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Coupling analysis

Coupling analysis. Analysis is based on the high statistics measurements in the last night of the first MD : For each plane, kicks of +- 40 m rad were applied to 2 correctors 90 ˚ out of phase in the first part of TI8 (~ 1 hour at each setting).

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Coupling analysis

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  1. Coupling analysis • Analysis is based on the high statistics measurements in the last night of the first MD : • For each plane, kicks of +- 40 mrad were applied to 2 correctors 90˚ out of phase in the first part of TI8 (~ 1 hour at each setting). • The analysis is based on autosave data from steering program. • Each data sample is averaged and then re-converted into new steering program file using UNIX shell and gawk scripts. • The difference orbits are analysed with the steering program to get a first idea of the possible source of coupling (if any). • The data is then converted to LOCO input and fitted with LOCO in a version that handles the coupled response. TI8 analysis / J. Wenninger

  2. Coupling – steering test / V1 Coupling from 80 mrad kick @ MCIAV.813 Correction with a single kick in H plane … MICADO picks QIF.824 : 1.4 mrad Before Difference After TI8 analysis / J. Wenninger

  3. Coupling – steering test / V2 Coupling from 80 mrad kick @ MCIAV.815 Correction with a single kick in H plane … MICADO picks again QIF.824 : 1.4 mrad Before Difference After TI8 analysis / J. Wenninger

  4. Coupling – steering test / H1 Coupling from 80 mrad kick @ MCIAH.816 Correction with a single kick in V plane … MICADO picks now QID.821 : -1.1 mrad Before Difference After TI8 analysis / J. Wenninger

  5. Coupling – steering test / H2 Coupling from 80 mrad kick @ MCIAH.818 Correction with a single kick in V plane … MICADO picks again QIF.824 : -3.3 mrad Before Difference After TI8 analysis / J. Wenninger

  6. 813 814 815 816 817 818 819 820 821 822 823 824 825 826 ‘Graphical’ analysis : V  H Have a look at the trajectories associated to the V correctors… From a naïve point of view the result from the steering prgram analysis can be explained : same kick because the trajectory phase & amplitude is the same ! A kick at 821 should appear for one corrector – does not fit with simple analysis of the trajectories… TI8 analysis / J. Wenninger

  7. 813 814 815 816 817 818 819 820 821 822 823 824 825 826 Graphical analysis : H  V Have a look at the trajectories associated to the H correctors… A kick at 821 should appear for both correctors – does not fit with simple analysis of the trajectories… Also it does not fit with the V  H ! From 824 there can only be a kick for corr. 818 – trajectory goes through 0 for 816. This is consistent with the steering program results…  the situation may be more complex : more than 1 or 2 sources ! TI8 analysis / J. Wenninger

  8. Coupling fit • The fit is done with the LOCO – full analysis of the response including cross-plane response. The fit includes BPM and corrector gains. • To handle the coupling, short (1 cm) skew quads are installed in the MADX sequence file in front of suspicious quadrupoles. • A full fit is performed, including skews. Very small skews are removed and the fit is iterated… • The skew strength Ks is converted into a quadrupole tilt f using : • The fit is redone with the tilts and skew strengths until the Ks 0. Two iterations are sufficient. TI8 analysis / J. Wenninger

  9. Fit results • Coupling : • QIF.824 is ‘outstanding’ with a tilt of 5 mrad corresponding to a2/b2 = 0.01. • The values for the tilts can be plugged directly into the TI8 sequence. • Coupling is at the level of 2% (defined as amplitude ratio). • Other fit results : • The spread of the BPM calibrations is 1.5%. This better than before – better statistics… • The average BPM gain is consisted with previous fits : • G = 0.898 H plane • G = 0.880 V plane • The residual fit-measurement is ~ 250 mm for the in-plane data. This is a factor ~ 10 higher than the statistical error on the data of ~ 30 mm : • Local errors ? • BPM effects ? non-linearities… TI8 analysis / J. Wenninger

