Beam-beam effect with Crabcavity
K. Ohmi
MAC2007 for KEKB
Mar. 19-21, 2007

Essentials of crab collision(head-on collision)• Symmetry of the collision.
• Symmetry breaking, what degrades the luminosity.
0.18
0.16
0.14

Crab crossing

xiy

0.12
0.1
0.08

Crossing angle=30 mrad

0.06

Perfect symmetrycase

N + γ + = N −γ −

0.04
0.02
00246
NHER (x E10)

810

Our operating condition
Equal tune shift condition
EεxNIbOperation

LER
3.5 GeV
18 nm
8.66x1010
1.39 mA
1.2 mA

1 N ∓ re1ξ y ,± =4π γ ± ε x ,∓κ ∓1/ 2 β 1/y ,∓2 β x1/,∓2

ξ y ,+ = ξ y ,−HER
824 nm5.05x1010
0.81 mA
0.67 mA

N +γ +ε x ,+=N −γ −ε x ,−

Luminosity at the condition• The emittance compensation is noproblem.
L (cm-2 s-1)

1.4e+33 1.6mA,18nmx0.7mA,18nm1.4mA,18nmx0.8mA,24nm
1.2e+33
1e+338e+326e+324e+322e+32002000 4000 6000 8000 1000012000
turnSymmetry breaking source• Optimization with a large number ofparameters• Offset ∆x, ∆y, ∆x’, ∆y’• Twiss parameters, β(waist), Ri=1,4, ηx,y, η’ x,yof each beam.

Tolerance for twiss parameters• Tolerance of all parameters are individuallyin controllable range.
4.E+31

4.E+31

3.E+31

3.E+31

2.E+31

2.E+31LL

1 unit for KEKB tuning: r4=0.021, η=0.00016

1.E+31

1.E+31L
Lgeo

0.E+00
00.05

LLgeo

0.E+00

0.1

0.15
r4

0.2

0.25

00.0002 0.0004 0.0006 0.0008

0.001

0.0012

etay (m)Difficulty for multi-parameters optimization

Horizontal scan• Luminosity

beam-beam kick
0.16

1.4mA,18nmx0.8mA,24nm0.5 mrad
2e+31
1 mrad2 mrad0 mrad1 mrad2 mrad0.140.12∆px (mrad)-2 -1

L (cm s )2.5e+31

1.5e+31
1e+31

0.1
0.08
0.06
0.04

5e+30

0.02

1.4mA,18nmx0.8mA,24nm

000050100150H OFFSET (µm)

50100200This figure is meaningful.
Even the two parameters, the search of the peak seems to be
hard: if residual crossing angle is 2 mrad, we can not realize theexistence of the peak.
We have to arrive the peak for multi-parameter.

150200Beam size and H-offset

180ee+ee+

160140σy (µm)σx (µm)120
100806040
201.4mA,18nmx0.8mA,24nm

0050

100
150H OFFSET (µm)

200

54.5
43.5
32.5
21.5
10.5
0-e (0 mrad)
e+ (0 mrad)e (1 mrad)+e (1 mrad)

1.4mA,18nmx0.8mA,24nm

050

100
H OFFSET (µm)

150200Life time and offset
5050

HOFS=0 um, ee+404030

HOFS=20 um, ee+NN30

202010100-0.003 -0.002 -0.001

0 µm

0-0.003 -0.002 -0.001

00.001 0.002 0.003
x (m)00.001 0.002 0.003

20 µm x (m)Life time may be short at H-offset 20, 40 µm, Jx=3 µm

•

40 µm

5050
40

HOFS=40 um, ee+

40

100 µm
HOFS=100 um, ee+

30

N

N

30
20

20

10

10

0-0.003 -0.002 -0.001

00.001 0.002 0.003
x (m)0-0.003 -0.002 -0.001

0x (m)

0.001 0.002 0.003

Beam-beam induced Life timeevaluation• Simplified method.
• Count the number of particle outgoingfrom the meshed area.
• Meshed area, +- 2.5 mm x 0.05 mm.
• Ax=7.8 µm, Ay=0.36 µm.
• Actual aperture Ax~12 µm Ay~1 µm.

Beam loss featureyyxy•••yxBeam particles are lost verticalfor large horizontal offset.
Beam particles are losthorizontal for horizontal offset
50 µm.
Electron beam is easily lost in
this condition.

Beam life at 11 mrad crossing• Life time is no problem, if coherent
motion does not occur

Simulation of the Crab voltage scan
88776654543322110246810122.5e+3101424681012LER crab angle (mrad)

HER crab angle (mrad)8220

2e+3114L (cm-2 s-1)σy (µm)σy (µm)• The size is minimum for no bunch tilt.

1e+31

7200

5e+30

6σy (µm)

180
σx (µm)1.5e+31160

5002468 10 12HER or LER crab angle (mrad)

43140

2120

101000246810HER crab angle (mrad)

1214246810HER crab angle (mrad)

121414

Measurement of HER voltage scan
• aIf there is not othererrors, we have ashape enhancement.

Vertical angle
φy(LER)= φy(HER): worst
φy(LER)= -φy(HER) and φy(LER)=0 : better

Most serious issue for the crab
operation• Asymmetry for the horizontal offset• Beam life time is very short in a region of a horizontaloffset.
• We still have just like “Egure” effect even in head-on
collision.
• This asymmetry can not be reproduced by the simulation.
Long life time

Short life timeHorizontaloffset scan
• The beam current
seems to belimited by theshort life time ofthe region.
• The region isenlarged for highcurrent.

HER life
LER life decrases
depending on thecondition

Collision center given by thebeam-beam kick

Beam-beam limit for us
For more sophisticatedparameters, theluminosity is higher.

Real world or the kingdom of Heaven?

L (cm-2 s-1)

2.5e+31
1.4mA,18nmx0.8mA,24nm0.5 mrad
2e+31
1 mrad2 mradWe may still loiterthis area or in justentrance.

1.5e+31
1e+31
5e+30
0050

100

150200H OFFSET (µm) and many other parameters,

which destroy the symmetry.