1. ATF2 Lattice v4.5 Matching and Tuning Performance with Lucretia Glen White, SLAC LCWS2011 Granada, Spain

2. Overview ATF2 v4.5 lattice New matching capability using Lucretia particle tracking. Matching results Tuning simulation results Analysis of Dec experimental tuning results. Summary & recommendations for goal 1 operations.

3. Lattice Version 4.5 Version 4.4 has the latest, KEK measured values for all magnet multipoles (Sext, Oct field strengths and angles). V.4.5 includes the new UK laserwire installation between QM14FF and QM13FF.

4. Optical Matching Routines in Lucretia New software written in Lucretia, a “Match” class for first and higher- order beam matrix matching using tracking engine, fast 3 rd -order polynomial fitting to IP beam particles and Matlab-based optimisation routines. – ‘lsqnonlin’ for first-order (Twiss) parameter matching This produces a “first-pass” solution with the desired optical parameters but with existing 2 nd and 3 rd order geometric and chromo-geometric aberrations present at IP still. – ‘fminsearch’ (Nelder-Mead) Remove higer-order aberrations by direct optimisation of sigma_11 and sigma_33 terms Generate range of matched FFS lattices with different IP beta functions. Match constraints – Waist at IP with given beta functions – Waists at MFB1FF and (MFB2FF OR LW1FF) Ensures correct phase advances for FFS feedbacks Match variables – Matching quads + final doublet for initial Twiss match – All FFS quadrupole and sextupole strengths plus SK1FF strength, for final beam size optimisation.

5. FFS Feedback Waists Sharp waists at MFB1FF and MFB2FF locations only sampling of IP phase in FFS. Need to ensure matching keeps waist at these locations for feedback.

6. V4.5 Lattices Generated Matched lattices generated and stored in MAD (xsif) and Lucretia input formats. – Available from flight-simulator subversion repository and SLAC web page (http://www.slac.stanford.edu/~mdw/ATF2/v4.5/) BX1BY1, BX2.5BY1, BX10BY1, BX2.5BY2.5, BX10BY0.3 – i.e. 1, 2.5, 10 times the nominal (4mm, 0.4mm) values. Different optics files generated for vertical waist at MFB2FF bpm location or at LW1FF location. Matching performed and results shown with horizontal emittance = 2nm. Here, show analysis of expected performance of different lattices and consider viability for use in Goal 1 tuning efforts.

7. FFS Matching Results BX1BY1BX2.5BY1BX10BY1BX10BY0.3BX2.5BY2.5 MFB2FF waist σ x /σ y (um) 232/0.48250/0.52216/0.94148/0.27235/0.89 IP σ x /σ y (um/nm)3.9/34.94.5/34.78.9/35.09.9/28.74.5/55 IP 3 rd order subtracted σ y (nm) 29.231.429.023.054.6 IP effective β y / mm0.0710.0820.070.0440.25 Dominant residual aberrations and contributions / nm T344(3.2), T322 (0.7) T344 (2.5), U3246 (0.2), T322 (0.1) T344(3.2), T322(0.9) T344 (3.6), U3446 (0.3) --- Only constrained IP σ y during optimisation. Optimiser found solutions with smaller than desired effective vertical beta functions. Dominant residual aberration found to be T344 term. Main contributions of this term come from QD0FF multipoles, with smaller contributions from QD4AFF and QD8FF multipoles. SD4FF I=80A

8. IP Vertical Beta Constrained Add constraint to optimiser that 3 rd order-subtracted beamsize be the same as the desired beta function implies (sqrt(emit*beta)). – Use similar penalty function for beam size and aberration corrected beamsize These lattices in file repository as ATF2lat_BX1BY1_bcons.saveline etc BX1BY1BX2.5BY1BX10BY1 MFB2FF waist σ x /σ y (um)275/0.67249/0.57150/1.16 IP σ x /σ y (um/nm)4.2/35.84.5/36.38.9/36.0 IP 3 rd order subtracted σ y (nm) 34.334.034.2 IP effective β y / mm0.0980.0960.097 Dominant residual aberrations and contributions / nm T344(0.8), U3246 (0.2) T344 (2.1), U3244 (0.1) T344(1.2), U3246(0.1)

9. Vertical Waist at LW1FF Matched lattices with upstream vertical waist at laserwire waist instead of MFB2FF Files in repository as ATF2lat_BX1BY1_lw1ff_bcons.saveline etc BX1BY1BX2.5BY1BX10BY1 LW1FF waist σ x /σ y (um)290/1.1274/0.54145/1.2 IP σ x /σ y (um/nm)3.5/36.14.5/36.08.9/35.8 IP 3 rd order subtracted σ y (nm) 34.1 34.3 IP effective β y / mm0.097 0.098 Dominant residual aberrations and contributions / nm T344(1.3), (0.2) T344 (1.5), U3246 (0.2) T344(1.2), U3246 (0.05)

10. Re-Matched Optics Beta functions through FFS for lattices with and without multipoles added.

11. Multipole Measurement “Error” Effects on Lattices Randomly assign a strength error (individually) to all multipole values. For 100 sets of error assignments (seeds), plot RMS change in beam size at IP versus level of assigned strength error.

