[PPT] - SPS Orbit studies Contents: - Motivation - Stabilization of orbit PowerPoint Presentation

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SPS Orbit studies

presented by Eliana GIANFELICE (Fermilab and CERN) APC Seminar, Fermilab, November 21, 2013

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Motivation This work has been triggered by the difficulties by transferring the beams to LHC ob- served after the SPS optics was changed to the Q20 one in September 2012 and transfer lines changed consequently. Being the measured beam emittance in LHC apparently not affected, an optics mis- match SPS-line-LHC is unlikely. The hypothesis that the SPS orbit at extraction is not well reproducible has been inves-

tigated. Issues to be addressed:
Are the observed orbit changes relevant?
Is it possible to correct them?
Is it possible to find a source?

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Preamble The CERN SPS was brought in operation in 1976 and accelerated protons for fixed target experiments, thus converted into a p¯ p collider, e± injector for LEP and currently used as LHC injector, for fixed target experiments and for producing neutrinos beams for the Gran Sasso experiments (CNGS). The orbit at extraction is not corrected by active elements. Few interlocked bumpers are used for steering the beam at the extraction points. At the beginning of operation

rbits at top energy are recorded and quadrupoles moved for minimizing the orbit ex-

cursion wrt reference. The SPS optics for neutrino production and for LHC injection being different, the ma- chine alignment is done for the more intense CNGS beam (going to be changed!).

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Orbit reproducibility at extraction (Q20, Fall 2012 measurements)

The variations are larger in the horizontal plane.
Is the spread relevant for the transmission stability in the lines?

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Those orbits at flat top have been analyzed and used for simulating the resulting trajec- tory in TI8/TI2. The starting conditions are found by a Fourier analysis of the difference closed orbit wrt. average. Resulting TI8 trajectories (computed)

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3σ envelopes (ǫN=1.7×10−6) with collimators at 5 nominal σ, including dispersion contribution with dp/p=0.0295% and excluding worst case (after run stop):

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Results are consistent with the trajectory actually measured

(L. Norderhaug-Drøsdal et al., IPAC13)

The SPS orbit variations may explain the losses in the transfer lines.

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Trajectory mis-match, which would lead to a large emittance dilution, is compensated by dampers in LHC, but time consuming manual steering by the machine crew was needed to keep transfer clean. Ongoing studies/improvements may solve/mitigate the

problem. If not:
Use of the already interlocked extraction bumpers for automatically correcting beam

position and slope at the extraction points wrt golden values. Advantages: – Compensating directly the source for the changing trajectory in extraction lines. – Potential for time saving. Best strategy (if any) to be found by simulations. Use of the large aperture BPMs located at the extraction points (BPCEs) may be problematic.

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Strategies for correcting the orbit at the extraction points Investigation goal: can we infer beam position at extraction points from orbit measured at BPMs along the ring (no BPCEs)? Simulation steps:

Introduce random radial misalignments and assign orbit to reference orbit.
Add new radial misalignments.

– Use all available “correctors” for steering to the reference orbit, thus compute

rbit due to correctors only. a (“fake correction”).
r

– Use Fourier analysis of difference orbit at BPMS and use main components to compute orbit all over the ring and in particular at the extraction points.

r

– Trajectory amplitude and phase fit.

Use bumpers for restoring radial position and angle at extraction septum keeping
rbit unchanged outside the bump.

aactually as we are not correcting the orbit, we can possibly use a larger number of elements if

convenient.

