Online Models for PEP-II Status

1. Online Models for PEP-II Status • brief review of PEP modeling • fully coupled “normal form” optics representation • Orbit Response Matrix (ORM) model calibration: “fudge factors” for quadrupole strengths • continuing work Mark Woodley (ILC)

2. PEP Online Modeling: Procedure • prepare input files for MAD • read reference input files • set magnets to configuration file values • apply ORM-derived fudge factors to quadrupole strengths • run MAD • use XCORs and YCORs to steer to measured absolute orbit • compute “effective” transfer matrices (RMATs) • generate model files for MCC • extract coupled lattice functions from RMATs Mark Woodley (ILC)

3. Database MAD AT RMATs, Twiss, nij RMATs, Twiss, nij Model Files Model Files LEGO Magnets, Orbit, Fudges Magnets, Orbit, Fudges MAD input LERmodel HERmodel Configuration Files Configuration Files Reference Files PEP Online Modeling: Process MCC (VMS) pepoptics (linux) Input Files AT 11 8 7 10 1 SCP Matlab 5 2 6 9 SCP, SSH MAD updated to v 8.51/15 4 DIMAD not used anymore 3 Mark Woodley (ILC)

4. Lattice parameters in highly coupled systems • MAD (v 8.51/15-SLAC) has been modified to output “effective” transfer matrices (first order expansion about the closed orbit; includes “feed down” effects from sextupoles) • Andy Wolski’s normal form analysis1 is used to extract coupled lattice parameters from the transfer matrices • 10 coupled lattice parameters (μ, β, α, η, η΄ for modes 1 & 2) and 8 elements of the normalizing transformation (n13, n14, n23, n24, n31, n32, n41, n42) at each element are returned to be loaded into the MCC database 1See http://www-library.lbl.gov/docs/LBNL/547/74/PDF/LBNL-54774.pdf Mark Woodley (ILC)

5. ORM analysis: LER • ORM analysis begins with the “config” lattice (actual magnet strengths, steered to the measured absolute orbit) • only quadrupole strength errors are fitted (no sextupole strength errors) • errors are assigned to quadrupole families (power supplies) • sextupole “feed down” effects are not explicitly fitted (even though they are important for LER) … the assumption is that the BPMs are correct (BBA) and that steering to the measured orbit is sufficient to model the feed down effects • “fudge factors” are computed by comparing the fitted quadrupole strengths with their config values; normal quadrupole fudge factors are multiplicative; skew quadrupole fudge factors are additive (since most skew quads should nominally be at or near zero) • the actual ORM analysis for LER is performed by Cristoph Steier (LBNL) using the Matlab-based version of the LOCO program See PT’s presentation on Recent ORM Results for further details … Mark Woodley (ILC)

6. QDBM6L • normal quadrupoles • skew quadrupoles ORM-derived fudge factors: LER (1) ORM data taken on December 11, 2003 Mark Woodley (ILC)

7. unfudged fudged unfudged ORM-derived fudge factors: LER (2) fudged Mark Woodley (ILC)

8. ORM-derived fudge factors: LER (3) unfudged fudged fudged unfudged Mark Woodley (ILC)

9. ORM-derived fudge factors: LER (4) Mark Woodley (ILC)

10. ORM-derived fudge factors: HER (1) • normal quadrupoles • skew quadrupoles ORM data taken on June 10, 2004 Mark Woodley (ILC)

11. ORM-derived fudge factors: HER (2) fudged unfudged unfudged fudged Mark Woodley (ILC)

12. ORM-derived fudge factors: HER (3) fudged unfudged fudged unfudged Mark Woodley (ILC)

13. ORM-derived fudge factors: HER (4) Mark Woodley (ILC)

14. Continuing work • steering to absolute orbits when generating the model in order to properly account for sextupole feed down effects requires accurate knowledge of BPM offsets → BBA1; many offsets for both HER and LER have been measured and are being routinely used to correct measured orbits; LER BBA is ongoing (more on this in a minute …) • continue to fine tune the ORM analysis setup to avoid degeneracy in the variables • fudge factors for individual magnets (?) • develop more robust steering algorithms for model generation to take into account bad BPMs (especially for LER) • create “fudged” design configs … move toward design optics in both rings • participate in the ILC design 1See Tonee Smith’s presentation on New BBA Hardware for further details … Mark Woodley (ILC)

15. BBA at PEP-II Status • large unexplained LER BPM offsets from BBA → uncoupled analysis of orbits in a highly coupled machine • new analysis algorithm • BPM offsets revisited Mark Woodley (ILC)

16. Unexplained large (~1 cm) LER BPM offsets from BBA … from Marc Ross’ summary at April MAC … Mark Woodley (ILC)

17. BBA Analysis • orbit fitting lies at the heart of our BBA analysis algorithm • move the beam in a quadrupole (using a closed bump), change the strength of the quadrupole, and look at the orbit change • if the orbit doesn’t change when the quadrupole strength is changed, the beam is passing through the center of the quadrupole; the reading on a nearby BPM under these conditions is the “BPM offset” • if you’re moving the beam in X, you look at the change in the X orbit, which should be proportional to the distance (in X) between the beam and the quadrupole center … in an uncoupled ring • if you’re moving the beam in X, and the beam happens to be offset in Y to begin with, the previous statement remains true … in an uncoupled ring • if you’re moving the beam in X, and the beam happens to be offset in Y, and your ring is highly coupled, you have to pay attention to what’s happening in both planes simultaneously (well duh) Mark Woodley (ILC)

18. QDBM3 simulated X data -10 mm Y offset uncoupled orbit fit Δx (mm) blue–o = MAD red--= orbit fit Mark Woodley (ILC)

19. Mark Woodley (ILC)

20. BBA Analysis Mark Woodley (ILC)

21. Coupled BBA Analysis Algorithm Change in closed orbit (Δxco,Δyco) due to a change in strength (K→K(1)) of a misaligned quadrupole (xbq,ybq): • includes closed orbit effects of ΔK (both kick and position shift) • includes optics effects of ΔK (change in closed orbit response matrix) • fits both planes simultaneously, including any known coupling †A. Wolski and F. Zimmerman, “Closed Orbit Response to Quadrupole Strength Variation”, http://www-library.lbl.gov/docs/LBNL/543/60/PDF/LBNL-54360.pdf Mark Woodley (ILC)

22. QDBM3 simulated X data -10 mm Y offset coupled orbit fit Δx (mm) Δy (mm) Mark Woodley (ILC)

23. LER BPM X Offsets: Then and Now Mark Woodley (ILC)

24. LER BPM Y Offsets: Then and Now Mark Woodley (ILC)

25. Uli Wienands, Jim Turner, Martin Donald, Gerry Yocky Yuri Nosochkov, Yunhai Cai, Yiton Yan Peter Tenenbaum, Marc Ross, Janice Nelson, Tonee Smith James Safranek, Andrei Terebilo Andy Wolski, Christoph Steier Acknowledgements & thanks! Mark Woodley (ILC)