15 0.20 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 Maximum error of ∆φ BPM resolution Maximum Closed-Orbit Excitation: σBPM/A 10.00 σ/A (worst) 5.94 σ/A (typ.) 4.35 σ/A (best) wo calibration error w calibration error

σmax

φ

= 2◦ needs σ

A=0.3%

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Betas from phases in the LHC arcs

1 2 3 4 5 5 10 15 20 25 30

• Max. β-measurement error [%]

Model rms ∆β/β [%] Betas from phases (σφ=0.25o) Horizontal Vertical

β1 =

cot φ12−cot φ13 m11/m12−N11/N12

Model unknowns and BPM noise contribute to β error Using β1,β2,β3 improves the error, works in IRs.

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Robustness of

• D/√βx

to errors in LHC

0.995 1 1.005 1.01 1.015 1.02 0.02 0.04 0.06 0.08 0.1 0.12 Ratio (err/model) Horizontal rms beta-beating 〈D/β1/2〉err/〈D/β1/2〉ideal 〈D〉err/〈D〉ideal 〈 β〉err/〈β〉ideal

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Normalized dispersion

AbpmN

Qx

= cbpmNcglobal

• βbpmN

x

Let XbpmN be the radial steering= cbpmNDbpmNδ, XbpmN AbpmN = δ cglobal DbpmN

• βbpmN

x

= c,

global

DbpmN

• βbpmN

x

Finally averaging XbpmN/AbpmN over all BPMs: XbpmN AbpmN

• = c,

global

DbpmN

• βbpmN

x

• ← frommodel

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Simulation of D/√βx measurement

0.01 0.02 0.03 0.04 5 10 15 20

• Max. Dβ-1/2 measurement error [m1/2]

Model rms ∆β/β [%] σBPM=0.2mm, kick=2σ, N=512turns, dp/p=0.15%

Effectively a model independent measurement!

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Dispersion from D/√β and β

• 4
• 3
• 2
• 1

1 2 3 2 4 6 8 10 12 14 16 Dispersion [m] Longitudinal location [km] σBPM=0.2mm, kick=2σ, N=128turns, dp/p=0.1% Simulation MAD

Very good measurement of D from D/√β and β

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Coupling (local)

(For global coupling correction see: R. Jones et al, CERN-AB-2005-083 BDI0) Let AH

Qy be the amplitude of the vertical tune in the

horizontal plane, hence |f1001| = 1 2

• AH

Qy

AH

Qx

AV

Qx

AV

Qy

• Calibration independent but BPM-tilt dependent
• Close to the resonance:

∆Qmin ≈ 4∆|f1001|

PRSTAB 8, 034001; PRSTAB 10, 064003

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Coupling: measurement around LHC

0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 5 10 15 20 25 |f1001| Longitudinal location [km] MADX Simulation

Random 2mrad BPM tilts, 400 turns, 4mm kick → Lo- cal coupling is measurable.

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Optics correction

• Using the model response matrix R, the change in

the quadrupole circuits ∆ k to achieve correction is given by: ∆ k = −R−1∆

• φ,
• Dx

√βx , Qx, Qy

• This equation applies the same for correction on 1

beam only or on 2 beams simultaneously.

• Similarly for local coupling correction:

∆ ks = −R−1

s

• ℜ(

f1001), ℑ( f1001), ℜ( f1010), ℑ( f1010)

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Correction: Simulation in 2006

0.1 0.2 0.3 0.05 0.1 0.15 0.2 RMS ∆βy/βy RMS ∆βx/βx

RMS β-Beat

Before After 0.2 0.4 0.6 0.1 0.2 0.3 0.4 Peak ∆βy/βy Peak ∆βx/βx

Peak β-Beat

Before After 2 4 6 1 2 Peak ∆Dx/√βx [x10-2] RMS ∆Dx/√βx [x10-2]

Peak Vs. RMS Dispersion

Before After

• 2
• 1

1 2

• 2
• 1

1 2 ∆Qy [x10-2] ∆Qx [x10-2]

