Optics modeling and correction

1. Optics modeling and correction Yiton T. Yan Stanford Linear Accelerator Center For optics working group: Y. Cai, W. Colocho, F-J. Decker, M. Donald, Y. Nosochkov, M. Sullivan, J. Turner, U. Wienands, W. Wittmer, M. Woodley, Y.T. Yan, G. Yocky, etc.

2. Outline • Offline modeling (MIA) • MIA data acquisition and symplecticity • Auto SVD-enhanced Least-Square fitting • Virtual machine • Optics correction with offline wanted model • MIA constraints and weights for wanted machine • MIA-to-Lego • Online model and online measurement • Optics correction with online model ___________________________MAC 2006 Y. Yan

3. MIA data acquisition and symplecticity check • Resonance excitation at the horizontal betatron (eigen) tune and then at the vertical tune and the synchrotron tune (thanks to William Colocho), each for about 1000 turns to get a complete set of data. • Considering BPM aberration only for linear gain and linear cross coupling, we can check BPM data symplecticity by calculating and comparing the invariant ratio without the need to know the BPM aberrations. • We also check BPM data correlation (SVD) to rank the BPM noise level. • So we have good bases for selecting reliable BPM data. Through years, we have helped PEP-II correct and improve BPM performance. • Obtaining three pairs of conjugate (sine- and cosine-like) orbits from zooming FFT (focused individual component analysis). • Calculating phase advances and Green’s functions among BPMs as well as dispersions (to a proportional scale) at BPMs. ___________________________MAC 2006 Y. Yan

4. Auto SVD-enhanced Least-Square fitting for Green functions and phases • Treating 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 as well as one energy scale as variables, we update the lattice model and calculate Green’s functions, phase advances, coupling ellipses, dispersions, etc. among/at BPMs. • Unlimited Green’s functions (no worry about degeneracy), providing sufficient constraints to guarantee Least-Square fitting convergence. • Orbits updated by linear BPM aberrations during fitting offers self-consistent phase advances and dispersions. • phase advances are independent from linear BPM gain but not from BPM cross coupling because BPM cross coupling and lattice coupling are not distinguishable. • Auto optimal selection of SVD modes for fitting iterations. Unstable modes are automatically avoided to guarantee convergence – no problem for near half-integer tune cases. ___________________________MAC 2006 Y. Yan

5. Virtual machine • We reserve eigen-plane projected (to the real x,y) coupling ellipses’ tilt angles and axis ratios without fitting to see if they are automatically matched for accuracy checking. • Once we are satisfied with the fitting accuracy, we call the updated lattice model the virtual machine (Virtual LER, Virtual HER). ___________________________MAC 2006 Y. Yan

6. Virtual machines – August 15, 2006comparing beta function between the machines and the ideal lattices These are the HER and LER beta functions right before the last shutdown. HER Beta beating resulted from operators’ IP matching tuning that reached the record luminosity 1.2e34. Correcting beta beating is not a challenge to us. It is the difference of the warm and cold machines that is most challenging at this time. LER ___________________________MAC 2006 Y. Yan

7. Virtual machines – August 15, 2006IP characteristics HER • Adding a beam-beam map in HER would reduce beta_x* • Beta_y*’s are reasonable. • IP wasits are reasonable. LER ___________________________MAC 2006 Y. Yan

8. Virtual machines – August 15, 2006comparing dispersion between the machines and the ideal lattices HER • There are still rooms for vertical dispersion correction. LER ___________________________MAC 2006 Y. Yan

9. Virtual machines – August 15, 2006comparing coupling between the machines and the ideal lattices HER • from the past experience, the couplings (coupling ellipse tilt angles and axis ratios) of these machines are the better ones. However, there are still a lot of rooms for improvement. LER ___________________________MAC 2006 Y. Yan

10. Optics correction with offline wanted model • Once we have the virtual machine, the model can be kept with MIA for an optics correction solution and/or fed to LEGO for beam-beam and optics studies . • we can select a limited number of key magnets for fitting to get a wanted model. We then generate a knob for dialing into the machine. The “cold” machine responded to our expectation very well. ___________________________MAC 2006 Y. Yan

11. 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 ___________________________MAC 2006 Y. Yan

12. Virtual HER – Feb 1, 2006comparing beta function bewteen the machine and the ideal lattice If you recall, we had a very strong HER X beta beat during the beginning period of the last run. We could have fixed it right away, however, due to more urgent problems, this high beta beat fix was postponed till mid-February, 2006. ___________________________MAC 2006 Y. Yan

13. Virtual HER after correction– Feb 16, 2006 • Beta beating fixing mainly from QF5 (we use only the left one). 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. ___________________________MAC 2006 Y. Yan

