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LOCO for LHC

Kajetan FuchsbergerOMCM Workshop, CERN 2011-06-21

Many thanks to:J. Wenninger, T. Baer, V. Kain, G. Mueller

K. Fuchsberger 2OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Contents

The LOCO principle

Challenges @ LHC

Examples

Implementation

Conclusion & Outlook

K. Fuchsberger 3OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Contents

The LOCO principle

Challenges @ LHC

Examples

Implementation & Remarks

Conclusion & Outlook

K. Fuchsberger 4OMCM Workshop, CERN 2011-06-21, LOCO for LHC

The LOCO principle

Difference vector:

SVD

Set of parameters

Set of observables

Sensitivity Matrix:(Jacobian)

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Orbit response

Possible parameters:• Corrector gains, tilts …• Monitor gains, tilts …• Arbitrary model parameters.

Orbit response matrix:

K. Fuchsberger 6OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Contents

The LOCO principle

Challenges @ LHC

Examples

Implementation

Conclusion & Outlook

K. Fuchsberger 7OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Challenges @ LHC

• # Monitors/beam (2 planes):• # Correctors/beam (2 planes):

Different problems/challenges for different applications:• Size of Sensitivity Matrix:• Memory consumption• SVD inversion time

• Calculation time for Sensitivity matrix:• # twiss runs

• Measurement time. ~ Shifts

K. Fuchsberger 8OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Memory Consumption

Size of Sensitivity Matrix:

• #rows • #columns #parameters.

E.g. Monitor- & Corrector Gains only:

1 beam, 2 planes: GB

2 beams, 2 planes: GB

K. Fuchsberger 9OMCM Workshop, CERN 2011-06-21, LOCO for LHC

SVD inversion time

Inversion time … #rows; … #cols

0 50 100 150 200 250 300 350 4000

0.20.40.60.8

11.21.41.61.8

f(x) = 0.00000003382228 x³ − 0.0000045479393 x² + 0.00027725 x − 0.0034078499

SVD inversion time for NxN matrices

N

time

[s]

𝑡 3×10−8×𝑀×𝑁2[ 𝑠]Est. on Intel Desktop PC (3.17 GHz):

K. Fuchsberger 10OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Monitor/COD Gain fits

0 100 200 300 400 500 6000

200

400

600

800

1000

1200Max #mon, #corr for mem & time (1 beam)

0.5 GB 1 GB 4 GB 5 min 1/2 h2 h

#correctors

#mon

itors

1088

530

8 GB, 12 h

Possible, but tedious…

K. Fuchsberger 11OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Optics parameter fits

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

100

120

140

160 Twiss times vs. #parameterstwiss time 2 corrtwiss time 4 corrtwiss time 8 corrSVD inversion time 8 corr

#params

time

[min

]

Dominated by twiss time; SVD inversion negligible.

K. Fuchsberger 12OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Contents

The LOCO principle

Challenges @ LHC

Examples

Implementation

Conclusion & Outlook

K. Fuchsberger 13OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Ex. I

Monitor Gains in Transfer lines and LHC

Average gain of 1.13: Resulting from uncorrected electronics (Correction was later on applied in frontends)

• Fits done with corrector gains fixed• At least 2 additional parameters (quad chains) to take care

of phase advance

K. Fuchsberger 14OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Ex. II – a

Phase advance error in Transfer line TI 8

MCIAV.81304

Growing Phase Error

Suspicion: Higher order field components in the main bends:• , : quadrupolar and sextupolar field error, respectively.

K. Fuchsberger 15OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Ex. II - b

• 4 correctors / measurement / plane• Fits with 4 parameters: , , and

𝑆=(𝑆1𝑆2𝑆3…𝑆7

)Off-momentum Kick response

Combined sensitivity matrix:

7 measurements with different values for (-2 … +2 permill)

Momentum offset:

Trimmed value

Unknown offset

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Ex. II - c

Measured Chromaticity (TI 8)

Nominal model Fitted model

about doubled, vanishes.

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Ex. III - a

TI8-LHC dispersion matchingInitial situation:

Beam

TI 8 LHC

Mismatch

K. Fuchsberger 18OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Ex. III - b

• MD: Letting MICADO select 2 most effective out of 10 individually powered quads.

• Later: SVD together with additional constraints to ensure phase advance at collimators (3 per plane)

𝑆=(𝑆𝐾

𝑆𝐷

𝑆𝐶)

Kick response

Dispersion

Additional Constraints

Combined sensitivity matrix:

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Ex. III - c

After correction: Almost perfect!

