Crab crossing and crab waist at super KEKB

39
Crab crossing and crab waist at super KEKB K. Ohmi (KEK) Super B workshop at SLAC 15-17, June 2006 Thanks, M. Biagini, Y. Funako shi, Y. Ohnishi, K.Oide, E. P erevedentsev, P. Raimondi, M Zobov

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Crab crossing and crab waist at super KEKB. K. Ohmi (KEK) Super B workshop at SLAC 15-17, June 2006 Thanks, M. Biagini, Y. Funakoshi, Y. Ohnishi, K.Oide, E. Perevedentsev, P. Raimondi, M Zobov. - PowerPoint PPT Presentation

Transcript of Crab crossing and crab waist at super KEKB

Page 1: Crab crossing and crab waist at super KEKB

Crab crossing and crab waist at super KEKB

K. Ohmi (KEK)Super B workshop at SLAC

15-17, June 2006

Thanks, M. Biagini, Y. Funakoshi, Y. Ohnishi, K.Oide, E. Perevedentsev, P. R

aimondi, M Zobov

Page 2: Crab crossing and crab waist at super KEKB

Super bunch approachK. Takayama et al, PRL, (LHC)

F. Ruggiero, F. Zimmermann (LHC) P.Raimondi et al, (super B)

2

x x y y

NL

xx

N

yy

x x y

N

( 1)x x

z

2

z y y

NL

xx

z x

N

yy

z y

N

Short bunch Long bunch1x x

z

x is smaller due to cancellation of tune shift along bunch length

Overlap factor

y z x xy

Page 3: Crab crossing and crab waist at super KEKB

Essentials of super bunch scheme

x xy

2

z y y

NL

xx

z x

N

yy

z y

N

Keep , and .y x xx

y x y

0y y

L • Bunch length is free.

• Small beta and small emittance are required.

Page 4: Crab crossing and crab waist at super KEKB

Short bunch scheme

• Small coupling• Short bunch

• Another approach: Operating point closed to half integer

Keep , and .yx xy

2

x x y y

NL

xx

N

yy

x x y

N

y z

0y y

L

0.5x y L

Page 5: Crab crossing and crab waist at super KEKB

We need L=1036 cm-2s-1

• Not infinity.

• Which approach is better?

• Application of lattice nonlinear force

• Traveling waist, crab waist

Page 6: Crab crossing and crab waist at super KEKB

Nonlinear map at collision point

• 1st orbit• 2nd tune, beta, crossing angle• 3rd chromaticity, transverse nonlinearity. z-

dependent chromaticity is now focused.

i i ij i j ijk i j kH a x b x x c x x x

( , , , , , ( / ))i x yx x p y p z E E x

1exp( : :) * [ , ] [ ,[ , ]] ...

2' ...i ij j ijk j k

M H H H H

a b x c x x

x x x x

Page 7: Crab crossing and crab waist at super KEKB

Waist control-I traveling focus

• Linear part for y. z is constant during collision.

2I yH ap z

Iy

y

Hy y y azP

P

2y

Hap

z

2 2

1t

a z az

T Taz

1

0 1

azT

=0

: : : :0

I IH He eM Μ

Page 8: Crab crossing and crab waist at super KEKB

Waist position for given z• Variation for s

• Minimum is shifted s=-az

22 2

( ) ( )1 1

t

a z az s az s az

M s M saz s az

Page 9: Crab crossing and crab waist at super KEKB

Realistic example- I

• Collision point of a part of bunch with z, <s>=z/2.

• To minimize at s=z/2, a=-1/2• Required H

• RFQ TM210•

21

2I yH p z

2

* 2

1

2

c pcV

e V~10 MV or more

Page 10: Crab crossing and crab waist at super KEKB

Waist control-II crab waist (P. Raimondi et al.)

• Take linear part for y, since x is constant during collision.

