� ✂ ✁ -Beating, dispersion and coupling correction in the LHC R. Tomás, R. Calaga, O. Bruning, S. Fartoukh, M. Giovannozzi, Y. Papaphilippou & F. Zimmermann LHCCWG-14 of June, 2006 Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.1/25
✂ Magnetic measurements and allocation - Realistic assessment of the beta-beating correction needs of realistic b2 errors in the machine - Magnetic measurements available in official databases - Information on both magnetic measurements plus slot allocation (MEB activity) are required - A code was developed in AT/MAS-MA by P. Hagen, J.-P. Koutchouk & E. Todesco. This code deals with all type of magnetic errors (multipoles) - Output: MAD-X file with magnetic errors. In case a magnet is already assigned to a certain slot its magnetic errors are assigned to this slot. Otherwise, errors are drawn from measured distributions. Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.2/25
✂ ✠ ✄ ✠ ✆ ✝✞ ✟ ✁ ✡ ✁ ✆☛ ☞ ✁ � ✄ ✠ ✂ ✟ ☞ ✆ ✂ � ✁ ✟ ✝✞ � � ✆✝✞ ✌ ✁ ✁ ✂ ✄ ☎ ✆☛ -beating observable The measurement of -functions needs good BPM calibration or good knowledge of focusing properties Not suitable for commissioning Phase advance between nearby BPMs is a robust observable independent of BPM calibration, offset and tilt and focusing errors, thus phase-beating: is measured with standard FFT or SVD techniques of kicked data Synergy with J. Wenninger’s LOCO? Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.3/25
✆ ✟ � ✁ � ✆ ✟ ✂ -beating Vs -beating 0.8 horziontal vertical 0.7 0.6 2 1/2 ∆ φ peak [rad] 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ∆ β/β peak 0.4 horziontal vertical 0.35 0.3 2 1/2 ∆ φ rms [rad] 0.25 0.2 0.15 Precise relation 0.1 between 0.05 and 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Rogelio Tom´ as Garc´ ıa ∆ β/β rms -Beating, dispersion and coupling correction in the LHC – p.4/25
☎ ✌ ✞ ✁ ✁ ✁ ✁ ✁ � ✄ ✆ ✞ ☎ ✠ � ✂ ✒ ✝ ✍ ☎✝ ☎ ✎ ✁ � � � ✄ ✁ � ✁ ✂ ✁ ✁ ✁ Dispersion observable Dispersion is normally measured using radial steering and BPM readings. Best BPM calibration error: 4% (LHC-BPM-ES-0004) BPM resolution (pilot bunch): 200 m Specification on Dispersion [Rep. 501]: ✟✡✠ ✁☞☛ In [ EPAC 02, F. Zimmermann et al. ] the pilot bunch BPM resolution was not enough to measure dispersion in the range ☎✑✏ Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.5/25
✠ ✏ ✝ � ✂ ✄ ☎ ✠ ✄ � ✡ ✌ � � ✁ � ✠ � ✄ ✠ ✠ ✂ � ✡ � ✠ � ✂ ✂ ✠ ✁ ✌ ☎ � ✂ ✄ ✂ -beating & dispersion correction We compute the non-square matrix R from ideal MADX model as are all quad circuits in MADX (210 per ring). we invert R using the SVD so the correction is ✄✆☎ ✄✞✝ are weights used to choose beta-beating or ✄✟☎✡✠ dispersion correction. However correction is not guaranteed Simulations are needed to prove correction and to assess performance. Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.6/25
☎ ✎ ☎ � � � ✁ � ✂ ✆ ✂ ✠ ✁ ☎ ✝ � � ✆ ✆ ✆ ✆ ✆ ✠ ✂ ✠ ✁ ✄ ✠ ✠ ✁ ✁ Simulation ingredients I All �✂✁ �✂☎ errors from measurements: 25 MQM MQY example not really Gaussian MQX 20 MQT not centered 15 Counts 10 5 0 -40 -20 0 20 40 60 80 b2 [units] Extra Gaussian noise of 5 units added to quad rms misalignments of chromaticity sextupoles, mm rms misalignments of MCS, mm Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.7/25
☎ � � ✂ ✁ � ☎ ☎ ✝ ☎ ✝ ✟ ✁☛ � ✆ ✎ ✝ ☎ ✆ ✆ ☎ ☎ ✆ ☎ ✆ Simulation ingredients II Gaussian noise, , added to the MADX phase to account for error measurements. depends on BPM noise ( m), decoherence time (N=400 turns) and kick amplitude (a=4 mm). From tracking simulations the error on the phase: 1 RMS: X RMS: Y Peak: X Peak: Y 0.8 Frequency [normalized] 0.6 0.4 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Horizontal ( ∆φ model - ∆φ meas ) rms [deg] To be on the pessimistic side we take . Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.8/25
