ANALYSIS OF BEPCII OPTICS AND CORRECTION Yuanyuan Wei

1. ANALYSIS OF BEPCII OPTICS AND CORRECTION Yuanyuan Wei 2007.05.10

2. Outline For BSR、BPR、BER respectively, • Beam based alignment of BPM offsets • Orbit correction • Optics analysis to determine quadruple strength errors, BPM gains and couplings, corrector kicks • Optics measurement after correction • Conclusion and problems

3. BSR BPM offsets Use the method of beam based alignment to determine all the BPM- to-quadrupole offsets Horizontal offset of R3IBPM03 is 0.16m Vertical offset of R2IBPM11 is -0.41m

4. 用响应矩阵方法进行轨道校正 BSR (2.5GeV with all wigglers on) orbit correction before (yellow) and after (blue) BPM offsets are applied

5. Optics analysis and correction using orbit response matrix Using LOCO (Linear Optics from Closed Orbits) to adjust the parameters of a computer model until the model response matrix best fits the measured response matrix. Determining the errors by, • ΔK q — error of quadrupole strength • ΔGi — error of BPM gain • Δθj — error of corrector strength • Δδj — energy shift when horizontal corrector strength change

6. BSR optics analysis and correction • Measure the response matrix with sextupoles off and determine the quadrupole strength errors using LOCO. • The change of quadrupole strengths to restore the optics is described by using the amplitude fudge factor. • Q3 and Q2, Q15 and Q16 , two Q17 are adjacent with same polarity. Furthermore, there is no BPM between Q15 and Q16, two Q17. Their strength errors are shown very large and fight each other. It seems that LOCO can not fit their errors accurately in this case.

7. The fit model predicts the measured horizontal and vertical Beta function. The Beta function is measured when sextupoles on.

8. The comparison of measured Beta function and design model after quadrupole strength errors from LOCO are corrected.

9. Measured dispersion of BSR before correction

10. Design chromaticityζx =4.935 ζy =4.803 Measured chromaticityζx =4.67 ζy =5.78

11. Design chromaticityζx =2.961 ζy =2.88 Measured chromaticityζx =3.42 ζy =3.83

12. Distribution of BPR BPM offsets BPR optics analysis and correction

13. BPR orbit correction before (yellow) and after (blue) BPM offsets are applied

14. BPR optics analysis Measure response matrix with sextupoles off The parameters varied in fitting the model to the measured response matrix were: BPM gains and couplings Corrector magnet kicks and couplings Strengths of all quadrupoles Difference between the measured response matrix and the model response matrix after fitting with LOCO Measured response matrix

15. BPR optics analysis Distribution of residual differences between measured and fitted orbit response matrix ,normalized to the noise level of the respective BPMs

16. BPR quadrupole strength errors BPR optics analysis • Measure the response matrix with sextupoles off and determine the quadrupole strength errors using LOCO. • There are still problems on the adjacent quadrupoles which have same polarity.

17. BPR BPM gains and couplings fitted with LOCO BPR optics analysis

18. BPR correctors kicks fitted with LOCO BPR optics analysis

19. BPR optics correction Response matrix is measured with sextupoles on. QIR and Q1A、Q1B are not fitted in LOCO. Replace the strengths of two adjacent quadrupoles which have same polarity by one parameter fitted in LOCO. As a result their strength errors are averaged . Design tune is 6.54/5.59, measured tune when measuring response matrix is 6.544/5.648, model tune after fitted with LOCO is 6.54485/5.64849, measured tune after correction is 6.539/5.589. Quadrupole strength changes to restore design optics

20. The comparison of measured Beta function and design model after quadrupole strength changes from LOCO are applied.

21. BPR optics correction The relative errors or Beta function after correction

22. BPR optics correction Comparison of measured dispersion before and after correction

23. Distribution of BER BPM offsets BER optics analysis and correction

24. BER orbit correction before (yellow) and after (blue) BPM offsets are applied

25. BER optics correction Response matrix is measured with sextupoles on QIR and Q1A、Q1B are not fitted in LOCO Replace the strengths of two adjacent quadrupoles that are the same polarity by one parameter fitted in LOCO (except for R1OQ15 and R1Q16). Design tune is 6.54/5.59, measured tune when measuring response matrix is 6.57/5.61, model tune after fitted with LOCO is 6.5706/5.6085, measured tune after correction is 6.5380/5.5903 Quadrupole strength changes to restore design optics

26. The comparison of measured Beta function and design model after quadrupole strength changes from LOCO are applied.

27. BER horizontal correctors kicks With the corrector kicks fitted by LOCO, we found the corrector strengths of inner ring are reduced a half by mistake.

28. Conclusion • All the BPM offsets are determined and orbit correction has been done successfully . After correction the average orbit is 0.2/0.08 mm, and rms orbit is 1/0.5 mm. • Analysis of the BEPCII measured orbit response matrix determined the quadrupole strength errors、BPM gains and couplings、correctors kicks and couplings. • The fudge factors of quadrupole are mostly within 1.01~1.02, that is means the real quadrupole strengths are lower than the design strengths. It can be explained by the effect of adjacent sextupole due to the short distance between them. • The fit model accurately predicted the tune、Beta function and dispersion . • The analysis also gave the best settings for quadrupoles to restore the design optics. • After correction, the measured Beta function at most BPMs can be restored within ±10% of design model, except for some places where the design Beta function are small have the relatively large discrepancies due to the measurement accuracy. The distortion of dispersion function is decreased.

29. Problems • The quadrupole errors are relatively large. The sources come from their construction tolerances, power supplies and effects of adjacent sextupole , are there any other systematic errors? Should longitudinal position of quadrupoles 、BPMs or correctors be considered? • In injection and interaction regions, because of the same polarity problems, the discrepancies are also large. Is there any ideal method to resolve this problem? In the futher, • Do some experiments to correct coupling. • Add some constraint conditions in fitting , such as the phase advance in injection region. • Try to determine the sextupole strength errors or offsets .

30. Thanks a lot !