LHC optics measurement, modeling, and correction with MIA

1. LHC optics measurement, modeling, and correction with MIA Yiton T. Yan SLAC

2. What is MIA? • We have a series of MATLAB programs called MIA that has been proven robust for PEP-II optics correction. • MIA, through a model-independent analysis (MIA) of turn-by-turn BPM orbit data and an auto SVD-enhanced fitting process, brings the real hardware storage ring to a computer -- the virtual machine that matches the real machine in optics. • MIA goes on figuring out an approachable better virtual machine (lower beta beat, lower coupling, lower dispersion beat, etc) for the real machine to listen to and follow. • MIA has helped PEP-II overcome many optics improvement milestones and has had major contributions for PEP-II luminosity enhancement. • For example, If there were no MIA, we could be wondering if we had been able to bring the Low-Energy Ring (LER) to operate at half integer, which helped nearly double PEP-II luminosity subsequently. ___________________________LARP Colaboration meeting 9 Y. Yan

3. Outline • Review MIA contributions to PEP-II improvement. • Propose MIA for LHC optics commissioning, and possible easier implementation of future upgrading. ___________________________LARP Colaboration meeting 9 Y. Yan

4. PEP-II MIA Buffer data acquisition • Resonance excitation at the horizontal, vertical betatron (eigen) tune and then at the synchrotron tune, each for about 1000 turns. • LHC needs driven oscillation and more turns. ___________________________LARP Colaboration meeting 9 Y. Yan

5. Validation of MIA data –symplecticity and noise check • Check BPM data symplecticity without the need to know the BPM aberrations – a strong criterion. • Check BPM data correlation (SVD) to rank the BPM noise level – a weak criterion. • So we have good bases for selecting reliable BPM data. Through years, we have helped PEP-II correct and improve BPM performance. ___________________________LARP Colaboration meeting 9 Y. Yan

6. Four independent linear orbits, dispersions, and phase advances • Obtaining three pairs of conjugate (sine- and cosine-like) orbits from zooming FFT (focused individual component analysis). • Phase advances can then be calculated by talking ratio of the conjugate orbits. • Betatron motion amplitude and dispersive motion amplitude can be calculated, • {Note that If there is no focused excitation, such as pulse-by-pulse jittered Linac BPM orbit data, then one uses principal component analysis instead of individual component analysis.} ___________________________LARP Colaboration meeting 9 Y. Yan

7. ___________________________LARP Colaboration meeting 9 Y. Yan

8. The linear Greens functions Where, in the measurement frame, R is a function of BPM gain and BPM cross-plane coupling. Q12 and Q34 are the two invariants representing the excitation strength.. MIA does not trust the BPM accuracy – MIA figures out BPM gain and cross coupling errors. ___________________________LARP Colaboration meeting 9 Y. Yan

9. Semi-Infinite Greens’ functions for enough constraints that add on accuracy and fitting convergence b a b Redondancy? ___________________________LARP Colaboration meeting 9 Y. Yan

10. The Coupling Ellipses ___________________________LARP Colaboration meeting 9 Y. Yan

11. Check MIA fitting accuracy:Are eigen ellipse tilt angles and axis ratios automatically matched? Yan/mia/ler/2004/OCT28/1 ___________________________LARP Colaboration meeting 9 Y. Yan

12. Auto SVD-enhanced Least-Square fitting for Green functions and phases • Variables: normal quad family strengths, individual skew quad strengths, normal and skew strengths for sextupole feed-downs, BPM linear gains and linear cross couplings and one invariant. • Response quantities: Green’s functions and phase advances, dispersion [coupling ellipses, etc.] among BPMs. • Unlimited Green’s functions • self-consistent phase advances • Auto optimal selection of SVD modes. Unstable modes are automatically avoided to guarantee convergence. ___________________________LARP Colaboration meeting 9 Y. Yan

13. Virtual machine • Once we are satisfied with the fitting accuracy, we call the updated lattice model the virtual machine (Virtual LER, Virtual HER). ___________________________LARP Colaboration meeting 9 Y. Yan

14. Optics correction with wanted model • we can select a limited number of key magnets for fitting the virtual machine toward a wanted model. We then generate a knob for dialing into the machine. The “cold” machine responded to our expectation very well. ___________________________LARP Colaboration meeting 9 Y. Yan