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“Fake correction method” (simulation for testing purposes) Horizontal misalignment of all quadrupoles δrms=0.25 mm + 0.10 mm, 10 seeds. Ex- pected A2 (20 seeds) in TI2, no BPCE’s, no BPMs reading errors: ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.250 ± 0.205 0.002 ± 0.001 trajectory 0.250 ± 0.205 0.003 ± 0.002 Corrector strengths: θnom θ (mrad) (mrad) kmpsh61402 0.000 0.007 ± 0.038 kmplh61655 0.512 0.502 ± 0.039 kmplh61996 0.094 0.101 ± 0.042 kmpsh62199 0.398 0.388 ± 0.035

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Add random BPM calibration errors. BPMs gain errors: EALIGN, MSCALX:=0.25*TGAUSS(1),MSCALY:=0.;

5 10 15 20 0.6 0.8 1 1.2 1.4

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No BPCE’s, with BPMs calibration errors: EALIGN, MSCALX:=0.25*TGAUSS(1),MSCALY:=0.; Expected A2 ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.250 ± 0.205 0.009 ± 0.015 trajectory 0.250 ± 0.205 0.010 ± 0.016 Correctors strength θnom θ (mrad) (mrad) kmpsh61402 0.000 0.005 ± 0.036 kmplh61655 0.512 0.501 ± 0.040 kmplh61996 0.094 0.098 ± 0.040 kmpsh62199 0.398 0.388 ± 0.035

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Now test with measured difference orbits. By a SVD fake misalignments for all quads are found which reproduce the measured orbit difference in the MADX model. Example: Ref.: ORBIT SPSRING 18-10-12 18-06-21 LHC2 CY64400 T18500.data (18/10/12) Orbit: ORBIT SPSRING 21-10-12 22-11-58 LHC2 CY4940 T18500.data (21/10/12)

1500
1000
500

500 1000 1500 20 40 60 80 100 120 x (µm) BPM index Q20 Difference Orbit Measured Difference MADX (offsets from fit)

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Use 589 measured difference orbits (from October 13 to 29 2012) a. Expected A2: ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.016 ± 0.024 0.020 ± 0.014 trajectory 0.016 ± 0.024 0.020 ± 0.014 Correction fails ! What is happening?

aL. Norderhaug Drøsdal courtesy

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A closer look to one “offending” case: ORBIT SPSRING 19-10-12 10-06-54 LHC2 CY161 T18500.data- ORBIT SPSRING 13-10-12 15-42-21 LHC2 CY52822 T18500.data

3000
2000
1000

1000 2000 3000 4000 0 1000 2000 3000 4000 5000 6000 7000 measured MADX-reconstructed MADX-corrected

Coordinates at septum x x′ ǫx (mm) (mrad) (µm) 0.54602

0.01384

4.7e-3

0.58676

0.00549 7.6e-3 nb: In the picture there is by mistake a longitudinal mis-match of 706 m between “MADX” and “measured” because of a different starting point!

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Including one MKE, MST and MSE for fake correction.

3000
2000
1000

1000 2000 3000 4000 0 1000 2000 3000 4000 5000 6000 7000 measured MADX-reconstructed MADX-corrected

Coordinates at septum x x′ ǫx (mm) (mrad) (µm) 0.54602

0.01384

4.7e-3

0.54028

0.00417 4.4e-3 nb: In the picture there is a longitudinal mis-match by 706 m between “MADX” and “measured” !

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A closer look to a second “offending” case: ORBIT SPSRING 24-10-12 02-33-37 LHC2 CY9160 T18500.data- ORBIT SPSRING 13-10-12 15-42-21 LHC2 CY52822 T18500.data

4000
3000
2000
1000

1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 6000 7000 measured MADX-reconstructed MADX-corrected

Coordinates at septum x x′ ǫx (mm) (mrad) (µm) 0.7094

0.0212

10.4e-3

1.113

0.012 24.6e-3 nb: In the picture there is a longitudinal mis-match by 706 m between “MADX” and “measured” !

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Including one MKE, MST and MSE for fake correction.

4000
3000
2000
1000

1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 6000 7000 measured MADX-reconstructed MADX-corrected

xS x′

S

ǫx (mm) (mrad) (µm) 0.7094

0.0212

10.4e-3

0.489

0.0 10.e-3 In both examples the corrected orbit shows similar spikes and a wiggling around 1300 m. nb: In the picture there is a longitudinal mis-match by 706 m between “MADX” and “measured” due to a different starting position.

