1. Nano-Beam Scheme for SuperKEKB Andrew Hutton Slides taken from talks by Haruyo Koiso, Yukiyoshi Ohnishi & Masafumi Tawada

2. Nano-beam Scheme The scheme proposed by P. Raimondi and SuperB Group.
Squeeze y* as small as possible: 0.27/0.41 mm.
Assume beam-beam parameter = 0.09 which has been already achieved at KEKB.
Change beam energies 3.5 / 8 -> 4 /7 GeV to achieve longer Touschek lifetime and mitigate the effect of intra-beam scattering in LER.

3. Parameter Optimization
Main parameters can be quickly optimized with this panel.

4. Beam Parameters KEKB Design KEKB Achieved : with crab SuperKEKB
High-Current
SuperKEKB Nano-Beam
Energy (GeV) (LER/HER)
3.5/8.0
4.0/7.0
by* (mm)
10/10
5.9/5.9
3/6
0.27/0.42
ex (nm)
18/18
18/24
24/18
3.2/2.4
sy(mm)
1.9
0.94
0.85/0.73
0.059 xy
0.052
0.129/0.090
0.3/0.51
0.09/0.09
sz (mm) 4
~ 6
5/3
6/5
Ibeam (A)
2.6/1.1
1.64/1.19
9.4/4.1
3.6/2.6
Nbunches
5000
1584
2503
Luminosity
(1034 cm-2 s-1) 1
2.11 53 80

5. SuperKEKB x 40 Gain in Luminosity e- 2.6 A
Colliding bunches
Belle II
New IR
e- 2.6 A
New superconducting /permanent final focusing quads near the IP
SuperKEKB
New beam pipe
& bellows
e+ 3.6 A
Replace long TRISTAN dipoles with shorter ones (HER)
Add / modify RF systems for higher beam current
Low emittance positrons to inject
Positron source
Redesign the HER arcs to squeeze the emittance
Damping ring
New positron target / capture section
Low emittance gun
TiN-coated beam pipe with antechambers
Low emittance electrons to inject
x 40 Gain in Luminosity

6. Comparison of Parameters
KEKB Design
KEKB Achieved
: with crab
SuperKEKB Nano-Beam
Energy (GeV) (LER/HER)
3.5/8.0
4.0/7.0
by* (mm)
10/10
5.9/5.9
0.27/0.41
ex (nm)
18/18
18/24
3.2/2.4
sy(mm)
1.9
0.94
0.059 xy
0.052
0.129/0.090
0.09/0.09
sz (mm) 4
~ 6
6/5
Ibeam (A)
2.6/1.1
1.64/1.19
3.6/2.62
Nbunches
5000
1584
2503
Luminosity (1034 cm-2 s-1) 1
2.11 80
SuperKEKB

7. Beam Energy
In SuperKEKB, the beam energy is changed to decrease the effect of the intra-beam scattering in LER, especially to make longer Touschek lifetime.
LER: 3.5 GeV → 4 GeV
HER: 8 GeV → 7 GeV
In HER, the lower beam energy makes lower emittance.
SuperKEKB

8. Luminosity Target Luminosity is 8x1035 cm-2s-1 in SuperKEKB.
Three fundamental parameters to determine the luminosity.
If sx* = sx+* = sx-* and sy* = sy+* = sy-*,
S = 1+sy*/sx*
(aspect ratio of the beam size at IP).
where
Target Luminosity is 8x1035 cm-2s-1 in SuperKEKB.
SuperKEKB

9. Beam-Beam Parameter KEKB Design KEKB Achieved : with crab
SuperKEKB Nano-Beam
Energy (GeV) (LER/HER)
3.5/8.0
4.0/7.0
by* (mm)
10/10
5.9/5.9
0.27/0.41
ex (nm)
18/18
18/24
3.2/2.4
sy(mm)
1.9
0.94
0.059 xy
0.052
0.129/0.090
0.09/0.09
sz (mm) 4
~ 6
6/5
Ibeam (A)
2.6/1.1
1.64/1.19
3.6/2.62
Nbunches
5000
1584
2503
Luminosity (1034 cm-2 s-1) 1
2.11 80
SuperKEKB