15. MIA constraints and weights for wanted machine – an example Initial constraint # weight snap-shot special Residuals start end start end residuals quantities 0.00041393 1 Tunex 1 1 1000 5000 0.0019588 38.5064 0.000169228 2 Tuney 2 2 1000 5000 0.00485956 36.581 0.000245875 3 nux 3 28 100 100 0.000305344 0.499811 0.00375321 4 nuy 29 54 100 100 0.00387669 0.496279 26.9007 5 Betax 55 425 0.5 1 10.7411 37.0005 4.88197 6 Betay 426 796 0.3 1 4.55298 24.0697 2.06367 7 axay 797 1538 0.3 1 0.836578 5.15022 0.306315 8 tiltxy 1539 2280 10 25 0.329449 0.330447 0.116435 9 axisRatio 2281 3022 10 25 0.151386 0.169479 0.0872007 10 sinPsxt 3023 3393 10 25 0.0806435 0.110078 0.0550547 11 bx**IP 3394 3394 1000 1000 0.00382164 0.306178 0.0016697 12 by*IP 3395 3395 5000 200 0.0021166 0.0096224 0.604155 13 ax*IP 3396 3396 300 2000 0.02563 0.0256379 0.00224 14 ay*IP 3397 3397 300 10000 0.000989 0.000989447 0.0468993 15 Tiltx*IP 3398 3398 100 5000 0.002646 0.00264634 1.52045 16 Tilty*IP 3399 3399 100 1000 0.00710 0.00710003 0.06326 17 bax*IP 3400 3400 100 1000 0.0133853 0.0133853 0.564624 18 bay*IP 3401 3401 100 200 0.425895 0.425895 0.17073 19 sinP0*IP 3402 3402 100 100 0.0533182 0.0533182 0.192546 20 eta13SF 3403 3506 20 30 0.163688 0.425425 0.165198 21 eta13SD 3507 4144 20 30 0.146349 0.381311 0.0716958 22 eta1234IP 4145 4148 100 30 0.0571557 0.0571557 0.0675275 23 eta1234SKEW 4149 4212 20 500 0.0667764 0.282782 0.0636338 24 eta1234INJ 4213 4220 20 2000 0.032879 0.43337 Tune - I Beta Beat coupling Beta* IP waist IP coupling dispersion ___________________________LARP Colaboration meeting 9 Y. Yan

16. We summarize MIA with the flow chart ___________________________LARP Colaboration meeting 9 Y. Yan

17. some examples of MIA for PEP-II optics improvement ___________________________LARP Colaboration meeting 9 Y. Yan

18. Example: Brought PEP-II LER to half integer working tune • MIA successfully brought LER to a half integer working tune and improve LER beta beats and linear coupling. Instantly, LER beam became the stronger one of the two (LER and HER beams). {Without MIA, this was almost impossible because of strong LER coupling.} • Indeed LER became way too strong for the HER. Nonetheless, consequently, PEP-II luminosity increased about 40% . ___________________________LARP Colaboration meeting 9 Y. Yan

19. mac2006 Example: fixed beta beat Virtual HER – Feb 1, 2006comparing beta function bewteen the machine and the ideal latticea dramatic example for beta beat fix we had a very strong HER X beta beat during the beginning period of 2006 run. ___________________________LARP Colaboration meeting 9 Y. Yan

20. Virtual HER after one-shot MIA correction– Feb 16, 2006 • Beta beating fixing mainly from QF5 (we use only the left one). mac2006 We have an updated ideal lattice at BetaX* =33 cm. • We had also added trombones, local and global skews to simultaneously improve couplings, dispersion, and IP optics. • We had a max-out of SQ3L that caused an imperfection of the offline solution. • Since then we had enjoyed an HER record-low residual from the ideal lattice till we ramped the currents at later stage of the run. ___________________________LARP Colaboration meeting 9 Y. Yan

21. mac2006 Example: Successful LER major orbit steering • Another key improvement for PEP-II optics in 2006 is the successful LER major orbit steering. • It is usually difficult to correct the optics after a major steering for the coupled LER. • We relyed on MIA modeling after the steering to generate wanted approachable optics model and dial in the solution for restoring the linear optics. ___________________________LARP Colaboration meeting 9 Y. Yan

