1. Y. Ohnishi / KEK KEKB-LER for ILC Damping Ring Study Simulation of low emittance lattice includes machine errors and optics corrections. Y. Ohnishi / KEK December 19, 2007

2. Y. Ohnishi / KEK 2 Emittance and Lattice Errors The purpose of this study is to check a feasibility of the low emittance with optics corrections for the KEKB-LER. For the preparation of e-cloud study(?) Evaluate KEKB-LER lattice includes machine errors. magnet alignment errors(displacement and rotation) and field gradient errors. BPM accuracy should be checked. BPM error consists of alignment error + jitter error. In the case of KEKB, alignment errors is estimated to be ~40 m and a few m for the jitter error. (H.Fukuma, M. Masuzawa) BPM system is an averaged mode(not single-pass). Simulation study The errors are generated according to Gaussian distributions with random seed numbers in the simulation.

3. Y. Ohnishi / KEK 3 E (GeV)2.3  x (nm) 1.5 x 47.53 y 42.59 s -0.013 pp 2.5x10 -4  z (mm) 4.3  s (ms) 75  x * (cm) 90  y * (cm) 3 KEKB-LER Lattice for ILC Damping Ring Study injection point IP Beam energy is changed from 3.5 to 2.3 GeV. wiggler Vc = 2 MV H. Koiso RF

4. Y. Ohnishi / KEK 4 2.5 Non-interleaved Sextupole Arc Cells -I' SD SF

5. Y. Ohnishi / KEK 5 Flexibility of Arc Cell Beam Energy = 2.3 GeV Momentum compaction  p Emittance (nm) 2.8 nm Contribution of wigglers is the same as the arc cells. Allowed region

6. Y. Ohnishi / KEK 6 Chromaticity Correction 54 sextupole families

7. Y. Ohnishi / KEK Simulation Study for Low Emittance Lattice at KEKB-LER Optics correction is performed to the lattice including machine errors to confirm the feasibility of the low emittance lattice. Especially, requirements for the BPM system... Single particle issue

8. Y. Ohnishi / KEK 8 Lattice Errors alignment error x (m) alignment error y (m) rotation error  (mrad) gradient error k/k Bending magnet 200 0.15x10 -4 Quadrupole magnet 100 0.21x10 -3 Sextupole magnet 200 0.22x10 -3 Multipole components and fringe field have been included in the model lattice. Following errors are produced with random numbers according to Gaussian. These numbers are one standard deviation(  ).

9. Y. Ohnishi / KEK 9 Optics Correction Correction of closed orbit distortion 454 BPMs 166 horizontal and 208 vertical steering magnets XY coupling correction measurement: vertical orbit response induced by a horizontal single kick due to a steering magnet. corrector: symmetric vertical local bumps at sextupole pairs(-I' connection) Dispersion correction measurement: orbit response changing rf frequency. corrector: asymmetric local bumps at sextupole pairs(-I' connection) Beta correction measurement: orbit response induced by a single kick due to a steering magnet. corrector: fudge factors to quadrupole magnet power supplies(families)

10. Y. Ohnishi / KEK 10 One of Results Before Optics Correction and After Optics corrections can achieve  y / x =0.2 %, where  x =1.5 nm. BPM accuracy of 3 m resolution(pulse-to-pulse jitter) and 40 m alignment error is enough to correct the lattice. COD correction only COD+XY+Dispersion+Beta correction  y (pm)  y /  y @BPM) (%) Error of BPMs:  jitter = 3  m,  align = 40  m 0.2% Each point means a different seed number to give machine errors. #samples : 100

11. Y. Ohnishi / KEK 11 BPM Resolution and Optics Correction  y /  x = 2% Black circle: COD correction only Red circle: COD+XY+Dispersion+Beta correction  y /  x = 0.2% Target emittance ratio BPM resolution (  m) Vertical emittance (pm) Jitter errors of BPM affects corrections of the lattice. BPM resolution is a few microns BPM resolution is a few microns BPM alignment error: 40  m #samples : 100

12. Y. Ohnishi / KEK 12 BPM Alignment and Optics Correction Blue circle: COD+XY+Dispersion+Beta correction  y /  x = 0.2% Target emittance ratio BPM alignment error (  m) Vertical Emittance (pm) Alignment errors of BPM does not affect corrections of the lattice. BPM alignment error is ~40 microns BPM resolution is 3  m. #samples : 100

13. Y. Ohnishi / KEK Dynamic Aperture Survey at KEKB-LER Low Emittance Lattice

14. Y. Ohnishi / KEK 14 Dynamic Aperture Horizontal aperture with J y = 0  p/p 0 (%) x0/xx0/x ←7.3 mm@IP No error machine error after optics correction

15. Y. Ohnishi / KEK 15 Dynamic Aperture (cont'd) Vertical aperture with J x = 0  p/p 0 (%) y0/yy0/y ←1.2 mm@IP No error machine error with optics correction

16. Y. Ohnishi / KEK 16 Dynamic Aperture for Injection Beam Horizontal aperture with J y /J x = 0.16 x0/xx0/x  p/p 0 (%) injection beam A x = 7.5x10 -6 m A y = 1.2x10 -6 m  x at injection = 120 m 77 mm

17. Y. Ohnishi / KEK 17 Intra-beam Scattering Emittance  x (nm) Particles/bunch ( x10 10 )  z (mm) Particles/bunch ( x10 10 ) Bunch Length  y /  x = 0.2 % Touschek lifetime ~ 130 min(  y /  x =0.2%, N=2x10 10 ) E = 2.3 GeV

18. Y. Ohnishi / KEK 18 Summary KEKB-LER (2.3 GeV): Emittance:  x = 1.5 nm,  y / x =0.2 % Requirements for the BPM system is: BPM resolution should be less than 20 m.  A few m is achieved at KEKB. BPM alignment error is not sensitive to the lattice after the optics correction.  Alignment error is estimated to be ~40 m. Dynamic aperture Dynamic aperture is enough for the injection beam. Touschek lifetime is estimated to be ~130 min (N=2x10 10,  x → 4.9 nm) from the dynamic aperture ( y / x =0.2%).

19. Y. Ohnishi / KEK 19 Backup Slides

20. Y. Ohnishi / KEK 20 Optics Corrections by using sextupoles (1) Sextupoles are located at arc sections and LCC(LER only). vertical bump (+) @sextupole xy coupling (+) vertical dispersion (-) induced by horizontal dispersion xy coupling (+) vertical dispersion (+) induced by horizontal dispersion vertical bump (-) @sextupole xy coupling (-) vertical dispersion (+) induced by horizontal dispersion cancel -I' vertical bump (+) @sextupole xy coupling corrector vertical dispersion corrector

21. Y. Ohnishi / KEK 21 Optics Corrections by using sextupoles (2) Sextupoles are located at arc sections and LCC(LER only). horizontal bump (+) @sextuple quadrupole element (+) horizontal dispersion (-) horizontal bump (+) @sextuple quadrupole element (+) horizontal dispersion (+) horizontal bump (-) @sextuple quadrupole element (-) horizontal dispersion (+) cancel -I' beta corrector horizontal dispersion corrector Not used