1. Low Emittance Lattices
Alex Bogacz, Geoff Krafft and Timofey Zolkin
USPAS, Fort Collins, CO, June 10-21, 2013

2. Outline Synchrotron radiation optimizations
Equilibrium emittance and storage ring lattice design
Emittance preserving lattices
Low emittance lattices, Natural emittance examples:
FODO Lattice
Double/Triple Bend Achromat Lattices (DBA, TBA )
Theoretical Minimum Emittance Lattice TME.
M. Sands, “The physics of electron storage rings, an introduction” SLAC
A. Wolski, University of Liverpool and the Cockcroft Institute, CAS 2009,
USPAS, Fort Collins, CO, June 10-21, 2013

3. Radiation Damping Re-cap
In the previous lecture we have:
discussed the effect of synchrotron radiation on the (linear) motion of particles in storage rings;
derived expressions for the damping times of the vertical, horizontal and longitudinal emittances;
discussed the effects of quantum excitation, and derive expressions for the equilibrium horizontal and longitudinal beam emittances in an electron storage ring.
USPAS, Fort Collins, CO, June 10-21, 2013

4. Synchrotron Radiation Integrals Re-cap
USPAS, Fort Collins, CO, June 10-21, 2013

5. Sand’s Integrals Re-cap
USPAS, Fort Collins, CO, June 10-21, 2013

6. Lattice Examples Practical implementations: FODO
DBA (double-bend achromat)
multi-bend achromat, including the triple-bend achromat (TBA)
TME (theoretical minimum emittance)
USPAS, Fort Collins, CO, June 10-21, 2013

7. Calculating the natural emittance in a lattice
USPAS, Fort Collins, CO, June 10-21, 2013

8. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

9. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

10. FODO lattice - natural emittance1
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11. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

12. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

13. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

14. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

15. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

16. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

17. FODO lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

18. DBA lattice - natural emittance
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19. DBA lattice - natural emittance1
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20. DBA lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

21. DBA lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

22. DBA lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

23. DBA lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

24. TME lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

25. TME lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

26. TME lattice - natural emittance
USPAS, Fort Collins, CO, June 10-21, 2013

27. TME lattice - natural emittance
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28. Summary: FODO, DBA and TME lattices
USPAS, Fort Collins, CO, June 10-21, 2013

29. Design for low emittance lattices
USPAS, Fort Collins, CO, June 10-21, 2013

30. 1350 FODO Cell 50.5 GeV phase adv/cell: Dfx,y= 1350 Arc dipoles:
$Lb=400 cm
$B=2.2 kGauss
$ang=0.3 deg.
$rho = 764 meter
Arc quadrupoles
$Lq=100 cm
$G= 1.2 kG/cm
USPAS, Fort Collins, CO, June 10-21, 2013

31. 〈H〉 averaged over bends
1350 FODO Cell
Emittance dispersion
〈H〉 averaged over bends
Momentum compaction
USPAS, Fort Collins, CO, June 10-21, 2013

32. Quasi-isochronous FMC Cell
Emittance dispersion
〈H〉avereged over bends
Momentum compaction
factor of 2.5 smaller than FODO
factor of 27 smaller than FODO
USPAS, Fort Collins, CO, June 10-21, 2013

33. Arc Optics – 1350 FODO vs FMC Cell
USPAS, Fort Collins, CO, June 10-21, 2013

34. FMC ‘Imaginary gt’ Cell
50.5 GeV
second stability region:
Dfx,y > 1800
Arc dipoles:
$Lb=400 cm
$B=2.2 kGauss
$ang=0.3 deg.
$rho = 764 meter
Arc quadrupoles
$G0= kG/cm
$G1= 5.06 kG/cm
$G2= kG/cm
$G3= 5.07 kG/cm
USPAS, Fort Collins, CO, June 10-21, 2013

35. FMC ‘Double Bend Achromat’ Cell
50.5 GeV
second stability region:
Dfx > 1800
Arc dipoles:
$Lb=400 cm
$B=2.2 kGauss
$ang=0.3 deg.
$rho = 764 meter
Arc quadrupoles
$G0= 2.05 kG/cm
$G1= 2.90 kG/cm
$G2= kG/cm
$G3= 2.97 kG/cm
USPAS, Fort Collins, CO, June 10-21, 2013

36. FMC ‘Theoretical Emittance Minimum’ Cell
50.5 GeV
second stability region:
Dfx > 1800
Arc dipoles:
$Lb=400 cm
$B=2.2 kGauss
$ang=0.3 deg.
$rho = 764 meter
Arc quadrupoles
$G0= 2.92 kG/cm
$G1= 2.89 kG/cm
$G2= kG/cm
$G3= 2.97 kG/cm
USPAS, Fort Collins, CO, June 10-21, 2013

37. Emittance growth due to quantum excitations
USPAS, Fort Collins, CO, June 10-21, 2013

38. Highest Arc Optics – Emittance growth
50.5 GeV, g = 105
TEM-like Optics
emittance increase (last arc): DexN = 4.5 mm rad (
total emittance increase (all 6 arcs): DexN = 1.25 × 4.5 mm rad =5.6 mm rad
USPAS, Fort Collins, CO, June 10-21, 2013

39. Arc Optics – Cumulative emittance growth
Arc 1 , Arc2
Arc 3
Arc 4 , Arc5
Imaginary gt Optics
DBA-like Optics
TEM-like Optics
total emittance increase (all 5 arcs): DexN = 1.25 × 4.5 mm rad =5.6 mm rad
USPAS, Fort Collins, CO, June 10-21, 2013

40. Arc Optics – FMC vs 1350 FODO 50.5 GeV, g = 105 FMC
Normalized emittance increase: DexN = 3.1 e-05 m rad (Dex = 0.3 nm rad )
1350 FODO
Normalized emittance increase: DexN = 7.9 e-05 m rad (Dex = 0.8 nm rad )
USPAS, Fort Collins, CO, June 10-21, 2013

41. Emittance dilution - quantum excitations

42. Equillibrium emittance - quantum excitations

43. Summary
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44. Summary cont.
USPAS, Fort Collins, CO, June 10-21, 2013