LHC NonLinear Measurements Outline NLchroma measurements performed Correction

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LHC Non-Linear Measurements Outline: • NL-chroma measurements performed • Correction of the NL-chroma •

LHC Non-Linear Measurements Outline: • NL-chroma measurements performed • Correction of the NL-chroma • Detuning with amplitude E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Scale of the Non-linear Chromaticity To get an idea of the order of the

Scale of the Non-linear Chromaticity To get an idea of the order of the non-linear effect consider the scale of values obtained in 2011 measurements at dp/p=10 e-3: d. Q [*10 e-3] (@ dp/p=0. 001) Q' Q''' ~2 ~ 2'000'000 2 1 0. 3 To get a feeling for the error one can look at the typical variation between the sets of measurements done in 2011. Typical variation Percentage of typical scale Q'' ~ 100 5% Q''' ~ 50'000 3% E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

2 nd July 2011: correction for 2 nd and 3 rd order chromaticity was

2 nd July 2011: correction for 2 nd and 3 rd order chromaticity was applied E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

2 nd July 2011: correction for 2 nd and 3 rd order chromaticity was

2 nd July 2011: correction for 2 nd and 3 rd order chromaticity was applied E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

2 nd July 2011: correction for 2 nd and 3 rd order chromaticity was

2 nd July 2011: correction for 2 nd and 3 rd order chromaticity was applied Measured d. Q’’ 1, 400 -920 Measured d. Q’’’ 1, 600, 000 -950, 000 Expected d. Q’’’ horizontal vertical 1, 300 -900 1, 600, 000 -910, 000 b 4 correction only horizontal vertical 1, 200 -840 -19, 000 11, 000 b 5 correction only horizontal vertical 110 -63 1, 600, 000 -920, 000 horizontal vertical Model: b 4 & b 5 correction E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Detuning with amplitude: before correction after correction Matched Q''x Measured Q'‘x model detuning measured

Detuning with amplitude: before correction after correction Matched Q''x Measured Q'‘x model detuning measured detuning -2, 100 -720 -11, 500 -3, 700 -12, 000 (200) -2, 900 (600) E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Reserve E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Reserve E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Recap of Non-Linear Chromaticity Measurements of the non-linear chromaticity were performed: • April 2010

Recap of Non-Linear Chromaticity Measurements of the non-linear chromaticity were performed: • April 2010 • 10 th June 2011 Ø lattice octupoles (MO) powered at nominal current 6. 5 A Ø lattice octupoles turned off without any de-gaussing Ø initial measurement with fully pre-cycled lattice octupoles • 2 nd July 2011 Ø NL-chroma of beam 2 measured Ø corrections of the b 4 and b 5 spool pieces applied to kill 2 nd & 3 rd order chroma E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

April 2010 Beam 1 0. 32 QH QV 0. 325 0. 32 0. 31

April 2010 Beam 1 0. 32 QH QV 0. 325 0. 32 0. 31 R 2 = 0. 9079 0. 315 0. 305 0. 28 0. 3 0. 27 Qy (beam 1) Qx (beam 1) 0. 31 0. 295 0. 26 0. 29 R 2 = 0. 9967 0. 25 0. 24 -0. 003 0. 285 -0. 002 -0. 001 0. 002 0. 28 0. 003 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

10 th June 2011 – lattice octupoles powered to 6. 5 A. Two measurements

10 th June 2011 – lattice octupoles powered to 6. 5 A. Two measurements were performed over ranges +-1 e-3 and +-2 e-3 dp/p. Beam 1 Qh 0. 283 Beam 1 horizontal with lattice octupole (MO) 0. 278 0. 273 R 2 = 0. 9829 R 2 = 0. 9824 0. 268 -0. 003 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0 0. 001 0. 002 0. 003 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

10 th June 2011 – lattice octupoles turned off, but not cycled. Two measurements

10 th June 2011 – lattice octupoles turned off, but not cycled. Two measurements were performed over ranges +-1 e-3 and +-2 e-3 dp/p. 0. 288 R 2 = 0. 8596 Qx (beam 1) R 2 = 0. 9702 0. 283 0. 278 0. 273 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0. 000 dp/p 0. 001 0. 002 0. 003 E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

10 th June 2011 – lattice octupoles powered to 6. 5 A. Two measurements

10 th June 2011 – lattice octupoles powered to 6. 5 A. Two measurements were performed over ranges +-1 e-3 and +-2 e-3 dp/p. 0. 325 Beam 1 vertical with lattice octupoles (MO) R 2 = 0. 9944 Qv (beam 1) 0. 32 R 2 = 0. 9937 0. 315 0. 31 0. 305 -0. 003 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0 0. 001 0. 002 0. 003 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