14. Successful LER major orbit steering • One of the key improvement for PEP-II optics in this run is the successful LER major orbit steering. • It is usually difficult to correct the optics after a major steering for the coupled LER. • We rely on offline modeling (MIA) after the steering to generate wanted approachable optics model and dial in the solution for restoring the linear optics. ___________________________MAC 2006 Y. Yan

15. MIA to LEGO • One of our major progress in this run is that the virtual machine obtained from MIA can be fed into the lattice program LEGO for Beam-Beam studies (YC), and/or for optics studies such as preparing beta bump dial-in solution (YC,FJD). ___________________________MAC 2006 Y. Yan

16. Online model • Once MIA buffer data are generated at mcc, we have a one-shot process (MW) to compress the data; send them to computer PEPOPTICS; run MIA to obtain the virtual machine; and then kick back the virtual machine to mcc as the updated online model after one extra step that requires mcc panel and passwords. • We could also perform offline MIA process for the virtual machine and use data transfer programs (MW, WC) to send it to mcc. ___________________________MAC 2006 Y. Yan

17. Phase advances – online measurement / online model -- LER 15AUG06 X Y • Phase advances between online measurement and online model are about 1 – 2 degree except in some questionable BPM locations. • BPM cross coupling play some role on these 1 to 2 degree online measurement deviations from the online model. ___________________________MAC 2006 Y. Yan

18. Beta – online measurement / online model -- LER 15AUG06 X Y • With the online model for LER, the online measurement of Beta* is more consistent with MIA results. We do not see something like 7mm Beta_y*. ___________________________MAC 2006 Y. Yan

19. C12 Bar – LER 15AUG06 Online measurement Online model • C12 Bar pattern between online measurement and the online model seems to be consistent. Indeed they are pretty much the same within acceptable error range. ___________________________MAC 2006 Y. Yan

20. Phase advances – online measurement / online model -- HER 15AUG06 X Y • BPM cross coupling play some role on these 1 to 2 degree online measurement deviation from the online model. ___________________________MAC 2006 Y. Yan

21. Beta – online measurement / online model -- HER 15AUG06 X Y • Beta between online measurement and online model are reasonable but not as much satisfied as parameters. ___________________________MAC 2006 Y. Yan

22. C12 Bar – HER 15AUG06 • C12 Bar pattern between online measurement and the online model seems to be consistent. Indeed they are pretty much the same within acceptable error range. Online model Online measurement ___________________________MAC 2006 Y. Yan

23. Online correction • Now that we have a rather accurate online model updated as needed, online correction such as orbit bump for coupling and/or dispersion correction can be performed much better. • Orbit steering can be performed better. • Chromatic correction can be benefited. • IP can be understood better. • … ___________________________MAC 2006 Y. Yan

24. Online orbit fit –LER AUG15 Courtesy FJD um ___________________________MAC 2006 Y. Yan

25. Online dispersed orbit fit – LER AUG 15 Courtesy FJD ___________________________MAC 2006 Y. Yan

26. Online partial orbit fit – HER AUG 15 ___________________________MAC 2006 Y. Yan

27. Online partial dispersed orbit fit – HER AUG 15 ___________________________MAC 2006 Y. Yan

28. Summary • We have been, for years, able to get accurate offline models with MIA. • MIA can provide offline wanted model for optics correction and the machine listens for beta beat correction, bringing operation to half integer, linear coupling reduction, …. • MIA to LEGO is a new development this year, which allows LEGO to study the real machine and to predict PEP-II luminosity more accurately. • MIA model is now used for online applications – the online model. • Online measurement shows more consistent results now. This will benefit our future online corrections. • But there are still challenges: • Warm machine vs. cold machine. • Beam-beam effect on the model. • Orthogonal and dynamical IP knob dialing technique. • And more always … Thanks! ___________________________MAC 2006 Y. Yan

29. Appendix Not part of the talk from here on. Just keep these slices for in case need

30. The linear Greens functions Where, in the measurement frame, R is a function of BPM gain and BPM cross-plane coupling. They, along with the phase advances are used for SVD-enhanced fitting to obtain a virtual accelerator Q12 and Q34 are the two invariants representing the excitation strength, of which we know the ratio very well. MIA does not trust the BPM accuracy – MIA figures out BPM gain and cross coupling errors. ___________________________MAC 2006 Y. Yan

31. Beta function from updated Online model – LER 15AUG06 ___________________________MAC 2006 Y. Yan

32. Residual of Online orbit fit –LER AUG15 Courtesy FJD ___________________________MAC 2006 Y. Yan

33. Residual of Online orbit fit – LER AUG 15 dispersion Courtesy FJD ___________________________MAC 2006 Y. Yan

34. Residual of online partial orbit fit – HER AUG 15 ___________________________MAC 2006 Y. Yan

35. Residual of online partial orbit fit – HER AUG 15 dispersion ___________________________MAC 2006 Y. Yan