10. Beam-Beam Parameter
The maximum value of the beam-beam parameter is assumed to be 0.09 in SuperKEKB.
The beam-beam parameter of 0.09 has been achieved in KEKB.
The horizontal beam-beam parameter becomes very small in the nano-beam scheme. xx~0.0028
Dynamic effects is also small since the small horizontal beam-beam parameter and the horizontal betatron tune is far from 0.5.
SuperKEKB

11. Beam-Beam Simulation Beam-beam simulation gives 8x1035 cm-2s-1
Difference between with and without the crab-waist is not so large.
L = 8x1035
LER
W-S
SuperKEKB

12. Vertical Beta Function at IP
KEKB Design
KEKB Achieved
: with crab
SuperKEKB Nano-Beam
Energy (GeV) (LER/HER)
3.5/8.0
4.0/7.0
by* (mm)
10/10
5.9/5.9
0.27/0.41
ex (nm)
18/18
18/24
3.2/2.4
sy(mm)
1.9
0.94
0.059 xy
0.052
0.129/0.090
0.09/0.09
sz (mm) 4
~ 6
6/5
Ibeam (A)
2.6/1.1
1.64/1.19
3.6/2.62
Nbunches
5000
1584
2503
Luminosity (1034 cm-2 s-1) 1
2.11 80
SuperKEKB

13. Vertical Beta Function at IP
By using the modern technique, the vertical beta function can be squeezed to be a few hundred micron at most.
by* ~ 1/20 of KEKB
Hourglass effect (HG) is a serious problem to squeeze the beta function in the head-on collision.
In order to satisfy HG, a collision of narrow beams with a large crossing angle is adopted. This is “nano-beam scheme”.
However, dynamic aperture (DA) will be reduced because of the nonlinear fringe, and kinematic terms in the interaction region (IR), and also strong sextupoles.
Natural chromaticity LER: xx/xy = -104/-789
HER: xx/xy = -187/-853
LER: xx/xy = -72/-123
HER: xx/xy = -70/-124
SuperKEKB
KEKB
SuperKEKB

14. Hourglass requirement
Collision Scheme
High Current Scheme
Nano-Beam Scheme sz
sx* d 2f
Head-on
Half crossing angle: f
overlap region = bunch length
overlap region (≠ bunch length)
Hourglass requirement
Hourglass requirement
~5 mm
~ mm
SuperKEKB

15. Hourglass Effect for Nano-Beam
2sx-
2sx+ d1 d2
LER waist e+ e-
With crab-waist, this term is zero
There are two kinds of
hourglass requirements.
Hourglass (H.G)
requirement without crab-waist:
SuperKEKB

16. Beta Function at IP
Machine parameters are chosen to be insensitive to the HG effect.
The vertical beta function:
The vertical beta functions in both rings satisfy the HG requirement.
To squeeze by*, low emittance and low bx* are needed.
SuperKEKB

17. Nonlinear Terms around IPK L*
Phys. Rev. E47, 2010 (1993)
LER
KEKB L R
SuperKEKB
by*
(mm)
5.9
0.27 K
(1/m2)
-1.777
-1.778
-4.425
-6.003 L*
(m)
1.332
1.762
0.7269
0.7680
Jy0 / A
8.425
4.221

18. Beam Current KEKB Design KEKB Achieved : with crab SuperKEKB Nano-Beam
Energy (GeV) (LER/HER)
3.5/8.0
4.0/7.0
by* (mm)
10/10
5.9/5.9
0.27/0.41
ex (nm)
18/18
18/24
3.2/2.4
sy(mm)
1.9
0.94
0.059 xy
0.052
0.129/0.090
0.09/0.09
sz (mm) 4
~ 6
6/5
Ibeam (A)
2.6/1.1
1.64/1.19
3.6/2.62
Nbunches
5000
1584
2503
Luminosity (1034 cm-2 s-1) 1
2.11 80
SuperKEKB

19. Luminosity gain is 1(xy) x 20(1/by*) x 2(I) = 40 times of KEKB.
Beam Current
In order to achieve the target luminosity, the beam current in nano-beam scheme becomes twice of KEKB.
The highest beam current is 2 A in LER and 1.4 A in HER at the KEKB operation.
1.8 A in LER / 1.35 A in HER at physics run
In SuperKEKB, the design beam currents are 3.6 A for LER and 2.62 A for HER.
Number of bunches is 2503 to get the suitable density of the overlap region (alternate buckets filled).
Bunch current becomes 1.44 mA in LER and 1.05 mA in HER.
Luminosity gain is 1(xy) x 20(1/by*) x 2(I) = 40 times of KEKB.
Then, we get 8x1035 cm-2s-1
SuperKEKB