� ✂ ✁ ✂ -beating correction ( ) β -beat correction, LHC injection 0.6 Uncorrected Corrected 0.5 0.4 ∆ β/β y,peak 0.3 0.2 0.1 0 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 ∆ β/β x,peak -beating correction works! Best peak corrections in the 5% level Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.9/25
✁ ✂ ✂ � What happens to dispersion? ( ) Dispersion-beating before and after correction 0.9 Uncorrected Corrected 0.8 0.7 ∆ D x,peak [m] 0.6 0.5 0.4 0.3 0.2 0.1 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 ∆ D x,rms [m] Dispersion remains unchanged (better than not con- sidering dispersion at all) Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.10/25
✂ Not considering dispersion (old table) �✂✁ Dispersion-beating before and after correction 1.4 Uncorrected Corrected 1.2 1 ∆ D x,peak [m] 0.8 0.6 0.4 0.2 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ∆ D x,rms [m] Dispersion gets spoiled -beating correction must consider dispersion Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.11/25
✁ ✂ ✂ � Comparing dispersion to specs. ( ) Dispersion-beating before and after correction 4.5 Uncorrected Corrected 4 x ) peak [10 -2 m 1/2 ] 3 rms spec. 3.5 3 2.5 ( ∆ D x / β 1/2 rms spec. 2 1.5 1 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 ( ∆ D x / β 1/2 x ) rms [10 -2 m 1/2 ] Peak specification is met for most of the seeds but not the case for the rms specification. Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.12/25
✁ ✂ ✂ � Strengths of quadrupoles ( ) I KQ[4-10] 1000 KQX KQF KQD KQT 100 Cumulative Counts 10 1 -20 -15 -10 -5 0 5 10 15 20 Power supply percentage deviation [%] Variation in the percent level with respect to nomi- nal setting at injection Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.13/25
✁ ✂ ✂ � Strengths of quadrupoles ( ) II Lower limit (not for KQT) KQ[4-10] 1000 KQX KQF KQD KQT 100 Counts 10 1 -120 -110 -100 -90 -80 -70 Strength percentage deviation with respect to collision[%] Strengths are within good limits Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.14/25
✂ ✁ ✂ � Can we correct dispersion only? ( ) No BPM calibration error has been assumed Dispersion-beating before and after correction 0.9 Uncorrected Corrected 0.8 0.7 ∆ D x,peak [m] 0.6 0.5 0.4 0.3 0.2 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 ∆ D x,rms [m] Some seeds’ dispersion-beating not correctable! Probably due to misuse of Q[7-7], to be clarified Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.15/25
✌ ✠ ✡ � ☎ ✠ ✝ ✡ ✌ ✝ ✠ ☎ ✡ ✌ ✝ ☎ ✠ ✡ ✝ ✝ ☎ ✄ � ✄ � ☎ ✌ � � � ✂ ✝ Coupling A robust global coupling correction is presented at: R. Jones et al, CERN-AB-2005-083 BDI0 Local coupling is also measurable from the secondary spectral lines of BPM data around the ring: Independent of BPM calibration errors and succesfully used at SPS and RHIC. What about LHC? The BPM data comes for free with the -beat correction Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.16/25
� � ✂ Local coupling measurement simulation Random quad tilts and rms orbit are assumed plus a large tilt error (15mrad) at 6km. BPM resolution=200 m, BPM tilts=2mrad, 400 turns. Thanks to A. Franchi 0.105 MADX 0.1 Simulation 0.095 0.09 0.085 |f 1001 | 0.08 0.075 0.07 Large tilt error identified 0.065 0.06 0.055 0 5 10 15 20 25 Longitudinal location [km] Measurable under realistic conditions Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.17/25
✁ � ✂ ✡ ✞ ✞ ✟ ✞ ✝ ✂ � ✞✡ ✝ ✂ ✁ Local coupling correction Using all the skew quadrupole correctors: 0.12 Uncorrected Corrected 0.1 0.08 ✞✠✟ |f 1001 | ✄✆☎ 0.06 0.04 0.02 ✄✆☎ 0 0 5 10 15 20 25 30 Longitudinal location [km] Satisfactory local correction Not perfect due to the particular distribution of errors/correctors. Best local correction is realignment Rogelio Tom´ as Garc´ ıa -Beating, dispersion and coupling correction in the LHC – p.18/25
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