1. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 MBA Designs

2. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Outline Introduction to lattice design Longitudinal gradient in the bendings Concept for Diffraction Limited Light Source Green field projects: MAX-IV and Sirius Upgrading processes: ESRF, APS, ANKA, ALS, ELETTRA, SLS MBA Designs : Contents

3. DBA -Lattice With  min and s* the emittance for the DBA-lattice is: In reality however it is a factor 3 to 4 higher. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 DBA - Structure

4. TME –Lattice gives the smallest emittance The emittance is by a factor of 3 smaller as for the DBA structure Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 TME - Structure

5. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Introduction to Lattice Design Cq=1.47*10-6 [m/(GeV^2]

6. Longitudinal Bending Gradient Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

7. Longitudinal Bending Gradient Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

8. The layout for the diffraction limited light source utilizing the MBA structure. The bending magnets in the unit cell with a deflection of 5 degrees and the matching section with an angle of 2.5 degrees. The lattices got the acronym DIFL Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Towards a Diffraction Limited Light Source

9. The arrangements of the magnets within a unit cell of the multi bend Achromat and the corresponding machine functions. The parameters of the magnets are: Bending: L=0.931482 m, ρ=10.674 m, B = 0.93749 T, k=-0.900 m -2 ; QF: L =0.35 m, k=1.992 m -2, g=19.92 T/m, g*L = 6.972 T; Sh:L= 0.1 m, m=53.347m -3, ΣSh*L=5.335 m -2 ; Sv: L=0.2 m, m = -42.730 m -3, ΣSv*L=8.546 m -2 Unit Cell of DIFL-Lattice TME Structure, E = 3.0 GeV, ε = 0.5 nmrad, φ = 5 degr.

10. Emittance of the unit cell as a function of the strength of the focusing quadrupole. Horizontal chromaticity of the unit cell of the lattice DIFL Characteristics of Unit Cell Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

11. Dynamic aperture of the unit cell for the energy deviations of Δp/p = -3% (green line), Δp/p = 0% (blue line), Δp/p = 3% (red line). Characteristics of Unit Cell Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

12. Machine function of the chosen lattice DIFL for the proposed diffraction limited light source Lattice of DIFL (7BA) Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 E=3.0 GeV, ε=500 pm*rad, C=404 m, N=12

13. Dynamic aperture of lattice DIFL for the energy deviations of Δp/p = -3% (red line), Δp/p = 0% (black line), Δp/p = 3% (blue line). Characteristics of DIFL X(s)=2*1.33* η(s)*( ΔE/E) A(s)=(X(s)^2)/ β(s), (ΔE/E)=3% A=5 mm*mrad, β(s=0)=5.2 m/rad ⇉ E(0)= +/- 5.2 mm Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

14. Summary (1995) 1995:According to this investigation it should be possible to build Synchrotron Light Sources with an reduction of the emittance by a factor of 10 in comparison to the existing machines. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

15. Parameters: E = 3.0 GeV C = 287.2 m N = 12 fold  = 4.67 degr.  x = 1.2 nmrad l = 4.6 m  x = 7.6 m/rad  y = 1.7 m/rad First proposal of MAX IV (2003) Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

16. Layout of MAX IV (2014) Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

17. Layout of MAX IV (2014) Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

18. Machine functions within one Achromat of the 5 MBA –lattice proposed by L. Liu et. al. (2013) for the Brazilian light source SIRIUS. The bending magnets are presented by blue boxes. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Layout of SIRIUS (Brazil)

19. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Comparison 7MBA and 5MBA The emittance with the high field bending in the middle of the magnet is: ε = 0.28 nmrad. The emittance without the high field bending in the middle of the magnet is: ε = 0.31 nmrad. Hence the emittance is decreased by roughly 10 % The emittance for the 7MBA is: ε = 0.326 nmrad and the emittance for the 5MBA is: ε = 0.280 nmrad. This is a ratio of: (7MBA/5MBA)=1.164. According to the number of the bendings the ratio should be: (5 / 7)^3 = 0.364, hence there is a factor of 3.2 between the ratios. This we have to understand!

20. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Comparison 7MBA and 5MBA The main reason is that the bending in the middle of the 5MBA-structure has a factor of 3 smaller contribution as the 3 bendings in the middle of the 7 MBA

21. Machine functions within one achromat of the 7 HMBA –lattice. 1.)The achromat has at the beginning and end a DBA structure and the DBA-structures are combined with combined bendings. 2.)The long bendings have a longitudinal gradient. 3.)The phase advance between the sextupole is ≈ n* π. Layout of ESRF-II (HMBA) Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

22. The people at APS made a comparison between the MAX IV lattice (7MBA) and the lattice of the ESRF (HMBA) and found that the HMBA as some advantages (the sextupole settings are smaller). Upgrade of APS: APS II (HMBA) Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

23. Longitudinal Field (HMBA) Change of the emittance for ESRF II with the longitudinal gradient: with gradient ε = 0.132 nmrad, without gradient ε = 2.41nmrad, with inverse gradient ε = 6.67 nmrad. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

24. Upgrade of DIAMOND (DDBA) Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

25. Upgrade of ANKA (DDBA) This proposal has been made by BINP (E.Levichev and his co-workers) Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015

26. TBA 9BA 26 Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Upgrade of ALS (9HMBA)

27. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Upgrade of Elettra

28. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Upgrade of SLS (Unit Cell) B=-0.3633 T k= 3.87 m^-2 Φ=-0.78 degr. B=0.70636 T k= -3.6441 m^-2 Φ=1.09 degr. E=2.4 GeV ε=134 pm*rad Sf Sd There are 5 bendings in a unit cell

29. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Achromat of SLS- II

30. Low Emitt.-Lat.-Design: MBA-Designs, D. Einfeld Barcelona: 23-24 th April 2015 Summary

31. Thank you very much Many thanks to the colleagues providing me with with some material: Andreas Streun, Emanuel Karantzoulis, Eugene Levichev, Riccardo Bartolini, Michael Borland, Hamed Tarawneh, etc.