22. Example: MIA for HER emittance improvement in 2007 MIA solution from Virtual HER06FEB07 Ideal HER lattice Virtual HER08FEB07 Virtual HER06FEB07 ___________________________LARP Colaboration meeting 9 Y. Yan

23. Proposal my proposal of MIA for LHC optics commissioning, and easier implementation of future upgrading. (recalling that, with MIA precision modeling, Franz-Josef, at one-shot, install many permanent skew quads at LER IR. Also Walter had tested successfully one-shot conversion of HER 60-degree machine to HER 90-degree machine) ___________________________LARP Colaboration meeting 9 Y. Yan

24. Fruitful visit to CERN and very much encouraged for applying MIA to LHC • Earlier this month I had a very fruitful visit to CERN. I had visited Oliver Bruning, Frank Zimmermann, and others. Especially I had very pleasant meetings with Rogelio Tomas, Frank Schmidt & Iiya Agapov, Rama Calaga, Akio Morita (KEK), Masamistu Aiba (KEK support), Javier Serrano, and M. Bai (BNL), . I visited AC dipoles and other facilities. I also gave a seminar on MIA. They had high expectation of my long-term visit. And actually has listed me as a collaborator. (shown in the presentation by S. Kopp for AC dipole report yesterday as I copied a small paragraph from a slide made by M. Bai below:) • “Meeting Summary: Rogelio • Yiton Yan offered his collaboration in the implementation of the MIA analysis for the LHC, with the advantage of obtaining a virtual machine that would reprocuce the observations. A perfect communication between the optics measurement on-line application and the on-line model application is being established.” • Indeed, I have been very much encouraged for applying MIA to LHC. ___________________________LARP Colaboration meeting 9 Y. Yan

25. MIA for LHC optics commissioning and improvement • Non-invasive (or tiny invasive) process – rely on orbit fluctuations – may be useful for identifying BPM problems. (unknown before a dedicated study with real data) • Invasive process but no machine stopping – need well done AC dipoles for adiabatic oscillation driving process to preserve emittance. Need to know LHC optics well beforehand(?). • Invasive process with dedicated MD time for MIA data acquisition just as we have done for PEP-II. 20 to 30 minutes needed(?) for a complete set of data acquisition. Beside the two AC dipoles (still under development at CERN) for applying MIA to driven oscillation, We would still wish to have synchrotron oscillation which Fox and companies had helped me done very well for PEP-II. (single bunch representing single-particle dynamics) ___________________________LARP Colaboration meeting 9 Y. Yan

26. CERN contacts • I wish to list my general contacts: Oliver Bruning and Frank Zimmerman at CERN. • My close-work contacts: Rogelio Tomas who is coordinating LHC optics correction at CERN, and Mei Bai for my visiting BNL. • Online-work contact: Frank Schmidt & Iiya Agapov for those MIA generated products that are judged suitable for online process. Indeed, I had given the two 13 slides talk during my visiting CERN. They expressed highly interest and urged me to contact them as often as possible. ___________________________LARP Colaboration meeting 9 Y. Yan

27. FTE, Time Frame and Milestones • I would propose myself at ½ FTE both for FY 2008 and FY 2009. • In 2008 before LHC has beam, preparation (modification) of MIA to suit for the proton (Heavy ion) storage rings is needed. • RHIC at BNL is a very good candidate for testing updated MIA, especially they have already made an invitation (from M. Bai). I would expect at least a visit or two in and after March 2008. the success of applying MIA to RHIC will definitely make a strong case for LHC. • I would expect that I could be at CERN at very beginning when LHC has beam for testing precision MIA measurement of the LHC optics and help identifying BPM problems if there is. It could be a long-term visit of 3 months in 2008. • I would also expect a long-term visit to CERN (a total of half a year) in 2009. In collaboration with the CERN team as mentioned in a previous slide, we would expect to get LHC optics model and start LHC optics improvement (beta beat and coupling correction, etc.) with MIA. • I would wish some time down stream, we could also have remote control process to LHC at SLAC for in-time test of MIA updated technique and certain minor studies of LHC optics. However, I understand, ultimately personal appearance at CERN is still needed. Thanks! ___________________________LARP Colaboration meeting 9 Y. Yan