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(Yet Another) TI2/8 Dispersion Study

(Yet Another) TI2/8 Dispersion Study. J. Wenninger December 2008. TI2 Dispersion. Ti2 horizontal dispersion match is not perfect. Consistently observed with a number of measurements, mostly LHC S23+ only (no TI2). This data is from the second injection test. Optics on L-side of IR3 fixed.

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(Yet Another) TI2/8 Dispersion Study

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  1. (Yet Another) TI2/8 Dispersion Study J. Wenninger December 2008

  2. TI2 Dispersion • Ti2 horizontal dispersion match is not perfect. Consistently observed with a number of measurements, mostly LHC S23+ only (no TI2). This data is from the second injection test. Optics on L-side of IR3 fixed. • In normalized coordinates, the amplitude is ~ 0.035. But it is consistent with having its origin at the start of the line / SPS.

  3. TI2 Dispersion V • Ti2 vertical dispersion is perfect.

  4. Dispersion • Dispersion measurements from August 24th (check), after rematching by M. Meddahi using initial conditions from May 2008 and before starting to change quads in TI8 !

  5. Dispersion : measurement - model Measured - Model Q5 (Measured – Model)/sqrt(beta) [sqrt(m)]

  6. TI8 Initial conditions • Initial conditions do not explain LHC beam 2 dispersion. • Top : fit on all data – poor. • Bottom : fit on LHC only. Does not match TI8. The phase is : • Phase = n + 0.054 +- 0.002 [2 pi] • Amplitude = 0.075

  7. DFS in YASP • A simultaneous correction of the trajectory/orbit and the dispersion was implemented in YASP. • The correction can be done with either MICADO or SVD, and the relative weight of the dispersion can be adjusted (wrt trajectory/orbit). • The dispersion response matrix is calculated from the optics data (beta, phase, dispersion, strengths) using analytic formulae that were checked against MADX. • See : http://jwenning.web.cern.ch/jwenning/documents/yasp/Disp-formulae.pdf • >> Applied to the dispersion data and corresponding trajectory of previous slides. • And the result is …

  8. Steering • YASP prediction for the dispersion correction. • The dispersion is improved significantly, but only when the dispersion is over-weighted wrt trajectory.

  9. Steering / II • YASP prediction for the trajectory correction. • To compensate the dispersion, the TI8 trajectory is degraded (a ~8mm oscillation is produced) in order to generate the required dispersion at the entrance to the LHC.

  10. Steering Summary • Evolution of the predictions for trajectory, kick and dispersion rms versus number of correctors used for MICADO, when the dispersion is over-weighted. • The results quickly stabilize. Adding more correctors does not help… • The results are similar with SVD (no surprise !).

  11. MADX Comparison Direct comparison with MADX. Here the nominal model. >> For comparison with next slides…

  12. MADX dispersion with YASP kicks MADX Check • YASP verification with MADX: • Add predicted corrector kicks (with inverted signs) to the nominal TI8 model in MADX and verify that the predicted dispersion and trajectory are consistent with the measurement, i.e. that the YASP correction is (theoretically) correct. • >> The model with kicks fits the data and is consistent with YASP.

  13. MADX Check / II >> The predicted trajectory with kicks is consistent with the YASP prediction for the trajectory difference (see previous slides) ! MADX trajectory with YASP kicks

  14. (Preliminary) Conclusion on DFS • DFS works. • DFS is able to correct/improve the dispersion in the LHC. • But a dispersion correction requires a degradation of the trajectory in TI8. • Possible conclusion : • The origin of the dispersion in the LHC is NOT due to trajectory kicks since the trajectory degradation seems to be ‘artificial’, i.e. used to compensate another cause.

  15. Food for Thoughts • The dispersion wave in the LHC seems to be of constant amplitude, and it SEEMS to start ~ location of Q5 (phase/2pi = 10.5). • Let’s try a naïve test…

  16. Q5 to … 0 !!!!!!!!!!!!!!!! • By some trial and error : set Q5 to 0 • >> Gives a vey good match ! • But it can’t be: • Resulting trajectory response is not consistent with data (Kajetan). • The beta-beat is HUGE, beta > 1km in the LHC. This would have ruined the aperture – inconsistent with observations. • In fact this is similar to the trims on the TI8 quads…

  17. More Thoughts / I • The normalized dispersion wave amplitude is ~ 0.075 to 0.1 m1/2 • The amplitude of a dispersion wave from a single kick (qk) is : • Assuming bk = 100 m and a single source, we need a kick of 7.5 to 10 mrad as a source ! Do we have a problem with missing dipoles or dipole signs in the MADX model ???????????????????

  18. More Thoughts / II • The normalized dispersion wave amplitude is ~ 0.075 to 0.1 m1/2 • The amplitude of a dispersion wave from quadrupole strength error DK is (equation to be checked): • Assuming bQ = 100 m, DQ = 1 m, LQ = 1m, and a single source, we need • DK = 0.0075 to 0.01 m-2 Taking into account the real beta and dispersion, this seems consistent with the attempts to correct the dispersion with a 9% trim on QIF.876. >> Try all quads with good phase wrt wave, estimate amplitude with equation. >> Try a fit using more than one quad + response (Kajetan).

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