2I yH axp

Iy

y

Hy y y axP

P

2

x x x y

Hp p p ap

x

1

0 1

axT

2 2

1t

a x ax

T Tax

: : : :0

I IH He eM Μ

Page 11: Crab crossing and crab waist at super KEKB

Waist position for given x• Variation for s

• Minimum is shifted to s=-ax

22 2

( ) ( )1 1

t

a x ax s ax s ax

M s M sax s ax

Page 12: Crab crossing and crab waist at super KEKB

Realistic example- II

• To complete the crab waist, a=1/, where is full crossing angle.

• Required H

• Sextupole strength

21I yH xp

*

2 *

1 '' 1 1

2 /x

y y x

B LK

p e

K2~30-50

Not very strong

Page 13: Crab crossing and crab waist at super KEKB

Crabbing beam in sextupole• Crabbing beam in sextupole can give the nonlin

ear component at IP• Traveling waist is realized at IP.

2I yH ap z

**

( )( ) ( )

sz s x s

*

2 *

1 '' 1 1

2 /x

y y x

B LK

p e

K2~30-50

Page 14: Crab crossing and crab waist at super KEKB

Super B (LNF-SLAC)Base PEP-III

C 3016 2200

x 4.00E-10 2.00E-08

y 2.00E-12 2.00E-10

x (mm) 17.8 10

y (mm) 0.08 0.8

z (mm) 4 10

ne 2.00E+10 3.00E+10

np 4.40E+10 9.00E+10

/2 (mrad) 25 14

x 0.0025

y 0.1

( ) ( / 2)yy

x z

Fz s z dzds

y

Page 15: Crab crossing and crab waist at super KEKB

Luminosity for the super B• Luminosity and vertical beam size as functions of K2• L>1e36 is achieved in this weak-strong simulation.

Page 16: Crab crossing and crab waist at super KEKB

DAFNE upgradeDAFNE

C 97.7

x 3.00E-07

y 1.50E-09

x (mm) 133

y (mm) 6.5

z (mm) 15

ne 1.00E+11

np 1.00E+11

/2 (mrad) 25

x 0.033

y 0.2479

Page 17: Crab crossing and crab waist at super KEKB

Luminosity for new DAFNE• L (x1033) given by the weak-strong simulation• Small s was essential for high luminosity

ne tune s L(K2=10)

15 20

6.00E+10 0.53, 0.58 0.012 4.27 3.79

6.00E+10 0.53, 0.58 -0.01 4.35 3.93

1.00E+11 0.53, 0.58 -0.01 4.07 5.66 5.53

6.00E+10 0.53, 0.58 0.012 z=10mm 4.32 2.47

6.00E+10 0.53, 0.58 -0.01 z=10mm 4.65 2.7

6.00E+100.057,

0.097-0.01 5.19(3.3)

1.00E+110.057,

0.097-0.01 13.21(4.8)

() strong-strong , horizontal size blow-up

Page 18: Crab crossing and crab waist at super KEKB

Super KEKBSuperKEKB Crab waist

x 9.00E-09 6.00E-09 6.00E-096.00E-

096.00E-09

y 4.50E-11 6.00E-11 6.00E-116.00E-

116.00E-11

x (mm) 200 100 50 100 50

y (mm) 3 1 0.5 1 0.5

z (mm) 3 6 6 4 4

s 0.025 0.01 0.01 0.01 0.01

ne 5.50E+105.50E+1

05.50E+1

03.50E+

103.50E+1

0

np 1.26E+111.27E+1

11.27E+1

18.00E+

108.00E+1

0

/2 (mrad) 0 15 15 15 15

x 0.397 0.0418 0.022 0.0547 0.0298

y 0.794->0.24

0.1985 0.179 0.178 0.154

Lum (W.S.) 8E+356.70E+3

51.00E+3

63.95E+

354.80E+3

5

Lum (S.S.) 8.25E35 4.77E35 9E35 3.94E35 4.27E35

Horizontal blow-up is recovered by choice of tune. (M. Tawada)

Page 19: Crab crossing and crab waist at super KEKB

• Particles with z collide with central part of another beam. Hour glass effect still exists for each particles with z.

