1. Status of SuperKEKB Design: Lattice and IR
Y. Ohnishi
July 7, 2009
3rd Open Meeting of the Belle II
collaboration
KEK
BELLE II
L=8x1035 !
“Tanabata”: Festival of the Weaver ?

2. Nano-beam scheme: Design concept Machine parameters Lattice and IR
Contents
Nano-beam scheme:
Design concept
Machine parameters
Lattice and IR

3. Design concept
Luminosity is determined by
3 parameters in principle.

4. Total projected cross section
Collision scheme
High current scheme
Nano beam scheme sz
sx* L 2f
Half crossing angle: f
Head-on frame
(rotation and Lorentz boost)
Total projected cross section
is equal for each other.

5. High Current
Nano Beam
Bunch length
requirement :
Hourglass requirement :
Luminosity :
Beam-beam parameter :

6. Small bx*, by* and small emittance is required.
Strategy of Nano beam
Smaller sy* provides higher luminosity.
Smaller by* provides smaller sy*, however longer sz is OK. (less HOM, no CSR)
Hourglass (H.G) condition requires smaller sx*, namely
smaller bx* is necessary.
Smaller beam-beam parameter is preferable, so ey should be smaller in proportional to by*
Small bx*, by* and small emittance is required.
Lattice design

7. Requirement: 8x1035 cm-2s-1
“Nano beam scheme” LER/HER ex = 2.8 nm / 2.0 nm bx*= 17.8 mm / 25 mm by* = 0.26 / 0.26 mm xy = ~ KEKB

8. Machine parameters Tentative parameters: LER HER Emittance ex 2.8 2.0nm
Coupling
ey/ex
0.74
1.80 %
Horizontal beta at IP
bx*
17.8
25.0 mm
Vertical beta at IP
by*
0.26
Horizontal beam size
sx*
7.06
7.07
Vertical beam size
sy*
0.073
0.097
Bunch length sz 5
Half crossing angle f 30
mrad
Beam Energy E
3.5
8.0
Beam Current I
3.84
2.21 A
Number of bunches nb
2252
Beam-beam parameter xy
0.079
Luminosity L
8x1035 (8.5x1035 with CW)
cm-2s-1
* Luminosity is obtained from beam-beam simulations.

9. Lattice design

10. item １
Low emittance
HER
Increase
number
of arc cells
LER
Longer
bends

11. item 2
Low beta at IP
Separated final quads
Closer to IP

12. Local chromaticity correction
item ３
Dynamic aperture
for injection,
Touschek lifetime
Local chromaticity correction
No/small emittance
generation

13. Summary of items LER HER Low emittance Low beta at IP
Longer bends
0.89 m to 4 m long
Increase number of arc cells
Smaller dispersion in bends
28 cells to 44 cells
Low beta at IP
Separated final quads.
Closer to IP
Superconducting or permanent magnets
Local chromaticity
correction (LCC)
(to get large DA)
KEKB-LER type
Chicane-like (reverse bends)
Geometrical flexibility
Emittance is generated.
ILC/SuperB type (modified to SuperKEKB)
Bending angle is necessary (no reverse bends).
Emittance can be ignored.

14. One of constraints is tunnel geometry.

15. TSUKUBA IR To Oho To Nikko LER/HER has an incident angle
of -10/+50 mrad for GX-axis.
outer wall
inner wall
LCC
LCC
HER
Nano-LER
LCC
Nano-HER
LCC
LER
Tsukuba

16. In case of HER, large incident angle(50 mrad) makes large bending angle at LCC. Consequently, large dispersion at LCC for HER. Then, chromaticity correction can be done with keeping dynamic aperture.

17. On the other hand, LER can use KEKB-LER type for LCC since wiggler sections can control emittance. Chicane type LCC is almost straight beam line from a global point of view although large dispersion can be made at LCC.

