Luminosity boost by head-on(crab) collision
KEKB Accelerator Review Committee, KEK,
10-11 Feb, 2003

K. Ohmi, M. Tawada, K. Oide (KEK)Introduction
Target luminosity
Ltot = 1035 ~ 1036 cm-2s-1
 fRF=500MHz
EL=3.5GeV
EH=8GeVLb = 2x1031 ~ 2x1032 cm-2s-1
NLξ/βy = 1.6x1012 ~ 1.6x1013 m-1
NH = 3.5 NL /8
N γ ξyf rep
Ltot =2 re β yHow do we choose theseparameters?
 L= 1035 cm-2s-1, NLξ/βy = 1.6x1012
βy =3mm, ξy = 0.05,
NL = 9.6x1010 , IL=8 A
Crossing angle =15 mrad

 L= 1036 cm-2s-1, NLξ/βy = 1.6x1013
βy =3mm, ξy = 0.2,
NL = 2.4x1011 , IL=19 A
without drastic change of Magnet and RF.

Super KEKBWWW pageDo we get the luminosity?
 Collision scheme
Flat beam with/without crossing angle
Long bunch
Round beam
Four-beam…………………
 Computer simulations of beam-beaminteractions inform the feasibility for thehigh luminosity.

Beam-beam simulation methods Weak-strong model
One beam is represented by macro-particles, while
another beam is represented by fixed Gaussian charge
distribution.

 Strong-strong model
Both beams are represented by macro-particles.

Weak strong

Strong-strong

Crossing angle and crab crossing
 Transformation fromLab. frame to headon frame.
x = tan φ z + [1 + h sin φ ] x**x

p *x = ( p x − h tan φ ) / cos φy * = y + hx* sin φ x
p *y = p *y / cos φz * = z / cos φ + hz* sin φ xp = p z − p x tan φ + h tan φ*z2h = pz + 1 −( p z + 1)2 − p x2 − p y2

(φ: half crossing angle)

Linear part0
1
 0 1 / cos φ
00
0
000

 0 tan φ0000100 1 / cos φ0000tan φ
0001 / cos φ00
0
0
0
0 1 

Crab cavity
 Crab cavity makes z dependent dispersion ζx= -φ at IP, which cancels the crossing angle
effect.
1 0
0 1
0 0

0 0
0 0
0 ζx0 0 ζx
0 01 00 10000 00 0100
0000 1 

Longitudinal slicing
 A bunch is divided into some slices which
include many macro-particles.
 Collision is calculated slice by slice.

Achieved beam-beam parameter Finite crossing angle scheme quite
succeeded in the present KEKB.
 Achieved beam-beam parameter was
not remarkably large, 0.04~0.05,
though it is just our design value.
 The world record is ~0.07 at CESR
and is ~0.1 at LEP.

Present KEKB Oct. 29, 2002
Luminosity Oct-29-02

02-Oct-29

7000
6000
5000

LL

9000
8000

Specific Luminosity

4000
300020001000
000.2

0.4

0.6
I+I-

0.8

11.2

1098765432
1002-Oct-29

00.2

0.4

0.6

0.8

1I+I-

 Lpeak=8.26x1033 cm-2s-1
Nb=1184
 N+= 7.7x1010
N-=5.0x1010
 ε+,x =18 nm ε-,x = 24 nm
 β = 7mm
 ν = 0.51/0.56

1.2

Simulation results for thepresent KEKB（Oct. 29, 02)
 Lspec obtained by simulation andexperiment.
KEKB Oct.29, 02

20

strong-strong
experiment

L spec15

weak-strong
strong-weak

1050
0.0

0.2

0.4

0.6I+I-0.81.0

Experiment and simulation
 Luminosity by simulation is somewhat higher
than experimental value.
 Experimental luminosity may be larger for
longer bunch spacing. In a measurement, it
was 20% larger.
 The agreement becomes better due to adetailed choice of parameters (Tawada).
 Weak-strong and strong-strong simulations
coincide each other.

Study for effects of crossing angle
Model lattice parameters
To avoid flip-flop phenomenon, Ν/γ iskept equal for the both rings.
εx = 18mrad
εy = 0.01 εx
βx = 60cm
βy = 7mm
N+= 8/3.5 Nσz = 7mm

Specific luminosity for various
current product (I+I-).
 φ = 0mrad and 11mrad
Weak strong

strong-strong

Weak-strong

Strong-strong

30353025o mrad
11 mrad

2025
Lspec

Lspec

o mrad11 mrad151020
15
1055

00

0.0

0.5

1.0
I+I-

1.5

0.0

0.2

0.4

0.6
I+I-

0.8

1.0

1.2

Beam-beam parameter
Strong-strong

Weak-strong
0.20

o mrad11 mrad

0.10

ξξ

0.15

0.05
0.00
0.0

0.5

1.0
I+ (mA)

1.5

2.0

0.12
0.10
0.080.06
0.04
0.02
0.00

o mrad11 mrad

0.0

0.5

1.0
I+ (mA)

1.5

2.0

Effect of crossing angle
 The weak-strong and strong-strong
show similar results for φ =11 mrad.
 No beam-beam limit for φ =0 mrad in
the weak-strong.
 There is a beam-beam limit for φ =0mrad in the strong-strong simulation.
 Crossing angle degrades luminosity ineither case.