12. Lucretia Tuning Simulation Specify list of errors – Generate a database which characterises every unknown aspect of the accelerator Generate 100 versions of machine lattice – Each lattice has a different set of errors generated from error table. – Typically, each error condition is generated from a gaussian distribution. Simulate initial steering/BBA/coupling/dispersion correction etc for each lattice seed. Calculate list of aberrations present at IP (up to 3rd order required). Make a knob to correct most common aberration from 100 seeds being simulated. Iterate 4&5, each iteration generate a knob (if new aberration) which is orthogonal with other knobs generated previously. Repeat until no further improvement seen in IP spot size on average across simulated seeds.

13. Tuning Simulation Steps Apply expected error distributions. Use EXT correctors + BPMs (EXT FB) to get orbit through EXT. Use FFS FB to get beam through FFS. Correct Dy/Dy' in EXT using skew-quad sum knob. Correct coupling in EXT using coupling correction system. Use FFS FB for launch into FFS. FFS Quad BPM alignment using quad shunting with movers. FFS Quad mover-based BBA. FFS Sext BPM alignment using Sext movers and IP BPM. Generate and apply IP tuning knobs. – Run 35 iterations of tuning knobs (cpu time constraints)

14. Error Parameters

15. Tuning Knob Orthogonality & Range Response of aberrations to tuning knobs for different lattice configurations. Both degree of orthogonality of knobs and their range differ across the lattices. BX1BY1 BX1BY1_bcons BX2.5BY1 BX2.5BY1_bcons BX10BY1 BX10BY1_bcons

16. Tuning Performance Summary BX1BY1BX1BY1_ bcons BX2.5BY1BX2.5BY1 _bcons BX10BY1BX10BY1_ bcons σ y (50% CL) / nm (core size) 39.645.735.541.934.8X σ y (90% CL) / nm (core size) 48.364.643.150.841.8X P(σ y <37nm) / %3210661277X AGauss Spread (50%CL) / nm 6.84.84.05.92.7X AGauss Spread (90%CL) / nm 19.939.111.9207.2X Convergence (lower better) 6957071183684992X Residual aberrations T324 T326 T314 T324 T322 T324 α y T324 T314 T326 T322 T324 T312 X Will not tune Will not tune

17. BX10BY1 Tuning Results

18. December Data Following ~expected curve. EXCEPT: – – Do not expect this aberration term to appear from simulations. – If corrected coupling at FFS entrance, nothing in FFS to introduce this (magnetically)

19. Coupling Aberration Induced at IP due to FFS Magnet Rolls and Offsets

20. Why do we see beam size improvement with application of knob? Alignment of IPBSM fringes with respect to FFS alignment frame? – If plane of fringes rotated by ~20 mrad (~3.5 degrees), provides a similar contribution to beamsize in tuning simulations as that seen in experiment. IMPORTANT: – If waist not centred on IPBSM exactly, generates, therefore MUST FIRST REDUCE AND α y TERMS BEFORE USING KNOB. – It could be that in Dec we hadn’t fully removed term and the waist was not exactly in place, and corrected with knob. Having source and source at IP greatly complicates tuning process, we should try to find and eliminate any sources manually first. Using a larger β x * optics also makes this problem worse. !--- Probably essential to have roll control of IPBSM fringes ---! – @ ~100urad level (for 10um σ x )

21. Tuning Performance with Rotated IP 20 mrad10 mrad1 mrad< 100urad σ y (50% CL)137 nm90.0 nm38.3 nm34.8 nm σ y (90% CL)190 nm73.4 nm47.6 nm41.8 nm BX10BY1 lattice simulated with rotated IP Added tuning knob (orthogonal knob using 4 EXT skew quadrupole magnets) Applied iteratively after each and waist knob during simulated tuning procedure Any amount of IP fringe rotation above 100urad level adversely affects final tuned spot size regardless of any attempt to include tuning knob (either skew-quad based or direct IP rotation-based)

22. Rotation of IPBSM Fringes wrt Beam x- y Profile? What is the relative angle of the fringe pattern compared with x-y profile of beam at IP? What is the angle of the scan pattern with respect to the beam profile? What is the reproducibility? Can we know this/control this at 100urad level? θ ?

23. Conclusions/Recommendations Full optics matching + tuning simulation for multiple ATF2 lattice options performed in Lucretia. These version 4.5 lattices released and available in subversion repository and from SLAC website. Have to decide which lattice to use for goal 1 tuning – How much do we care about σ x * ? Better performance with larger values, but further away from ILC specs. – How much do we care about “correct” β y * value (100um)? No “penalty” for ATF2 for lowering β y *, but there is at ILC (hourglass effect + backgrounds), so again further away from ILC specs. – Suggest BX2.5BY1 lattice- slightly reduced probability of <37nm spot size but similar 50/90 CL performance and less sensitivity to IP rotation. Then study “bcons” lattice options some more. Need to think seriously about how to measure and control IPBSM fringe orientation/direction of scan.

24. Further Work Evaluate longer-term tuning (beyond standard 35 tuning steps). – “Dither feedback”, randomly select and apply knobs over time to slowly drop beam size. Look at “best seed” solutions found by tuning simulation. – Is there a better initial solution that includes both standard quad/sext strength matching + deliberate magnet offsets as default lattice. – How does such a lattice tune and respond to standard errors? How to tune the beam if we cannot eliminate coupling source? – Investigate tuning on IP vertical emittance instead of vertical beam size. – Requires multiple scans of IP beam size with waist in different location (maybe by horizontal scan of a sextupole).