2 nd July 2011 – lattice octupoles were properly pre-cycled, MCOs were powered to

2 nd July 2011 – lattice octupoles were properly pre-cycled, MCOs were powered to +-3 A depending on polarity to give zero field. Measurements done for beam 2 only. E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

3 measurements of the Non-linear chromaticity have been made. Q''x Q''y Q'''x Q'''y 2010

3 measurements of the Non-linear chromaticity have been made. Q''x Q''y Q'''x Q'''y 2010 April beam 1 beam 2 -3, 100 -2, 700 -790 -220 740, 000 230, 000 -1, 800, 000 -1, 200, 000 2011 June beam 1 beam 2 -1, 800 // 870 820 -2, 200, 000 // 780, 000 910, 000 2011 July -2, 100 740 -1, 900, 000 800, 000 beam 2 With octupoles: 2011 June Q''x Q''y Q'''x Q'''y beam 1 -5, 600 2, 600 -660, 000 1, 000 beam 2 -5, 800 2, 200 -2, 100, 000 1, 300, 000 E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

B 3 Static model Q'x Q'y natural chromaticity -86. 2 -82. 1 b 3

B 3 Static model Q'x Q'y natural chromaticity -86. 2 -82. 1 b 3 errors turned on -272. 9 83. 1 -77. 4 -82. 7 2. 0 natural chromaticity -86. 2 -82. 1 b 3 errors turned on -282. 6 89. 4 -76. 3 -83. 2 2. 0 b 3+b 3 spool+lattice sextupoles Errors including dynamic part & put into model as normal b 3+b 3 spool+lattice sextupoles 10 of June, extracted errors and corrections overwrite corresponding elements of static model natural chromaticity -86. 2 -82. 1 b 3 errors turned on -282. 3 91. 6 -76. 2 -82. 9 -4. 4 -20. 9 b 3+b 3 spool+lattice sextupoles E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Potential fine tuning of b 3 spool piece natural chroma correction - multiplication factor

Potential fine tuning of b 3 spool piece natural chroma correction - multiplication factor horizontal 10 KCS. a 12 B 1*z KCS. a 23 B 1*z KCS. a 34 B 1*z KCS. a 45 B 1*z KCS. a 56 B 1*z KCS. a 67 B 1*z KCS. a 78 B 1*z KCS. a 81 B 1*z vertical Q' - Q' natural 8 6 4 2 0 /l. MCS ; /l. MCS ; -2 -4 0. 95 0. 96 0. 97 0. 98 0. 99 1. 00 1. 01 multiplication factor (*KCS) Q' - Q' natural chroma correction - regular increment 12 10 8 6 4 2 0 -2 -4 -6 -0. 0012 horizontal vertical -0. 0010 -0. 0008 -0. 0006 increment -0. 0004 (KCS. a 12 B 1 -z) (KCS. a 23 B 1 -z) (KCS. a 34 B 1 -z) (KCS. a 45 B 1 -z) (KCS. a 56 B 1 -z) (KCS. a 67 B 1 -z) (KCS. a 78 B 1 -z) (KCS. a 81 B 1 -z) -0. 0002 /l. MCS ; /l. MCS ; 0. 0000 E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

10 th June 2011 – lattice octupoles turned off, but not cycled. Two measurements

10 th June 2011 – lattice octupoles turned off, but not cycled. Two measurements were performed over ranges +-1 e-3 and +-2 e-3 dp/p. 0. 320 R 2 = 0. 9913 R 2 = 0. 9961 Qy (beam 1) 0. 315 0. 310 0. 305 -0. 003 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0. 000 dp/p 0. 001 0. 002 0. 003 E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

April 2010 Beam 1 0. 32 QH QV 0. 325 0. 32 0. 31

April 2010 Beam 1 0. 32 QH QV 0. 325 0. 32 0. 31 R 2 = 0. 9079 0. 315 0. 305 0. 28 0. 3 0. 27 Qy (beam 1) Qx (beam 1) 0. 31 0. 295 0. 26 0. 29 R 2 = 0. 9967 0. 25 0. 24 -0. 003 0. 285 -0. 002 -0. 001 0. 002 0. 28 0. 003 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

