1. Upgrade plan of KEKB from 2012 to 20XX Y. Ohnishi / KEK
2008 January 24-26
Atami, Izu, Japan

2. What is luminosity ? Luminosity is defined by:
N is a number of events should be observed.
We want to increase N to decrease a statistical error.
s is a cross section of an interesting physics process.
We can do nothing. s is a constant.
T is a duration of an experiment.
Compare with our lifetime. Is T~10 years reasonable ?
What we can do is to increase a luminosity.

3. What is luminosity ? (cont'd)
Luminosity is defined by:
N+(N-) is a number of particles per bunch for positron (electron).
sx*(sy*) is a beam size in the horizontal(vertical) plane.
Usually, flat-beam, sy* << sx*
f is a collision frequency of positron and electron bunch.
f = nb/T0, nb is a number of bunches, T0 is a revolution time.
RL is a luminosity reduction.
geometrical loss due to a crossing angle and an hour-glass effect

4. Reductions to luminosity
Crossing angle
Hour-glass effect
overlap
region
beam envelope s IP
bunch length
sy*
focusing
defocusing
sy > sy* y
Beam

5. What limit the luminosity ?
Money ?
☞ This might be true !
Reduction from the geometrical loss ?
Bunch length, sz < by*, where sy* = (eyby*)1/2.
Larger impedance in a ring makes bunch length longer.
Head-on collision is preferable.
Nonlinear effects limit the luminosity.
Beam-beam force is a nonlinear force.
Most elements in an accelerator are nonlinear transformations.
Machine errors with beam-beam effects decrease luminosity significantly.

6. Beam-beam force v z e+ e- v e- cylindrical beam r Fr lEr v Bj z e+ e- v a e-
cylindrical beam r Fr l
The electric and magnetic field can be written by:
Lorentz force can be expressed by:
Beam-beam force is proportional to the electric field and an attracting force.
l is a longitudinal line
charge density.

7. Beam-beam force (cont'd)
If the positron beam is a Gaussian distribution, a momentum deviation of the electrons is:
Horizontal and vertical deflection angle can be expressed by:
where p pr
kick angle q
re: classical electron radius
w(z): complex error function

8. Beam-beam force (cont'd)
Horizontal
Vertical
Analytic formula
charge density
sy*=3 mm
sx*=200 mm
Beam-beam force is nonlinear.
This region is almost linear.
Dpx/p
Dpy/p
We call this slope(xx,y) a beam-beam parameter.

9. Luminosity Luminosity can be expressed by the formula:
However, we do not use above formula for the machine design. Instead an alternative formula is used.
This describes L in terms of the lattice parameter by*, beam-beam parameter xy, eliminating the explicit dependence on beam size.
* means value at IP
(flat-beam case)

10. Improvement of luminosity at KEKB upgrade
If small by* while keeping by*/ey constant, larger L can be realized.
However, by* > sz to suppress the hour-glass effect.
Crab-crossing and nx→0.5 to mitigate nonlinear effects makes larger xy,max with increasing I.
High current scheme

11. How large can we achieve beam-beam parameter ?
KEKB(crab)
mitigate nonlinear effects
Beam-beam limit ?
Luminosity is proportional to a beam-beam parameter.

12. Crab crossing Head-on(crab) Crossing angle 22 mrad KEKB
Crab crossing will increase the beam-beam parameter by a factor of 2.
K. Ohmi, et al.
Head-on(crab)
(mA)
KEKB
(exp. with crab)
KEKB
(Strong-strong simulation)
Crossing angle 22 mrad
Vertical beam-beam
(at the optimum tune)
Superconducting crab cavities have been
produced, and under beam test at KEKB.
Input Coupler
Liq. Helium Vessel
Stub Support
Coaxial Coupler
Copper Bellows
80 K Liq. Nitrogen Shield
Notch Filter
RF Absorber
Aluminum
End Plate
SUS Support Pipe
K. Hosoyama, et al.