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Analysis of 589 difference orbits repeated including those “correctors”. ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.016 ± 0.024 0.012 ± 0.012 trajectory 0.016 ± 0.024 0.012 ± 0.012 Correctors strength θnom θ (mrad) (mrad) kmpsh61402 0.000

0.003 ± 0.003

kmplh61655 0.512 0.503 ± 0.006 kmplh61996 0.094 0.090 ± 0.004 kmpsh62199 0.398 0.392 ± 0.005 It is better, but this is not the explanation...

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Find out whether this is an artifact of my way of reproducing the measured difference

rbits. Does some BPM lie?

Make Fourier analysis of measured difference orbits! ORBIT SPSRING 29-10-12 21-49-57 LHC2 CY20354 T18500.data - ORBIT SPSRING 13-10-12 15-42-21 LHC2 CY52822 T18500.data

20000
10000

10000 20000 30000 40000 50000 20 40 60 80 100 120 position (µm) BPM # reference

rbit

difference 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 Amplitude (a.u.) Component # Fourier components

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Keeping components 20 and 21:

4000
3000
2000
1000

1000 2000 20 40 60 80 100 120 meas. from FT

There are some suspicious BPMs.

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Summary of BPM response dedicated studies (Spring 2013) (Bartosik, Cettour, Salvant, MSWG, 26 March 2013)

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Suspicious BPMs:

from fit from MSWG from fit from MSWG 5 BPH.11008 too large

64 BPH.41208

too small

6 BPH.11208

too large

66 BPH.41608

too large gain=1.28 10 BPD.11906 too large gain=1.24 67 BPCE.41705 too small not working 11 BPH.12008 too large

68 BPCE.41801

too small

14 BPH.12408

too small not working 69 BPCE.41931 too large not working 21 BPH.13608 too small

72 BPH.42408

too large

23 BPH.20408

too small

74 BPH.42808

too large

25 BPH.20808

too small

75 BPH.43008

too small

32 BPH.22008

too large

76 BPH.43208

too small

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Suspicious BPMs (cont.):

from fit from MSWG from fit from MSWG 33 BPH.22208 too large not working 86 BPH.51608 too small

35 BPH.22608

too large

90 BPH.52408

too large

37 BPH.23008

too large not working 98 BPH.60408 too large gain=1.20 41 BPH.30208 too small

100 BPH.60808

not working not working 42 BPH.30408 too small

101 BPH.61008

too large gain=1.24 43 BPH.30608 too small

102 BPH.61208

too small

51 BPH.32208

too large

103 BPH.61408

too small gain=0.08 52 BPH.32408 too small

104 BPH.61608

too small

54 BPH.32808

too large

108 BPH.62008

too large gain=1.43 57 BPH.33408 too small

115 BPH.63408

too large

62 BPH.40808

too small

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It seems that the calibrations of the BPMs have been not corrected and that some non working BPMs get an undeserved “OK” flag. Determined a minimum set of BPMs which seem not working properly in more than one file, in addition to all BPCEs. from fit from MSWG 6 BPH.11208 too large

14 BPH.12408

too small not working 33 BPH.22208 too large not working 37 BPH.23008 too large not working 66 BPH.41608 too large

85 BPH.51408

too large

Exclude those BPMs for determining fake quads offsets, but not from the MADX orbit

correction a and analyze the MADX resulting orbit.

athe idea behind is that there is no reason why they should not work in principle!

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ORBIT SPSRING 24-10-12 02-33-37 LHC2 CY9160 T18500.data- ORBIT SPSRING 13-10-12 15-42-21 LHC2 CY52822 T18500.data

2000
1500
1000
500

500 1000 1500 2000 1500 3000 4500 6000 position (µm) BPM position (m) meas. MADX-reconstructed MADX-corrected

xS x′

S

ǫx (mm) (mrad) (µm) 0.901

0.018

11.1e-3 0.270

0.005

1.0e-3 Spikes in MADX corrected orbit disappeared; there is still the wiggling around 1300 m which disappears when some more BPMs in that region are excluded. nb: the longitudinal mis-match in this picture has been corrected!