 Crab cavity upgrades luminosity.

Super KEKB Target: Lb = 2x1031 ~ 2x1032 cm-2s-1
 Super KEKB: Lb = 2x1031 cm-2s-1,
crossing angle 15 mrad.
 Hyper KEKB: Lb = 2x1032 cm-2s-1,
head-on collision and higher current.

Simulation for Super KEKB
parameter (weak-strong)
3.0E+32
2.5E+32
2.0E+32
1.5E+32
1.0E+32
5.0E+31
0.0E+00

Luminosity for various nx0 mrad
15 mrad

LL

Luminosity (nx=0.5156)

ss

0.0

2.0

4.0
6.0
I+I- (mA^2)

8.0

10.0

nx=0.5156
0.5256
0.53260.649

3.0E+32
2.5E+32
2.0E+32
1.5E+32
1.0E+32
5.0E+31
0.0E+00
0.0

2.0

4.0
6.0
I+I- (mA^2)

8.0

 The luminosity Lb = 2x1031 cm-2s-1 was achieved
for the crossing angle 15mrad.
 The luminosity Lb = 2x1032 cm-2s-1 was achieved at
NL=2.2x1011 NH=1011 .
 Luminosity behavior depends on tune.

10.0

Beam-beam parameter obtained by
the weak-strong simulation
0.30
0.25
0.20
0.15
0.10
0.05
0.00

Beam-beam parameter for various nx

0 mrad15 mradξξBeam-beam parameter (nx=0.5156)

0.0

2.0

4.0
I+ (mA)

6.0

0.30
0.25
0.20
0.15
0.10
0.05
0.00

nx=0.5156
0.5256
0.53260.649 PEP-II

0.0

2.0

4.0
I+ (mA) ξ is limited about 0.25 for the head-on collision,
while is limited 0.09 for the crossing angle 15mrad.
 ξ behavior depends on tune.

6.0

Crossing angle dependencesigz=3.5mm
2.5E+32
2.0E+32
1.5E+32
LLgeo
Lws

1.0E+32
5.0E+31
0.0E+00
0510152025

Half crossing angle (mrad) Luminosity at φ =0 mrad is very high.
 Narrow peak near φ =0 mrad.
 This behavior is remarkable for large ξ.

Strong-strong simulation
Is Lb = 2x1032 cm-2s-1 obtained even by the strong
strong simulation?

 Lb = 8~9x1031 cm-2s-1 < 2x1032 cm-2s-1.
 A beam-beam limit is seen in the strong-strong.
 Ltot = 4x1035 cm-2s-1 can be expected.

Candidate of Hyper KEKB
parameter Low beta and head-on collision makepossible a higher ξ. It means that theluminosity is achieved by lower total current.
 βx = 15 cm, βy = 3 mm, σz = 3.5 mm, φ =0mrad, εx = 33 nm, εy = 0.33nm,
NL=2.2x1011 NH=1011
 Lb = 2x1032 cm-2s-1, Ltot = 1x1036 cm-2s-1 ,ξ = 0.2 by the weak-strong.
 Lb = 8~9x1031 cm-2s-1 , Ltot = 4x1035 cm-2s-1
ξ = 0.09~0.1 by the strong-strong.

Which is reliable w.s. or s.s.?
 Is w.s. model reliable to estimate thebeam-beam limit?
 Unphysical numerical noises (PIC algorithm
or longitudinal slicing) may degrade in thes.s. simulation in such a high current.
 We need more studies why the beam-beamlimit observed in the s.s. simulation.
 We do not discard the result of weak-strongnow.

Results for other machinesobtained by w.s..

CESR

0.12
0.10
0.08

4.00

WS 0mard
WS 2.3mrad
CESR (45 bunch)

3.50

Exp

2.50

0.06
0.04
0.02
0.00
0.000

Sim

3.00

L sp e c

ξ

0.16
0.14

PEP-II

2.00
1.50
1.00
0.50

0.005

0.010
I

0.015

0.00
0.00

1.00

2.00

3.00

4.00
I+I-

5.00

6.00

7.00

Four beam(with Ohnishi)

 Collision of neutralized beams
containing both of e+ and e- charge.

3.5 GeV

8 GeV

Eigenmode of dipole motion ν=ν0+ξ φ β ( e ± ) − φ β ( e ∓ ) = πφ β ( e± ) − φ β ( e± ) = 0

 ν=ν0-ξ φ β ( e ± ) − φ β ( e ∓ ) = 0
φ β ( e± ) − φ β ( e± ) = π ν=ν0φ β ( e+ ) − φ β ( e− ) = 0
φ β ( e+ ) − φ β ( e− ) = 0

Coherent tune shift similar as that of two-beam4 eigenmodes of four-beam collisionx,yz

No tune shift
ν=ν0
Focusing
ν=ν0+ξDefocusing
ν=ν0-ξ

Eigenvalue of each mode

unstableStrong-strong simulation (2D) Hyper KEKB parameter Stable tune for the dipole mode.

 Strong coherent motion is seen.

Summary for four-beam scheme(preliminary) Incoherent effect is cancelled by theneutralization, but coherent effect remains.
 Twice more resonances.
 Weak Landau damping.
 Does feed-back help the coherent mode?
 We have not had a reliable solution for thefour beam scheme yet.