18. Beam axis and Solenoid axis
*GY is parallel to OHO/NIKKO
straight section.
GX is perpendicular to GY.
SuperKEKB HER
KEKB LER
New BELLE
Solenoid? GY
KEKB HER GY
SuperKEKB LER
50 mrad
= mrad
4.55 mrad
mrad GX
-10 mrad GX
BELLE
Solenoid=LER
What is the Belle solenoid axis ?
Solenoid axis is:
LER axis -> mrad
½ of finite-crossing angle -> mrad
or no solution to rotate BELLE

19. LER IR optics
bx*/by*=17.8 mm/0.26 mm
LCC
LCC
uc = 0.44 keV

20. HER IR optics
bx*/by*=25 mm/0.26 mm
LCC
LCC
Y. OHNISHI / KEK

21. HER arc to IR optics Arc Normal cell LCC(Vertical) LCC(Horizontal)
Y. OHNISHI / KEK

22. LER whole ring
C = m (same as KEKB-LER)
Y. OHNISHI / KEK

23. HER whole ring C = 3016.262 m (same as KEKB-HER) #arc cells：40
Y. OHNISHI / KEK

24. IR magnets (Preliminary)

25. Dynamic aperture

26. HER dynamic Aperture (stored)
bx*/by*=25 mm/0.26 mm
NO ERROR
2Jy/2Jx= 1.8%
ne = 6.17x1010
ttouschek = 17 min
x/sx
Dp/p0

27. HER dynamic aperture (injection)
bx*/by*=25 mm/0.26 mm
NO ERROR
Injection Aperture:
(synchrotron injection)
2Jx= 3.7x10-9 m
(1.23x10-9 m in injector)
2Jz=0.5%+0.15%
2Jy/2Jx= 4%
Injection Aperture:
(betatron injection)
2Jx= 5x10-7 m
2Jy=2x10-8 m
2Jz=0.15%(sd=0.05% in injector)
x/sx
Dp/p0

28. LER dynamic aperture (injection & stored)
Injection Aperture:
(betatron injection)
2Jx= 5x10-7 m
2Jy=2x10-8 m
2Jz=0.25%
Touschek lifetime
~400 sec
np = 10.7x1010
k = 0.74 %
Injection Aperture:
(synchrotron injection)
2Jx= 1.2x10-8 m
(4x10-9 m in injector)
2Jz=0.5%+0.25%

29. Synchrotron injection
injected beam
septum wall (w = 5 mm)
stored beam
injection kicker
injection kicker
*This scheme is applied in LEP.
1) Energy of injected beam is shifted by d0, then an injection orbit is adjusted
to be a closed orbit of the ring. (X0,X0’)=(h,h’)d0
2) The coherent betatron oscillation due to the injection error should be zero
since the betatron oscillation is transformed to the synchrotron oscillation.
X0 = 2.5 sinj + 3 sring + w = 6~6.5 mm
h = 1.28 m (LER) / 1.2 m (HER) for d0 = 0.5 %

30. To make this possible, the injection point will be moved from the FUJI straight section to the arc section. -> Remodel the BT lines

31. Good quality of injected beam is quite necessary
Good quality of injected beam is quite necessary. e- low emittance RF gun and e+ DR

32. IR magnet configuration: Permanent magnet + S. C
IR magnet configuration: Permanent magnet + S.C. corrector (alternative)
Final focus quadrupoles(QC1) can be closer to IP than S.C. magnets only.
This makes larger dynamic aperture.

33. QC1P/E(Permanent Magnet)
Preliminary
Correction S.C.
magnet IP
2009/7/2
IR技術打合せ/ N. Ohuch

34. Summary The lattice of “Nano beam scheme” is still being developed.
Dynamic aperture is not enough so far for injection/Touschek lifetime.
It strongly depends on IR magnet configuration.
We are considering both permanent
and superconducting magnets.

36. Appendix

37. L= 0.89 m → 4 m LER Arc Cell ap ex (nm) ex = 8.8 nm ap = 3.3x10-4

38. HER arc cell 2.5p non-interleaved sextupole chromaticity correction
Y. OHNISHI / KEK

39. HER arc cell #magnets increases by 60%
Emittance (nm)
Momentum Compaction

40. QCS1Pコイル長：305.93mm [磁石長370mm] QCS1Eコイル長：460.896mm [磁石長500mm]
磁石位置（IPから）
QCS1P＝1126.4mm 　(910mm : 5/1 optics )
QCS1E＝1571.4mm 　(1460 mm)
2009/7/2
IR技術打合せ

41. LER IR optics
bx*/by*=17.8 mm/0.26 mm
LCC
LCC