Collision Scheme inUpgrade and Super KEKB
K. Ohmi for superKEKB design group
MAC2009 at KEKB
9-11 February, 2009

Introduction• Limitation of the bunch length,
Travel focus scheme• present KEKB status• Super Bunch scheme

Tentative Design Parameters K. OIDEzero bunch
current

design bunch
current

sigz

56mm

sige

7.1

8.0

10-4

LER

sigz

4.5

5.3mm

neg.
alpha

sige

7.1

8.5

10-4

sigz

33.6mm

sige

6.8

7.0

10-4

HER sigz

33.1mm

neg.
alpha

6.8

7.7

10-4

LERHERsige

Luminosity optimization under thebunch length limit• Using travel focus only in LER• Diﬀerent β,ε for two beams.
• Longer damping time of LER,6000-8000(LER) and 4000 turns(HER).

• β =0.2m or 0.4m.
xWaist control‐I traveling focus• Linear part for y. z is constant during collision.
α=0• Minimum β is shifted at s=‐az

How to configure the crab cavity and sextupoles• Head on collisioncrab cavity• Head on + travel focus
sextupolecrab cavity• Actual Configuration

See H. Koisoʼs slide6

Crabbing beam in sextupole• Crabbing beam in sextupole can give the nonlinear
component at IP• Traveling waist is realized at IP.

• At the sextupole positionz* =β x (s)
θx(s)
*βx
K2~30‐50• The same€strength as the crab waist sextupoleTravel waist in the weak‐strong model• Reduction of z degree of freedom• Travel focus• This transformation does not include z.
• This beam‐beam system is two degree of freedom(x‐y).
8

Travel focusing results• σz,HL=3mm, βy=3mm,εx=18/24nm• σz,HL=5mm, βy=3mm,
εx=18/24nm

Travel focus gives a little luminosity increase, though the integrability of thebeam-beam system improves. Life time is improved.

Extremely high beam-beam tune shift
Strong-strong
ξ~0.3

•

• weak-strong

ξ~0.4Parameters -positive αβx (m)

0.2

0.4

βy (mm) 6H/3L

6H/3L

εx (nm)

12/20

12/20

τ/T0

4000/8000

4000/8000

σz(mm)

3.5/6

3.5/6

L5x1035

3-4x1035

Parameters -negative α-• Simulation

Present KEKB luminosity• Life time issue is solved. Aperture
limits the life time and also gave its
asymmetry behavior.

Y. Funakoshi et al.,• The luminosity drop is reduced, andthe luminosity behaves to keep a
constant beam-beam parameter forchanging current.

• The beam-beam parameter is aroundξ=0.09(ξN=2reβL/γNf=0.06).

Specific Luminosity and beam-beam parameter
Before summer 2008
y=-16.35x+26.54 Green Ratio=100%

ξy~0.093 (HER) (April 3 2007)

Crab crossing•49-sp βx*=80, 84cm
εx=18, 24 nm•3.5-sp βx*=80cm•3.06-sp βx*=80cm•3.06-sp βx*=90cm

22 mrad crossing

Green line

Speciﬁc luminosity for crab and noncrab collisionLine for ξ=0.09 (ξn=0.06)

Green: crab

Blue: Non crab

Lspec without crab is better than simulation.
Couling may be better than 1%.

Specific Luminosity given by Y. Cai

Nonlinear chromaticity measurement
and estimation with SAD• SAD : no error• SAD xy : 1% coupling with Vertical oﬀset errors ofsextupole.

• Measurement

Chromaticity

Symplectic expression of the chromaticity• Hamiltonian which gives the chromaticity
is obtained and is used in the beambeam simulation.

• 10xn coeﬃcients are determined from
10xn chromaticities.

Y. Seimiya at al.

Beam size scan simulation without BB• SAD no error(νy=0.58)

D. Zhou et al.

• SAD 1% coupling with with Vertical oﬀset errors ofsextupole.

Measured beam size scan (Y. Ohnishi et al.,)Beam size and luminosity simulation under theD. Zhou et al.
presence of the chromaticity

R chromaticity scansimulation

D. Zhou et al.

Summary for the present operation
time issue is solved. The beam‐beam parameter is• Lifethe highest in the world except LEP.
can be achieved 2x10 soon, but still• Luminosity
lower than our expectation.
X‐Y coupling and dispersion errors does not• Linear
seem to be well controlled.
• Their chromatic effect is next subject.
sextupole magnets placed at dispersive section• Skew
can control the chromaticity, and is installed this34

shutdown.

very high beam‐beam parameter seems to be• The
hard to realize.
cavity works well, thus we continue the tuning of• Crabthe parameters with taking the data.
• It may be the time to study another possibilities.

SuperBunch‐crab waist option• We have some difficulties to go the scheme with keeping thepresent luminosity.
• To increase the luminosity step by step, βx at IP should be reduced,with keeping εx. Because the present ξx, which is >0.1, should bedecrease first.
• Low βx had been tried a long ago. In present KEKB, βx<0.5m seems
to be difficult to inject the beam, though dynamic β may affect.
• We should try low βx at another tune operating point far from 0.5
again.