20. Crossing Angle The full crossing angle is 83 mrad in SuperKEKB.
Separation of two beams is necessary to put final focusing magnets closer to IP as much as possible. This affects the magnet design and the dynamic aperture.
The angle between the solenoid axis and the beam line is 41.5 mrad, respectively. This angle is determined by optimization of the vertical emittance generated by SR from the solenoid fringe.
SuperKEKB

21. Emittance Redesign of arc cells to make low emittance
(hx:dispersion)
Redesign of arc cells to make low emittance
2.5 p non-interleaved sextupole cell (-I’ connection)
chromaticity is corrected and nonlinear kick is cancelled.
LER (4 GeV)
Longer bending radius is adopted.
HER (7 GeV)
Number of cells increases to reduce dispersion.
SuperKEKB

22. Emittance
Local chromaticity correction (LCC) is necessary to correct large chromaticity generated in the vicinity of IP.
However, the LCC generates some emittance to make dispersion region.
The emittance generation at the LCC should be reduced as much as possible. This is a trade-off between DA and emittance.
SuperKEKB

23. Emittance
In SuperKEKB, the horizontal emittance is 3.2 nm in LER and 2.4 nm in HER, respectively.
2.7 nm in LER and 2.3 nm in HER at the zero beam current
Coupling parameter of 0.4 % in LER and 0.35 % in HER are assumed. (challenging!)
Vertical emittance induced by SR from solenoid fringe field can not be ignored. (suggested by E. Perevedentev)
In order to suppress it, rate of change of Bz should be reduced and/or decrease angle between the solenoid axis and the beam axis.
Machine error also should be reduced and corrected.
SuperKEKB

24. Vertical Emittance originated from Solenoid Fringe
Crossing angle = LER angle + HER angle = 83 mrad
proportional to q4
Solenoid axis
= angle bisector
Energy ratio
4/(4+7)
We choose 41.5 mrad and the contribution of solenoid fringe is ~4 pm.
SuperKEKB

25. Bunch Length
In SuperKEKB, the bunch length is 6 mm in LER and 5 mm in HER which are similar to the present KEKB.
The “bunch length” means a value includes intra-beam scattering and wake field from the ring impedance at the design beam current.
SuperKEKB

26. = Nano-Beam Scheme Head-on Frame narrow and long bunch
with large crossing angle
short bunch with head-on =
Y. Ohnishi / KEK

27. Parameter Consideration
In SuperKEKB, the luminosity performance depends on the lattice performance significantly.
Especially, Touschek lifetime becomes serious in the nano-beam scheme due to lack of DA.
Target lifetime is 600 sec in both rings. The large DA in the momentum direction is necessary.
Transverse aperture is also necessary for the “betatron injection”. If enough transverse aperture cannot be kept, “synchrotron injection” should be considered. The emittance of the injected beam should be small, therefore e+ damping ring (DR) and RF-gun are considered.
Y. Ohnishi / KEK

28. IR design HER LER Detector solenoid axis
QC2LP
Horz. F PM
LER
QC2RE
Horz. F PM
HER
QC1RE
Vert. f
QC1LP
Vert. f
41.5 mrad
Detector solenoid axis IP
41.5 mrad
QC2LE
Horz. F PM
QC1RP
Vert. f
QC1LE
Vert. f
QC2RP
Horz. F
LER and HER beam are focused by separated quadrupole doublet, respectively
SuperKEKB

29. IR Magnets design
Use both of superconducting magnets and permanent magnets
Superconducting magnets
Leakage fields of superconducting magnets are canceled by correction windings on the other beam pipe
Warm bore
Permanent magnets for QC2LE, QC2LP, QC2RE
Pros.
Cryostats are small
Assembly of vacuum chamber can be simple
Vacuum pump can be located near IP
Cons.
Need to develop a permanent magnet
Fine temperature control is required
Extra magnets are required to change beam energies
SuperKEKB