13. Beam-beam effect and “Chaos”
1-dimensional
2-dimensional
*near-integrable surface
x0 = 0
x0 = 5% x sx py py
xy=0.02 y y
Particles are confined in KAM*.
"chaos"
Large beam-beam parameter py py
xy=0.053 y y
KAM is destroyed.
Beam size growth py py
xy=0.10 y y

14. High beam-beam parameter
Total degree of freedom is 3N, where N is #particles.
Crab cavity resolves x-z coupling.
Betatron tune close to half integer(nx→0.5) resolves x-y coupling(y is symmetric for x or -x).
System becomes one dimensional and avoids bad resonances, the beam-beam parameter can be increased. 3N
(x-y-z) x 3N
2N+N
(x-y+z) z y x
N+N+N
2N+N
(x+y+z)

15. Tune Scan with Beam-beam Simulation
Crab-crossing collision
Tune Survey in upgraded KEKB
without parasitic collision effect.
ex=24 nm case:
Lpeak=4.0x1035 cm-2s-1
(L/bunch=8.0X1031, Nb=5000)
Beam-beam
parameter
Head-on }
y ~0.2
Betatron tunes
(.503, .550)
Better working point is
very close to the half integer !
Simulation by K. Ohmi and M. Tawada

16. Experiences at KEKB ex=24 nm 1.7x1035 9.4/4.1 A nb=5018
Lower bunch current product makes luminosity twice of the crossing-angle collision.
However, slope of the specific luminosity is NOT understood well.
If the reason is an electron cloud, no problem after upgrade.
If luminosity is limited by something else, we must investigate it.
Synchro-beta resonance ?
Other nonlinear effects ?
ex=24 nm
1.7x1035
Crab crossing
49 sp
nb=50
what is a slope ?
Crab crossing
3.06 sp
nb=1548
22 mrad crossing
3.5 sp
nb=1388
9.4/4.1 A
nb=5018

17. Luminosity upgrade Assumptions:
Specific luminosity/#bunches > 22x1030 cm-2s-1mA-2 with crab cavities(factor of 2 at least)
achieved at KEKB
High specific luminosity at high currents(9.4 A at LER) can be kept.
5000 bunches can be stored.
No electron cloud and a bunch-by-bunch feedback system works completely.
Believe a beam-beam simulation

18. Beam-beam simulation(Strong-Strong )
#turns
L/#bunches (cm-2s-1)
ex=12 nm
ex=24 nm
30%
ey/ex=0.5%, sz=3 mm
L/#bunches (cm-2s-1)
#turns
tx=84/47 msec
tx=84/84 msec
tx=47/47 msec
ey/ex=0.5%, sz=3 mm
#turns
L/#bunches (cm-2s-1)
sz=3 mm
sz=4 mm
16%
ey/ex=0.5%, ex=12 nm
HER(13 nm, 47 msec)
LER(12 nm, 84 msec)
<y2> (m)
#turns
ey/ex=0.5%, sz=3 mm

19. Luminosity upgrade (cont'd)
Luminosity gain and upgrade items (preliminary)
Item
Gain
Purpose
beam pipe
x 1.5
high current, short bunch, electron cloud
IR(b*x/y=20cm/3 mm)
small beam size at IP
low emittance(12 nm)
& nx → 0.5
x 1.3
mitigate nonlinear effects with beam-beam
crab crossing
x 2
RF/infrastructure
x 3
high current
DR/e+ source
low b* injection, improve e+ injection
charge switch
x ?
electron cloud, lower e+ current
3 years shutdown

20. Projected luminosity (preliminary)
operation time : 200 days/year
Integrate luminosity
(ab-1)
Peak luminosity
(cm-2s-1)
Year
3 years
shutdown
Damping
Ring
RF upgrade
KEK
roadmap
Target for
roadmap
Target for
roadmap