April 2010 Beam 2 0. 32 QH 0. 325 QV 0. 32 0. 31

April 2010 Beam 2 0. 32 QH 0. 325 QV 0. 32 0. 31 R 2 = 0. 6488 0. 315 0. 31 0. 29 0. 305 0. 28 0. 3 0. 27 0. 295 R 2 = 0. 997 0. 26 0. 25 0. 24 -0. 003 0. 29 0. 285 -0. 002 -0. 001 0. 002 0. 28 0. 003 E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Beam 1 Qh 0. 283 Beam 1 horizontal with lattice octupole (MO) 0. 278

Beam 1 Qh 0. 283 Beam 1 horizontal with lattice octupole (MO) 0. 278 R 2 = 0. 9829 0. 273 R 2 = 0. 9824 0. 268 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0 0. 001 0. 002 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

0. 325 Beam 1 vertical with lattice octupoles (MO) R 2 = 0. 9944

0. 325 Beam 1 vertical with lattice octupoles (MO) R 2 = 0. 9944 Qv (beam 1) 0. 32 R 2 = 0. 9937 0. 315 0. 31 0. 305 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0 0. 001 0. 002 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Qh (beam 2) 0. 283 Beam 2 horizontal with lattice octupoles 0. 278 R

Qh (beam 2) 0. 283 Beam 2 horizontal with lattice octupoles 0. 278 R 2 = 0. 9728 0. 273 R 2 = 0. 9552 0. 268 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0 0. 001 0. 002 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

Qh (beam 2) 0. 283 Beam 2 horizontal with lattice octupoles 0. 278 R

Qh (beam 2) 0. 283 Beam 2 horizontal with lattice octupoles 0. 278 R 2 = 0. 9728 0. 273 R 2 = 0. 9552 0. 268 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0 0. 001 0. 002 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

0. 325 Beam 2 vertical with lattice octupoles R 2 = 0. 9932 Qv

0. 325 Beam 2 vertical with lattice octupoles R 2 = 0. 9932 Qv (beam 2) 0. 32 R 2 = 0. 9834 0. 315 0. 31 0. 305 -0. 002 -0. 001 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean 0 0. 001 0. 002 dp/p E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

10 th June 2011 – lattice octupoles turned off, but not cycled. Two measurements

10 th June 2011 – lattice octupoles turned off, but not cycled. Two measurements were performed over ranges +-1 e-3 and +-2 e-3 dp/p. 0. 288 R 2 = 0. 8596 Qx (beam 1) R 2 = 0. 9702 0. 283 0. 278 0. 273 -0. 002 -0. 001 0. 000 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean dp/p 0. 001 0. 002 0. 003 E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

10 th June 2011 – Octupoles off (but not cycled) 0. 320 Qy (beam

10 th June 2011 – Octupoles off (but not cycled) 0. 320 Qy (beam 1) R 2 = 0. 9913 0. 315 R 2 = 0. 9961 0. 310 0. 305 -0. 003 -0. 002 -0. 001 0. 000 dp/p 0. 001 0. 002 0. 003 E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

10 th June 2011 – Octupoles off (but not cycled). Measurement in x plane

10 th June 2011 – Octupoles off (but not cycled). Measurement in x plane for beam 2 spoiled by tune drift. 0. 320 Qy (beam 2) R 2 = 0. 9889 0. 315 R 2 = 0. 9942 0. 310 0. 305 -0. 0030 -0. 0020 -0. 0010 0. 0000 dp/p 0. 0010 0. 0020 0. 0030 E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

10 th June 2011 - initial measurement, with de-gaussed latttice octupoles was clipped. 0.

10 th June 2011 - initial measurement, with de-gaussed latttice octupoles was clipped. 0. 282 Beam 1 horizonal Qh (beam 1) 0. 281 0. 280 R 2 = 0. 9702 0. 279 0. 278 -0. 0015 R 2 = 0. 9873 -0. 0010 -0. 0005 0. 0000 0. 0005 0. 0010 0. 0015 dp/p 10/06/11 W. Höfle, R. Steinhagen, F. Schmidt, E. Maclean E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

2 nd July 2011 – lattice octupoles were properly de-gaussed, MCOs were powered to

2 nd July 2011 – lattice octupoles were properly de-gaussed, MCOs were powered to +-3 A depending on polarity to give zero field. Measurements done for beam 2 only. E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011

2 nd July 2011 – lattice octupoles were properly de-gaussed, MCOs were powered to

2 nd July 2011 – lattice octupoles were properly de-gaussed, MCOs were powered to +-3 A depending on polarity to give zero field. Measurements done for beam 2 only. E. H. Maclean, CERN, Fi. Del Meeting, 19/7/2011