  10. Fit results - plots Fit residual are slightly larger than errors (~ 30 mm) HV 816 HV 818 VH 813 VH 815 TI8 analysis / J. Wenninger

  11. Stability analysis / 1 The BPMs are high correlated in a line/ring, and one can profit from this property through a Singular Value Decomposition (SVD) of the BPM data. This decomposition is a powerful way of extracting modes out of the data. The BPM data is put in the form of a matrix B. The reading of BPM i for measurement j represented by bij . Each trajectory corresponds to a line of B : N = no. of BPMs M = no. measurements assume M > N ! time space TI8 analysis / J. Wenninger

  12. Stability analysis / 2 The matrix B is decomposed by SVD into : • where : • U is a matrix of normalized and orthogonal time patterns. • V is a matrix of normalized and orthogonal space patterns. • W is a diagonal matrix with the eigenvalues of the space patterns. • Each ‘mode’ / spacial pattern has an associated weight / eigenvalue that characterizes its amplitude and an associated time pattern. • This method is often referred to as MIA (Model Independent Analysis). • It is an interesting and (sometimes) powerfull way to extract characteristic ‘behaviours’ from the data. TI8 analysis / J. Wenninger

  13. Stability data • The analysis is based on the stability measurement from the first night (SatSun) of the first MD (pilots). • For each plane, the trajectories are combined into a file suitable to be read in by the SPS multi-turn acquisition program where the MIA method is implemented. • SVD is applied and the eigenvectors are scanned for ‘meaningful’ information. • Except for the ‘static’ trajectory (one mode), there is nothing of interest (just noise and BPM junk) except for one mode in the horizontal plane. • The ‘meager’ outcome is probably due to the fact that the noise of 200-300 mm and bad BPM readings tend to dominate. TI8 analysis / J. Wenninger

  14. Eigenvalues When the analysis is applied to TI8 data (H and V) there is only one interesting signal : the 5th horizontal eigenvalue shows a clean betatron oscillation starting at the beginning of the line… time structure spacial structure (BPMs) TI8 analysis / J. Wenninger

  15. MSE candidate • The spacial vector is fed back into steering program for analysis : • Search for most efficient corrector with MICADO. • MICADO picks MSE (or MDMH.4001 that is ~ at the same phase) as possible source of the perturbation ! Before corr. Difference After corr. with MSE TI8 analysis / J. Wenninger

  16. Cross-check • Pick 2 extreme trajectories (large MSE contribution according to MIA) : • Compute trajectory difference to get largest possible signal. • Search for most efficient corrector with MICADO. • MICADO picks MSE – OK ! H traj difference Before corr. Difference After corr. RMS is ~ consistent with noise… TI8 analysis / J. Wenninger

  17. MSE contribution to (in)stability • Largest kicks : ± 4.5 mrad  ± 3.8×10-4 relative error. • RMS kick : 1.4 mrad  ± 1.2×10-4 relative error. • The oscillation amplitude corresonding to the RMS kick is ~ 100 mm • which corresponds to ~ s/8 for a nominal emittance. • The expected RMS stability at the location of the TCS (Dm = 158˚) is ~ 40 mm. • BUT : I cannot see a correlation with the logged MSE currents !! ?? TI8 analysis / J. Wenninger

  18. Long term average • Trajectory difference (average) after 5 hours : • RMS ~ 50 mm – practicaly consistent with the noise. • No significant coherent oscillation visible. TI8 analysis / J. Wenninger

  19. Further work… One could search for coherent oscillations by fitting betatron oscillations to the BPM data : A fit to the entire line should find the signal observed with MIA and find/set a limit of the signal that is 90˚ out of phase  sensitive to ‘incoming’ signals. A fit to the end of the line (last 4-5 BPMs ?) may give and indication on contributions coming from the line itself (+ incoming). Could resurect / adapt my LEP fit program… TI8 analysis / J. Wenninger

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