21. Machine parameters (preliminary)
LoI (updated)
Upgrade (LER/HER)
Emittance ex 24
12/13 nm ey
0.18
0.060/0.066
Beta at IP
bx*
200 mm
by* 3
Beam size at IP*1
sx*
50.0
37.5/39.8
sy*
1.0
2.11/2.28
Bunch length sz
Transverse damping time tx 47
84/47
msec
Betatron/synchrotron tune
nx/ny/ns
M+0.506/N+0.545/-0.031*1
M+0.505/N+0.550/-0.025
M,N:integer
Beam Energy
E+/E-
3.5/8.0
Beam current
I+/I-
9.4/4.1 A
#bunches Nb
5018
Crossing angle
2fx
30 → 0 (crab crossing)
mrad
Beam-beam*2 xx
0.135
0.153 xy
0.215
0.296
Beam-beam
reduction*3
Rxx
0.99
Rxy
1.11
Luminosity reduction*3 RL
0.86
Luminosity L
4.0x1035
5.5x1035
cm-2s-1
*1 include beam-beam effects *2 calculated from luminosity *3 nominal values

22. Miscellaneous Energy asymmetry is determined by a physics requirement.
Larger asymmetry is preferable so far.
Power consumption does not change so much, even though HER energy is decreased. Instead we will give up wigglers.
Final focus magnets and detector solenoid affects both beams of LER and HER. We can not change energy asymmetry easily because beam orbits is already optimized by the IR design lattice.
Energy is not flexible in principle due to the above reason.
The range between U(3S) and U(5S) can be available.
Extremely low energy operation is not trivial. If detector solenoid can be scaled to the energy, it is possible.
Polarization is not considered.
Very difficult so far
rB=106 m (HER) >> 16 m (LER)

23. Backup slides

24. Sensitivity of physics
Higher asymmetry can achieve higer sensitivity for the physics results.
Lower aymmetry(LER E=3.8 GeV), luminosity degradation is about 10~12 % luminosity.
B→J/YKs
B→fKs
Tajima

25. Synchrotron Radiation Loss
LER wiggler
Prad (MW)
total
LER
LER wiggler
HER
LER E (GeV)
*E=3.8 GeV in LER is maximum to perform Y(5S) experiment.

26. No. ARES cavities No. SCC in HER = 8 (fixed) No. ARES cavities
No wiggler in LER / #SCC is 8.
#RF cavities = ~40 → constant
LoI: ARES/SCC=16/12
LER E (GeV)
No. ARES cavities
No. SCC in HER = 8 (fixed)
LER
HER
LER+HER

27. Power consumption (RF only)
No wiggler in LER / #SCC = 8 in HER
Total power consumption is 60~66 MW less dependent of energy asymmetry.
LER+HER
AC plug power (MW) [RF only]
LER
HER
LER E (GeV)

28. Horizontal Tune close to Half Integer nx=0.5
In the collision of two beams, particles interact with fixed beam at either x or -x for nx=0.5.
In the case of crab crossing, the phase space structure in y-py at x is the same as that at -x because of symmetry of the fixed beam.
System becomes one dimensional and avoids bad resonances, the beam-beam parameter can be increased.
This technique realizes high luminosity at KEKB/SuperKEKB. To make this possible, machine errors must be reduced significantly. x y
n: turn number (integer)
3 DOF
2+1 DOF
1+1+1 DOF
Crab-crossing
(resolve xz coupling)
nx=0.5
(resolve xy coupling)

29. Beam-beam simulation ~10% I+/I- = 9.4/4.1 A E+/E- = 3.5/8.0 GeV
Nb = 5018
ex = 12 nm
ey/ex = 0.5 %
nx/ny = .505/.550
LER/HER trans. damping time
L(x1035)= *t
47/47 msec
57/57 msec
Luminosity (x1035 cm-2s-1)
Luminosity (x1035 cm-2s-1)
~10%
57/47 msec
84/84 msec
Trans. damping time (msec)
Number of turns