Tune Shift: ∆Q

• Errors: 80% measured & as installed, 20% extrapolated
• Additional 2mm random sext. misalignments + 5 units random B2

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Correction: present status, preliminary

0.1 0.2 0.3 0.1 0.2 0.3 RMS ∆βy/√βy RMS ∆βx/√βx

LHC Beam 1, 60 Seeds

(Mutlipole Errs upto B10/A10)

RMS β-Beat

Before After 0.2 0.4 0.6 0.2 0.4 Peak ∆βy/βy Peak ∆βx/βx

Peak β-Beat

Before After 2 4 6 8 10 1 2 3 4 5 Peak ∆Dx/√βx [x10-2] RMS ∆Dx/√βx [x10-2]

Peak Vs. RMS Dispersion

3 RMS Spec

Before After

• 3
• 2
• 1

1 2 3

• 3
• 2
• 1

1 2 3 ∆Qy, ∆Q’y, ∆y ∆Qx, ∆Q’x, ∆x Tune Shift [x 10-2] Chrom Shift [x 10] Orbit Shift [cm]

• Errors: 100% measured & as installed
• No additional misalignments added, no orbit correction

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Correction: observations

Correction is achieved for most of the seeds if:

• σφ < 1◦
• failing BPMs < 10%
• σ D

√β ≈ 0.01m1/2

(see support slides for details)

→ Might be tight for LHC commissioning...

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Coupling correction

Using all the skew quadrupole correctors:

0.02 0.04 0.06 0.08 0.1 0.12 5 10 15 20 25 30 |f1001| Longitudinal location [km] Uncorrected Corrected

∆Qmin ≈ 0.01 ∆Qmin ≈ 0.001

→ Not perfect due to the particular distribution of errors/correctors. Best local correction is realignment

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RHIC exp.: 6 random quads used

0.2 0.4 0.6 0.8 1 1.2 0.5 1 1.5 2 2.5 3 3.5 4 (∆φ) [Q Units] Longitudinal Position [km] Opp Polarity BPMs

Horizontal

Ideal Model Baseline Quad Trimmed 0.2 0.4 0.6 0.8 1 1.2 0.5 1 1.5 2 2.5 3 3.5 4 (∆φ) [Q Units]

Vertical

Ideal Model Baseline Quad Trimmed

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RHIC exp.: MAD reconstruction, ∆φ

• 6
• 4
• 2

2 4 6 0.5 1 1.5 2 2.5 3 3.5 4 δ(∆φ) [x10-2, Q Units]

Longitudinal Position [km]

Effect of 6 Trim Quads Horizontal

Reconstructed MADX Meas

• 6
• 4
• 2

2 4 6 0.5 1 1.5 2 2.5 3 3.5 4 δ(∆φ) [x10-2, Q Units]

Vertical

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RHIC exp.: Quad strengths

• 8
• 6
• 4
• 2

2 4 6 0.5 1 1.5 2 2.5 3 3.5 4 ∆KL [1/m x 10-3] Longitudinal Position [km]

Trims: [bi8-tq4, bo7-tq5, bo11-tq4] Trims: [bi8-tq6, bo3-tq6, bo11-tq6]

R-Matrix (3 Iters)

• 6
• 4
• 2

2 4 6 0.5 1 1.5 2 2.5 3 3.5 4 ∆KL [1/m x 10-3] Machine Input Simplex (5000 Iters)

The 6 quads are found!

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Phase error in RHIC versus Q’

5 10 15 20 25 30 35 40 45 5 10 15 20 Occurrences phase advance rms error [deg] baseline chrom+1 chrom+2 5 10 15 20 25 30 35 40 45 0.2 0.4 0.6 0.8 1

kick data Chromaticity has a dramatic impact in the phase of some BPMs → AC dipole is a solution

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RHIC exp: AC dipole Vs kick data

10 20 30 40 50 60 70 80 90 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Number of Occurances RMS Phase Error [deg] Kicked: σφ ≈ 0.25 AC Dipole: σφ ≈ 0.15 AC Dipole Kicked Data 10 20 30 40 50 60 70 80 90 0.2 0.4 0.6 0.8 1

AC dipole gives smaller phase error.