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Analysis of 589 difference orbits repeated including the extra “correctors” and excluding those BPMs as an attempt: ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0059 ± 0.0060 0.00085 ± 0.0009 trajectory 0.0059 ± 0.0060 0.00085 ± 0.0009 Much better! Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.002 ± 0.003

kmplh61655 0.512 0.510 ± 0.005 kmplh61996 0.094 0.092 ± 0.003 kmpsh62199 0.398 0.397 ± 0.004

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Check robustness against BPMs random errors. EALIGN, MSCALX:=0.25*TGAUSS(1),MSCALY:=0.; ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0061 0.0006 ± 0.0007 trajectory 0.0063 ± 0.0061 0.0006 ± 0.0007 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.002 ± 0.004

kmplh61655 0.512 0.510 ± 0.006 kmplh61996 0.094 0.091 ± 0.004 kmpsh62199 0.398 0.397 ± 0.005

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Change seed for BPM calibration errors (from 23 to 27)... ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0061 0.0010 ± 0.0011 trajectory 0.0063 ± 0.0061 0.0010 ± 0.0011 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.002 ± 0.003

kmplh61655 0.512 0.510 ± 0.005 kmplh61996 0.094 0.092 ± 0.003 kmpsh62199 0.398 0.397 ± 0.004

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One more seed (15) ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0061 0.0009 ± 0.0010 trajectory 0.0063 ± 0.0061 0.0009 ± 0.0010 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.002 ± 0.003

kmplh61655 0.512 0.510 ± 0.005 kmplh61996 0.094 0.092 ± 0.003 kmpsh62199 0.398 0.397 ± 0.004

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Alternative Methods for fitting the Orbit: Fourier Analysis

Fourier analysis of measured orbit difference.
Analytical computation of position and slope change at the septum using main

Fourier components.

Bumpers used for correcting the changes keeping closed orbit unchanged outside.

Simulation steps:

Same 589 measured difference orbits used for finding 589 fake sets of quadrupole

misalignments through SVD, excluding the same last set of BPMs as before.

MADX used to evaluate orbit and extraction trajectory in presence of such misalign-

ments.

Code for orbit Fourier analysis invoked within MADX script and results read back

with the MADX script.

Correction of computed value of (∆x, ∆x′) at MSE.61852 with a closed orbit

bump using the 4 bumpers.

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ORBIT SPSRING 24-10-12 02-33-37 LHC2 CY9160 T18500.data- ORBIT SPSRING 13-10-12 15-42-21 LHC2 CY52822 T18500.data All BPMs used for fitting, only BPCEs excluded.

2
1.5
1
0.5

0.5 1 1.5 2 1500 3000 4500 6000 x(µm) s(m) Radial Orbit at BPMs MADX ’meas.’ Orbit from Fourier components

(x, x′) at MSE.61852 xS x′

S

(mm) (mrad) MAD-X 0.935

0.020

Fourier 0.682

0.016

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Results (summing components 20 ± 2) for 589 difference orbits: ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0061 0.0008 ± 0.0012 trajectory 0.0063 ± 0.0061 0.0008 ± 0.0012 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.003 ± 0.003

kmplh61655 0.512 0.509 ± 0.004 kmplh61996 0.094 0.091 ± 0.003 kmpsh62199 0.398 0.397 ± 0.003 Results are similar to those obtained by using the “fake correction” method, the uncer- tainty is a bit larger.

