1. 1 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Smoothing Based on Best-fit Transformation C. Yu

2. 2 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Outline Introduction Principle Application in SSRF Application in NSLS-II More Consideration Conclusion

3. 3 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China What’s Smoothing a technique to achieve accurate relative alignment of components a main concern of accelerator alignment The reason for smoothing: limitation of survey control network slow floor movement tight relative alignment tolerance loose global alignment tolerance Introduction Smoothing techniques cubic spline functions (DESY) First Principle Component analysis (APS) Based on best fit transformation

4. 4 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China What’s best fit transformation Mathematically, take out the overall translation or rotation between reference and as-built coordinate systems Smoothing Requirement Reference value of fiducials As-built value of fiducials Check the as-built location WRT reference and can be realized by best fit transformation Best Fit Transformation Benefits Easy to understand Readily available in software Handily available with regard to reference and as-built data And more From Spatial Analyzer User Manual 3 translation, 3 rotation and 1 scale parameters

5. 5 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China How to use it for one set of girders or magnet groups? Obtain reference data Obtain as-built data Perform best-fit transformation Compare the residuals of fiducials Decide if the beam orbit is smooth according certain criteria. What has been done by best-fit transformation is taking out of the rotations and translations of as-built values with respect to global coordinate system and showing the deviations relatively. Repeat many times to check the whole ring Smoothing Based on Best Fit Transformation-Basics Layout of C08G2 and C08G4 girder fiducials and best- fit deviations of NSLS-II Storage ring Comparison of C08G2 and C08G4 girder fiducials before and after best-fit transformation.

6. 6 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China In practice, 3 adjacent girders are used Overlap between cells is important. The number of best fit transformation equals to the number of girders. It’s important to have accurate as-built survey data In order to describe the deviations clearly and make them easy to understand, local frames for each girder should be established. The fiducials should be sorted in each group according to their location with respect to beam When a girder is determined to be adjusted, its upstream and downstream girders will be used to transform the as-built survey data to reference data The method is not limited to circular accelerator. Smoothing Based on Best Fit Transformation-More

7. 7 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Application in SSRF (1) SSRF storage ring 432m Initial alignment 2007 Re-alignment in 2012 The best-fit transformation based smoothing technique was initialized. Sextupoles and quadrupoles centers were used during best- fit transformation process. Girders were rotated based on the roll angle Multiple iterations (Realized by MP of Spatial Analyzer) to minimize the residuals

8. 8 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Application in SSRF (2) Computed adjusted amount in horizontal directionComputed adjusted amount in vertical direction The good Circumference error >10 mm ignored. Most of the adjustment below 300 micron First attempt to apply this innovative idea, alignment result was excellent The bad 7 beam lines of phase 1 had to be re- adjusted

9. 9 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Application in NSLS-II (1) Storage ring ~791.5m Girder alignment for ~1 year No final survey before commissioning Epoch 7 survey during shutdown in May 2014 shows deviations of components. Smoothing based on best fit transformation of girder fiducials were used.

10. 10 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Application in NSLS-II (2) Steps: Perform comprehensive survey for girder of interested and its upstream and downstream ones. Compute the measured relative location of 3 girders. Perform a best-fitting between the measured and reference coordinates to see if there are large deviations. As a rule of thumb, the fitting RMS in both X and Y direction should be below 0.05. If the fitting result is larger than 0.05, the downstream fiducials of upstream girder and upsteam fiducials of downstream girder will be used to establish girder adjustment control network. The nominal coordinates of those 4 fiducials will be used to best-fit and transform the measured point group. The measured point group will be used as survey control network and the reference coordinates will be used as alignment goal. “DX Goal” and “DY Goal” shows the goal of adjustment.

11. 11 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Application in NSLS-II (3) The fiducial deviations after best-fit transformation among all 3 adjacent girders. Fiducial best-fit result Each fiducial will be shown 3 times RMS deviation in X and Y direction is 0.034 mm and 0.021 mm respectively Work has been done 22 girders which had been checked 8 girders had been adjusted The maximum adjustment amount is below 300 micron.

12. 12 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Application in NSLS-II (4) The girder center deviations before and after smoothing. Global deviation All girder centers WRT epoch 7 survey Still not a smooth curve, but relative girder alignment is well within tolerance. Nomenclature “O” means original survey “C” means it has been checked “A” means it has been aligned. Lessons learned Girders should be checked in a consecutive manner

13. 13 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Discussions The best-fit transformation based smoothing technique is easy to understand and use Its application is successful for the partial alignment of NSLS-II project. It also yielded excellent alignment quality when it was applied in SSRF for a whole machine re-adjustment during 2012 shutdown. The best-fit transformation based smoothing technique can tackle beamline alignment constraints by avoid moving girders around straight section unless it’s absolutely necessary. By surveying and adjusting the storage ring cell by cell, good storage ring alignment can be maintained. This is important for a new machine as no major shutdown will be necessary at the early stage of running due to large floor settlement.

14. 14 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Summary Best-fit transformation is a basic technique for accelerator alignment in the current time, but smoothing seems a little bit fancy as it usually associates with different language, such as Fourier function, cubic spline or Principal Curve Analysis etc. But the application of best-fit transformation makes smoothing a lot easier and any surveyor can do it. It’s not only a great tool for partial and whole alignment of an accelerator at the beginning of running a machine, but also a possible solution for long term maintenance of storage ring when more constraints present. With dedicated script, the whole smoothing process can be fully automated and high efficiency is expected.

15. 15 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Acknowledgment The author would like to thank all the staff who involved in the NSLS-II and SSRF alignment activities.

16. 16 BROOKHAVEN SCIENCE ASSOCIATES 13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China Thanks for your attention!