TI 8 LHC

Constrained by Kick-Response!

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Ex. IV

Fit:• Circulating beam• 60 correctors (distribute)• All BPMS• No monitor/corrector gains fitted• 9 Parameters:• 1 Systematic per sector• Systematic detuning of quads

Result:

Model prediction (WISE) well reproduced.

Systematic in LHC arcs

K. Fuchsberger 21OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Other Observations

• Fitting corr+monitor gains mostly doubtable result (Errors distributed between corr and monitor gains). Works well, if one is fixed.

• Check of COD polarity was done ‚visually ‘.• LHC BPMs can have many different problems:• Polarity flip• Plane flip• Beam flip• Wrong rotation (e.g. BPMS, rotated by 45 deg)• + Any combination of these.

Not easily covered by automatic fit.

K. Fuchsberger 22OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Contents

The LOCO principle

Challenges @ LHC

Examples

Implementation

Conclusion & Outlook

K. Fuchsberger 23OMCM Workshop, CERN 2011-06-21, LOCO for LHC

LOCO @ LHC

Aloha - “Another Linear Optics Helper Application”

• Input Data: Kick-Response, Dispersion, Beta-Beat (from TBT)• Algorithms: SVD, MICADO• Works for every accelerator with existing MadX model• Plug-In system: Easy to add e.g. new input formats, algorithms….

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JMad

Tight coupling to model All MadX parameters can be used

JMad: Java API for MadX

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General Remark

Optics analysis is an interactive process.It is not sufficient to have good algorithms, we also need

good tools (preferable online):

• Well integrated

• Interactive and Intuitive

• Good Software

GUIs

well designed, tested, documented, reusable…

K. Fuchsberger 26OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Contents

The LOCO principle

Challenges @ LHC

Examples

Implementation

Conclusion & Outlook

K. Fuchsberger 27OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Conclusions & Outlook

• LOCO for LHC? Yes, we can! (And we did!)• LOCO principle was intensively used during LHC

commissioning, especially for single-pass applications (Transfer lines, injection tests).

• Full BPM+COD gain fit for ring should be possible but is problematic (8GB ram, 12 h). The effort is questionable.

• Optics fit in ring works fine, but better covered by multiturn measurements. (faster, no influence of gains)

• It would be useful to join efforts to better integrate/merge different optics measurement methods/tools e.g. „Optics Analysis Workbench“? (Aloha could serve as starting point; Plug-In System)

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The end

Thank you for your attention!

K. Fuchsberger 29OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Additional Material

K. Fuchsberger 30OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Ex. II

Example: MCBH.14R7.B2

September 2008, first injection B2 to point 7:

Clear result: Inversion of Q6.L7.B2

Blue bars: measured, red dots: model.

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Influence on response matrix

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Full Sensitivity matrix

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Column factors

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LOCO principle

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Kick-Response

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The LOCO principle

Observables Parameters

Difference vector

Sensitivity matrix :

Fit minimizes by solving

SVD

,

K. Fuchsberger 37OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Kick response

Possible parameters:• Corrector Gains• Monitor Gains• Arbitrary model parameters

Positions COD kicks, ,

Response matrix

,

K. Fuchsberger 38OMCM Workshop, CERN 2011-06-21, LOCO for LHC

SVD inversion time

Inversion time … #rows; … #cols

0 50 100 150 200 250 300 350 4000

0.20.40.60.8

11.21.41.61.8

f(x) = 0.0000000338223 x³ − 0.00000454794 x² + 0.00027725 x − 0.00340785

SVD inversion time for NxN matrices

N

time

[s]

0 50 100 150 200 250 300 350 4000

0.5

1

1.5

2

2.5

3

3.5

f(x) = 0.0000286499 x² − 0.00111712 x + 0.0253119

time vs #cols (1000 rows)

#columns

time

[s]

0 1000 2000 3000 4000 5000 60000

0.2

0.4

0.6

0.8

1

1.2

f(x) = 0.00022854127251 x − 0.016572244898

time vs #rows (100 cols)

#rows

time

[s]

𝑡 3×10−8×𝑀×𝑁2[ 𝑠]

Estimation on Intel Desktop PC (3.17 GHz):

K. Fuchsberger 39OMCM Workshop, CERN 2011-06-21, LOCO for LHC

Monitor/COD Gain fits II

0 100 200 300 400 500 6000

2

4

6

8

10

12

14

0

1

2

3

4

5

6

7

8

required time for gain fits (1088 mon)

SVD inversion time [h]twiss time [h]total time [h]mem [GB]

#correctors

time

[h]

mem

[GB]