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Check robustness against BPMs random errors by adding BPMs random errors with EALIGN, MSCALX:=0.25*TGAUSS(1),MSCALY:=0.: BPCEs excluded assuming they are known to be bad. Fourier components used for computing the orbit: 20 ± 2. Results: ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0061 0.0011 ± 0.0013 trajectory 0.0063 ± 0.0061 0.0011 ± 0.0013 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.002 ± 0.003

kmplh61655 0.512 0.510 ± 0.003 kmplh61996 0.094 0.092 ± 0.003 kmpsh62199 0.398 0.397 ± 0.003

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Check robustness against BPMs random errors by adding BPMs random errors: EALIGN, MSCALX:=0.25*TGAUSS(1),MSCALY:=0.; seed: 27. Results: ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0061 0.0008 ± 0.0012 trajectory 0.0063 ± 0.0061 0.0008 ± 0.0012 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.003 ± 0.003

kmplh61655 0.512 0.509 ± 0.003 kmplh61996 0.094 0.091 ± 0.004 kmpsh62199 0.398 0.397 ± 0.003

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Check robustness against BPMs random errors by adding BPMs random errors: EALIGN, MSCALX:=0.25*TGAUSS(1),MSCALY:=0.; seed: 15. Results: ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0061 0.0008 ± 0.0011 trajectory 0.0063 ± 0.0061 0.0008 ± 0.0011 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.002 ± 0.003

kmplh61655 0.512 0.509 ± 0.004 kmplh61996 0.094 0.091 ± 0.003 kmpsh62199 0.398 0.397 ± 0.003

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Include those bad BPMs in the SVD for setting the MADX model. Results (summing components 20 ± 2) for 589 difference orbits (no calibration errors): ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0056 0.0010 ± 0.0013 trajectory 0.0063 ± 0.0056 0.0010 ± 0.0013 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000

0.002 ± 0.003

kmplh61655 0.512 0.508 ± 0.003 kmplh61996 0.094 0.091 ± 0.003 kmpsh62199 0.398 0.396 ± 0.002

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Alternative Methods for fitting the Orbit: A, φ, ∆p/p fit

Amplitude, phase and ∆p/p are found through a best fit of the measured orbit

difference

Analytical computation of position and slope change at the septum using fit results.
Bumpers used for correcting the changes keeping closed orbit unchanged outside.

Simulation steps:

Same 589 measured difference orbits used for finding 589 fake sets of quadrupole

misalignments through SVD, excluding the same last set of BPMs as before.

MADX used to evaluate orbit and extraction trajectory in presence of such misalign-

ments.

Fitting code invoked within MADX script and results read back with the MADX

script.

Correction of computed value of (∆x, ∆x′) at MSE.61852 with a closed orbit

bump using the 4 bumpers.

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ORBIT SPSRING 24-10-12 02-33-37 LHC2 CY9160 T18500.data- ORBIT SPSRING 13-10-12 15-42-21 LHC2 CY52822 T18500.data All BPMs used for fitting, only BPCEs excluded.

2000
1500
1000
500

500 1000 1500 2000 300 1500 4500 6000 x(µm) s(m) Radial Orbit at BPMs MADX ’meas.’ Orbit Fit

(x, x′) at MSE.61852 xS x′

S

(mm) (mrad) MAD-X 0.935

0.020

FIT 0.825

0.013

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Results for the same 589 measured difference orbits: ǫerr

x

ǫcorr

x

(µm) (µm) closed orbit 0.0063 ± 0.0061 0.0019 ± 0.0016 trajectory 0.0063 ± 0.0061 0.0019 ± 0.0016 Correctors strength: θnom θ (mrad) (mrad) kmpsh61402 0.000 0.000 ± 0.003 kmplh61655 0.512 0.506 ± 0.005 kmplh61996 0.094 0.093 ± 0.003 kmpsh62199 0.398 0.393 ± 0.003

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Preliminary conclusions:

The “fake correction” and the Fourier analysis method seem to be almost equivalent

and more promising than the amplitude-phase-∆p/p fit method.

Both methods are robust against BPMs random calibration errors.
The Fourier analysis do not get mess up if non working BPMs are included in setting

the MADX model. To be done:

Check effect of missing monitors.

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Looking for sources of orbit drift Best fit orbit differences with one “corrector” a and ∆p/p.