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Future SPS tests

• Phase measurement from FT and COD (using

Jorg’s YASP orbit corrector scan)

• Betas from phases, but large error bars due to the

90◦ phase advance

• Normalized dispersion
• Phase noise versus chromaticity
• Possible correction using orbit bumps at

sextupoles.

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Controls Application

Beta−Beat Java Gui Verena’s app. On−line to the controls as a knob Correction setting sent model BPM file from YASP C.O.D. Sussix Drive & Python scripts

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Summary: measurement requirements

• pilot bunch, 5×109 protons
• CO measurement, YASP
• Turn-by-turn BPM acquisition system
• Chromaticity correction
• H & V kickers (4σ kick)
• H & V AC dipole (4σ kick)
• Beam size monitors

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Summary and discussion

• A big collaborative effort is being done to

guarantee the measurement and correction of the LHC optics

• From simulations, 5-10 iterations are enough to

correct the optics with good BPM performance

• Machine reproducibility assumed perfect here,

might become a limitation → AC dipole could then be the solution

• Use of K-modulation to measure βs would be
• complementary. Status of k-modulation?

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Support Slides

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1◦ error in phase

• 0.1

0.2 0.3 0.4 0.1 0.2 0.3 0.4 RMS ∆βy/βy RMS ∆βx/βx

RMS β-Beat

Before After 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Peak ∆βy/βy Peak ∆βx/βx

Peak β-Beat

Before After 1 2 3 4 5 6 1 2 3 Peak ∆Dx/√βx [x10-2] RMS Dx/√βx [x10-2]

Peak Vs. RMS Dispersion

3 RMS Spec

Before After

• 2
• 1

1 2

• 2
• 1

1 2 ∆Qy [x10-2] ∆Qx [x10-2]

Tune Shift: ∆Q

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10% faling BPMs

0.05 0.1 0.15 0.2 0.25 0.05 0.1 0.15 0.2 0.25 RMS ∆βy/βy RMS ∆βx/βx

RMS β-Beat

Fixed Sample Random Sample 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 Peak ∆βy/βy Peak ∆βx/βx

Peak β-Beat

Fixed Sample Random Sample 2 4 6 8 10 1 2 3 4 5 Peak Dx/√βx [x10-2] RMS Dx/√βx [x10-2]

Peak Vs. RMS Dispersion

3 RMS Spec

Fixed Sample Random Sample

• 1

1

• 2
• 1

1 2 ∆Qy [x10-2] ∆Qx [x10-2]

Tune Shift: ∆Q

Fixed Sample Random Sample

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Simulation of D/√β measurement

• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.1 0.15 0.2 0.25 2 4 6 8 10 12 14 16 18 Dx/βx

1/2 [m1/2]

Longitudinal location [km] Simulation MAD

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Simulation of β measurement

100 200 300 400 500 600 700 2 4 6 8 10 12 14 16 18 βx [m] Longitudinal location [km] Simulation MAD

128 turns, σbpm=0.2mm, kick=2σ

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φ-beating Vs β-beating

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 21/2∆ φpeak [rad] ∆ β/βpeak horziontal vertical 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 21/2∆ φrms [rad] ∆ β/βrms horziontal vertical

Precise relation between ∆φrms and ∆β/βrms

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Not considering dispersion

0.2 0.4 0.6 0.8 1 1.2 1.4 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ∆Dx,peak [m] ∆Dx,rms [m] Uncorrected Corrected

→ Dispersion gets spoiled → β-beating correction must consider dispersion

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Some specifications

• Best BPM calibration error: ±4% (LHC-BPM-ES-0004)
• BPM roll: ±1 mrad
• BPM rms resolution (pilot bunch, high current):

200µm, 50µm

• CO resolution (high intensity): 5µm
• Peak β − beat < 16% [Rep. 501]
• Specification on Dispersion [Rep. 501]:
• ∆D

√βx

• < 0.013√m,
• ∆D

D

• QF < 30%,

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