26

SuperBunch/Micro‐beta approach• Decrease βx and βy with keeping (εx βx)1/2/βy• ξy~(βy /εy)1/2, ξx~βx• L~N/(βy)1/2

εx β x<1
θ hσ z2Nξ yN€ L~~βyθ hσ z εy β yξx ~xs€ξy ~€€βyεyNθ hσ zβy >€Nβ xθ h2σ z2εx β xθh27

parameters of several cases (5000 bunches)
Normal εSuper KEKBLER low-ε L/H low-ε

KEKB test

εx (nm)18H/24L

10/10

1/10

1/1

18/18

εy(nm)

0.09/0.24

0.1

0.01/0.04

0.01/0.01

0.18/0.18

βx (mm)

200

10/10

10/101050βy (mm)6/3

0.6/0.6

0.8/0.2

0.2

3σz (mm)

3.5/66666

φσz/σx0.0

928/928

2.2ne

5.25x1010

2.2x1010

2.2x1010

2.2x1010

1.75x1010

np

12.x1010

3.3x1010

3.3x1010

3.3x1010

4x1010

015

15

15

11

ξν,x

0.397

0.00170.00180.00180.0108ξν,y0.3

0.047/0.031

0.035/0.11

0.09

0.069

Lum (W.S.)

5x10351x10352x10355x10354x1034

Lum (S.S.)

5x1035φ/2 (mrad)

Strong‐strong simulation for thesuper Bunch scheme• Slice longitudinal direction, 150 slices for φσz/σx=
15‐25.
• Collisions of 150x150 times were calculated for
one revolution. The i‐th and j‐th slices collides atsij= (zi‐zj)/2.
• Two type of the strong‐strong simulation– Gaussian approximation– PIC solver, but Gaussian approximation is used for φsij/
σx>2.5 (preliminary).
29

Super B (Italy)
Circumference
Energy
εx/εy
σz
βx/βy
N±νx/νy/νs
φ (φσz/σx)• M. Biagini et al.

HER
3016
7
1.6x10‐9/4x10‐120.006
0.02/0.00039
5.52x1010
0.57/0.60/0.01
0.024(25)LER
42.8x10‐9/7x10‐120.0060.035/0.00022
5.52x1010
0.57/0.60/0.01‐1530

Luminosity• Gaussian approximation• PIC simulation, which is the first trial,showed alow luminosity now. Numerical errors are
doubted. Revised simulation is on going.

31

Beam size
• The beam sizes given by Gaussian approximationagree with those by the weak‐strong simulation.
• Strange behavior in PIC model.

32

Coherent motion in Gaussian model• Coherent motion is seen at the early stage
maybe due to a miss‐match, but damp in a few
radiation damping time.

Growth of a coherent motion is seen,
but a numerical error is doubted.
33

DAFNE• Measured luminosity=4.5x1032 cm‐2s‐1.

34

Summary• Super KEKB design with crab cavity. Beam‐beamperformance is L=5x1035cm‐2s‐1 for βx=0.2m. It
degrade 20‐30% for βx=0.4m.
• A steady effort should be continued with thecrab cavity operation.
• Every trials to increase the luminosity should beperformed in KEKB. Travel focus is combined
scheme of crab cavity and crab waist.
• To study the superbunch‐crab waist scheme withkeeping or improving the present performance,
low βx operation (~5‐10cm) should be tried.
35

Beam‐beam parameters for e+e‐ colliders
DAFNE

DAFNE

beforeKEKB

KEKB

BEPC-II

2008.12.10

2008.11.21

2008.11.21

CESR

2008.3.202001.2 Rice

CN bunch

97
110

97
105

3016
1993016
1585

240
90

768.4
45

I+ (mA)N+

1.1
2.02E+101.106
2.13E+100.262
8.27E+101.600
6.34E+100.500
2.78E+100.350
1.24E+110.51
1.50.511.431

3.50.162

3.50.970

1.890.500

5.290.350

2.75E+100.51
3.40E-072.75E+10
0.51
2.50E-07

5.11E+108
1.80E-08

3.84E+108
1.80E-08

2.78E+10
1.89
1.44E-07

1.24E+11
5.29
2.05E-07

1.70E-09
1.7

1.25E-09
0.26

9.00E-11
1.5

9.00E-11
1.5

1.44E-09
1.00E+00

2.05E-09
0.9381

0.017
1100000.00951100000.00594000

0.00594000

1.50E-02
31900

0.018
0ξν+=2 re β L/γ N fξν−=2 re β L/γ N f

0.02100.01540.03150.02430.08610.06090.08020.05790.00730.00730.0561
0.0561

L (measure)

1.5E+32

4.05E+32

2.90E+33

1.65E+34

1E+32

1.25E+33

E+INEεx
εyβx
βy
τx/T

37

Near the half integer tune in Horizontal• Transformation38

Vertical motion• Vertical map• Fy fluctuates due to• If horizontal motion is chaotic, stochasticity ofthe vertical motion increases, with the resultthat emittance growth is enhanced.

39

• Beam‐beam force for a flat beam, σx/σy=100.

40• y=0 μm• 0.505

Horizontal motion
0.510

0.520

0.550

• y=2 μm•m
• The ﬁgures are roughly independent of y.

νx=0.505• X motion is clearly solved at νx=0.505.
• Y motion is bound on surface. No emittance
growth.
x-px

y-py-xy-py-xHorizontal tune near the half integer is betterfor luminosity.

νx=0.55 and 0.6• When νx=0.55, 0.6, x motion is chaotic. y motion isstrongly chaotic, emittance growth.
y-py-xy-py-xνx=0.52x-px

y-py-xy-py-xνx=0.55x-px
43

x-y coupling, νx=0.505• R1=3.17e-3,
R2=-0.22e-3,
R3=0.059, R4=0.025(1 unit of KEKB knobscan)

44