400
200

200 400 600 800 1000 1200 1400 1600 100 200 300 400 500 600 xrms (µm) Orbit # Best fit results: Horizontal before after dp/p (1e6)

10 20 30 40 50 60 70 80 500 1000 1500 2000 Occurrence Element # MSE MBA.634 MBB.103

(Ring starts with MBA.61390) The more often appearing element are MBA.634nn and MSE.6nnnn with 111 and 31

ccurrencies respectively (they are 180o a part). It is worth noting that the MSE in

sectors 2 and 4 never appear.

aany element except drifts

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Fit all orbits by using only MBA.63430 or MSE.61872. In 10 occurrences among the first 190 orbits they fail to improve the orbit. The very last ones are best corrected by VVFA.61957 (an instrument!).

500 1000 1500 2000 100 200 300 400 500 600 xrms (µm) Orbit # before MBA MSE VVFA

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Main dipoles are known to have dipolar errors. Too few BPMs (113 in the horizontal plane) for a meaningful fit attempt of single errors. “Systematic” dipolar errors in the bending magnets: use all 361 MBAs and 384 MBBs for a 2 parameters fit.

8
6
4
2

2 4 6 8 100 200 300 400 500 Kick (µrad) Orbit # MBs best kicks (horizontal) MBA MBB 200 400 600 800 1000 1200 1400 100 200 300 400 500 RMS (µm) Orbit # Difference Orbit RMS values (horizontal) measured subtracting MBs

Intriguing behaviour of kicks but disappointing fit quality...

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MSE fringe field a

a SL-Note-99-053 MS

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Correcting MSE.61852 kicks:

2

2 4 6 8 10 12 14 100 200 300 400 500 Kick (µrad) Orbit # MSE.61852 kicks MSE

Assuming the septum moves for instance by 10 mm it is in the worst case Θ = ∆B∆L Bρ = 0.00276 − 0.00205 1501 = 0.47 µrad which is too small.

SLIDE 48

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Looking for the best couple of elements for fitting the measured orbit differences QDA.61910 appears quite often! If used alone it happens to correct as well as the MSE’s and MBA’s even for the few cases were they failed!

200 400 600 800 1000 1200 1400 1600 100 200 300 400 500 xrms (µm) Orbit # before MSE MBA QDA

SLIDE 49

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2

2 4 6 8 10 12 14 16 18 20 100 200 300 400 500 Kick (µrad) Orbit #

Needed quadrupole drift: δ = Θ kLQ = 14 0.0359 µm = 390 µm

SLIDE 50

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Idea: there is an extraction bump leakage and the other magnets simply mimic its effect! Effect of single bumpers:

200 400 600 800 1000 1200 1400 1600 100 200 300 400 500 xrms (µm) Orbit # before MPLH.61655 MPLH.61996 MPSH.62199

None of the 3 bumpers is responsible alone for the orbit drifts, with the exception of last ≃50 orbits which are corrected by MPLH.61996 alone.

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8
6
4
2

2 4 6 8 10 100 200 300 400 500 Kick (µrad) Orbit # MPLH.61655 MPLH.61996 MPSH.62199

nb: MPLH.61655 and MPLH.62199 are about 180o a part.

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Use them in pairs. MPLH.61996 and MPSH.62199:

200 400 600 800 1000 1200 1400 100 200 300 400 500 xrms (µm) Orbit # before after

10
5

5 10 15 100 200 300 400 500 Kick (µrad) Orbit # MPLH.61996 MPSH.62199

SLIDE 53

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Use them in pairs. MPLH.61655 and MPLH.61996:

200 400 600 800 1000 1200 1400 100 200 300 400 500 xrms (µm) Orbit # before after

6
4
2

2 4 6 8 10 12 14 100 200 300 400 500 Kick (µrad) Orbit # MPLH.61655 MPLH.61996

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Use them in pairs. MPLH.61655 and MPSH.62199:

200 400 600 800 1000 1200 1400 100 200 300 400 500 xrms (µm) Orbit # before after

80
70
60
50
40
30
20
10

10 100 200 300 400 500 Kick (µrad) Orbit # MPLH.61655 MPSH.62199

Used in pairs they can correct the orbit drift. Results are consistent with the fact that whatever is the error of the 3 bumpers, the bump may be always closed by any two of them.