30. IR design with PM version
N. Ohuchi
Cryostat
Anti solenoid-R
QC1LP
+corr. coil
QC1RE
+corr coil
QC2RE PM
QC2LP PM IP
QC2LE PM
QC2RP
+corr. coil
QC1LE
+corr. coil
QC1RP
+corr. coil
Anti solenoid-L
Cryostat
QC1RE
SuperKEKB

31. The magnet design of QC1R/L-P
N. Ohuchi
Vac ch ID 20mm
Magnet Parameters
Magnet inner radius=22 mm, outer radius=27.55 mm
Magnet current=1511 A
Field gradient=75.61 T/m
Current density, JSC= A/mm2
Magnetic length Leff = m
Peak field w/o solenoids = 2.24 T
Operation temperature = 4.4 K
Cable Parameters
Size =2.5mm  0.93mm
Number of SC strand=10
Diameter of the strand=0.5mm
Cu ratio=1.8
Ic= T and 4.2 K
Beam envelop
Coolant path
SC correctors:
Normal Octupole
Skew Quadrupole
Normal Dipole
Skew Dipole
SC correctors:
Normal Sextupole
Normal Quadrupole
Normal Dipole
Cross section of QC1 RP
1.123
1.013
Designed new SC cable for main quadrupole
7.0
0.93
3.9
2.5
Leakage fields are canceled by the correction windings on the other beam pipe
1.057
KEKB
QCS
0.967
S-KEKB
H-Current
0.9
S-KEKB
NanoBeam

32. ○ Belle Detector 8m(W)×8m(L)×10m(H) Total weight: 1300tons
　650tons (Barrel Yoke)
　600tons (End Yoke)
　 50tons (Others)
H. Yamaoka 32
15th KEKB Review

33. Anti solenoid
H. Koiso
Vertical emittance degradation depends on the anti-solenoid field profile
Anti-solenoid Ver.2
HER:53mrad Bz
SuperKEKB

34. IR vacuum chamber Positron
K. Kanazawa
Positron
Vacuum level will be worse due to poor vacuum conductance.
IR assembly is a big issue
BPM can’t be fixed rigidly on the quadrupole magnet
SuperKEKB

35. Physical Aperture Required acceptance for injection
2Jx=5x10-7 (m), 2Jy=2x10-8(m), 4% coupling
Dynamic effects are ignored because nominal nx = 0.53
Physical aperture is not enough for the design β-functions
COD is not taken into account
No margin for error
QC1LP
QC1RP
QC1LE
QC1RE
QC2LP
QC2RP
QC2LE
QC2RE
Physical
Aperture
(mm) 20 30 60 70
Required
Aperture (Horz.)(mm)
11.2
10.0
16.4
17.2
25.6
28.4
47.6
48.4
Vert.
15.8
14.8
18.2
9.4
9.6
15.4
10.6
SuperKEKB

36. COD (Belle)
A. Morita
COD in Belle detector depends on the solenoid field profile
COD(LER 41.5 mrad)
COD(HER 41.5 mrad)
100um
200um
4mm
1mm IP IP
QC2RP
QC1RP
QC1LP
QC2LP
QC2RE
QC1RE
QC1LE
QC2LE
SuperKEKB

37. Machine Parameters of SuperKEKB
2010/Feb/08
LER
HER
Emittance ex
3.2(2.7)
2.4(2.3) nm
Coupling
ey/ex
0.40
0.35 %
Beta Function at IP
bx* / by*
32 / 0.27
25 / 0.41 mm
Horizontal Beam Size
sx*
10.2(10.1)
7.75(7.58)
Vertical Beam Size
sy* 59
Bunch Length sz
6.0(4.9)
5.0(4.9)
Half Crossing Angle f
41.5
mrad
Beam Energy E 4 7
GeV
Beam Current I
3.60
2.62 A
Number of Bunches nb
2503
Energy Loss / turn U0
2.15
2.50
MeV
Total Cavity Voltage Vc
8.4
6.7 MV
Energy Spread sd
8.14(7.96)x10-4
6.49(6.34) x10-4
Synchrotron Tune ns
Momentum Compaction ap
2.74x10-4
1.88x10-4
Beam-Beam Parameter xy
0.0900
0.0875
Luminosity L
8x1035
cm-2s-1
(): zero current parameters

38.
SuperKEKB