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Excursus following the meeting discussion Assume only one of the 3 bumpers is “wrong”. Thus

1. By using each of them in turn I should be able to find one which corrects perfectly

the orbit.

2. If I use the other two too. Perfect bump:

xo

i = Ti,1θ1 + Ti,2b θ1 + Ti,3c θ1

Error for instance in the second bumper: xi = xo

i + ∆xi = Ti,1θ1 + Ti,2b θ1 + Ti,3c θ1 + Ti,2∆θ2

Using the first and last bumpers the correction program should find a minimum of the rms orbit with θc

1 = ∆θ2/b and θc 3 = c∆θ2/b. This means that the ratio of

the correcting kicks is fixed to the bump ratio, namely: θc

3/θc 1 = c.

We do not observe 1) nor 2).

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However when using MPLH.61655 and MPLH.62199, the ratio is almost constant (see right picture in slide 53). MPLH.61655 and MPLH.62199 kick ratios

0.2 0.4 0.6 0.8 1 100 200 300 400 500 600 Θ3/Θ1 Orbit # Kick Ratios c

In particular for the last 50 orbits it is indeed θc

3/θc 1 ≃ c= 0.77.

This agrees with the fact that those last 50 orbits are indeed well corrected by the second bumper, MPLH.61996, alone (see picture in slide 49)!

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More in general when each bumper has an error it is xi = xo

i + ∆xi = Ti,1θ1 + Ti,2b θ1 + Ti,3c θ1 + Σ3 k=1Ti,k∆θk

This can be rewritten for instance as xi = xo

i + ∆xi = Ti,1(θ1 + ∆θ1) + Ti,2b θ1 + Ti,3c θ1 + Σ3 k=2Ti,k∆θk

xi = ¯ xo

i + ∆¯

xi = Ti,1 ¯ θ1 + Ti,2b ¯ θ1 + Ti,3c ¯ θ1 + Σ3

k=2Ti,k∆¯

θk with ¯ θ1 ≡ θ1 + ∆θ1, ∆¯ θ2 ≡ ∆θ2 − b∆θ1 and ∆¯ θ3 ≡ ∆θ3 − c∆θ1. Therefore the situation with errors on all three bumpers is equivalent to a rescaling of the bump amplitude plus two errors and therefore can be compensated by any couple

f bumpers. The relationship between the two correcting kicks is in this case not fixed.

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Using all three bumpers.

200 400 600 800 1000 1200 1400 100 200 300 400 500 xrms (µm) Orbit # 3 Kicks Fit before after

60
50
40
30
20
10

10 20 30 100 200 300 400 500 600 Orbit # 3 Kicks Fit MPLH.61655 MPLH.61996 MPSH.62199

The large scatter of MPLH.61655 and MPLH.62199 kicks is related to the fact that they are about 180o a part. Excursus end

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There is an extraction bump also in LS4: what happens if the bumpers in LS4 are used instead?

200 400 600 800 1000 1200 1400 100 200 300 400 500 xrms (µm) Orbit # before after

10
8
6
4
2

2 4 100 200 300 400 500 Kick (µrad) Orbit # MPLH.41994 MPSH.42198

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Bumpers ripplea:

a L. Norderhaug Drøsdal courtesy

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Summary

Drifts of the SPS closed orbit at extraction have been observed and related to the
bserved losses in the transport lines.
Algorithms for steering the beam back to a golden orbit using only the interlocked

bumpers and not relying on the BPCEs have been studied and seem providing a substantial reduction of the oscillation amplitude in the transfer lines.

Bad and good news: the quest for the sources of the orbit drift is pointing to the