• No big gain in Lum.!• Life time is improved.

x=24 nm y=0.18nm x=0.2m y=1mm z=3mm

Traveling waist

Page 20: Crab crossing and crab waist at super KEKB

Small coupling

Page 21: Crab crossing and crab waist at super KEKB

Traveling of positron beam

Page 22: Crab crossing and crab waist at super KEKB

Increase longitudinal slice

x=18nm, y=0.09nm, x=0.2m y=3mm z=3mm

Lower coupling becomes to give higher luminosity.

Page 23: Crab crossing and crab waist at super KEKB

Why the crab crossing and crab waist improve luminosity?

• Beam-beam limit is caused by an emittance growth due to nonlinear beam-beam interaction.

• Why emittance grows?

• Studies for crab waist is just started.

Page 24: Crab crossing and crab waist at super KEKB

Weak-strong model

• 3 degree of freedom• Periodic system• Time (s) dependent

1 1 2 2 3 3( , , , , , ; ) '( , , , , , ; )x y zH x p y p z p s H J J J s

( ) ( ) 2s L s

Page 25: Crab crossing and crab waist at super KEKB

Solvable system• Exist three J’s, where H is only a function of J’s,

not of ’s.• For example, linear system. • Particles travel along J. J is kept, therefore no

emittance growth, except mismatching.

• Equilibrium distribution

( )2 ( )

d H Jd J

ds J

0 constdJ H

Jds

31 2

1 2 3

( ) exp : emittanceJJ J

J

Page 26: Crab crossing and crab waist at super KEKB

y

py

Page 27: Crab crossing and crab waist at super KEKB

One degree of freedom• Existence of KAM curve• Particles can not across the KAM curve.• Emittance growth is limited. It is not essential for

the beam-beam limit.

Page 28: Crab crossing and crab waist at super KEKB

• Schematic view of equilibrium distribution

• Limited emittance growth

Page 29: Crab crossing and crab waist at super KEKB

More degree of freedomGaussian weak-strong beam-beam model

• Diffusion is seen even in sympletic system.

Page 30: Crab crossing and crab waist at super KEKB

Diffusion due to crossing angle and frequency

spectra of <y2>

Only 2y signal was observed.

Page 31: Crab crossing and crab waist at super KEKB

Linear coupling for KEKB• Linear coupling (r’s), dispersions, (, =crossing angle

for beam-beam) worsen the diffusion rate.M. Tawada et al, EPAC04

Page 32: Crab crossing and crab waist at super KEKB

Two dimensional model• Vertical diffusion for =0.136• DC<<D for wide region (painted by black).• No emittance growth, if no interference. Actually, simulation including

radiation shows no luminosity degradation nor emittance growth in the region.

• Note KEKB D=5x10-4 /turn DAFNE D=1.8x10-5 /turn

5

10

15

20

nux

510

1520

nuy

00.00050.001

0.00150.002

5

10

15

20

nux0

0.00050.001

0.00150.002

2.5 5 7.5 10 12.5 15 17.5 20

2.5

5

7.5

10

12.5

15

17.5

20

(0.51,0.51)(0.51,0.51) (0.7,0.51)

(0.7,0.7)(0.51,0.7)

(0.7,0.51)

(0.51,0.7)

KEKB D=0.0005

Page 33: Crab crossing and crab waist at super KEKB

3-D simulation including bunch length (z~y)Head-on collision

• Global structure of the diffusion rate. • Fine structure near x=0.5 Contour plot

5

10

15

20

nux

510

1520

nuy

00.000250.0005

0.000750.001

5

10

15

20

nux0

0.000250.0005

0.000750.001

2.5 5 7.5 10 12.5 15 17.5 20

2.5

5

7.5

10

12.5

15

17.5

20

(0.51,0.51)

(0.7,0.51)

•Good region shrunk drastically.

•Synchrobeta effect near y~0.5.

• x~0.5 region  remains safe.

Page 34: Crab crossing and crab waist at super KEKB

Crossing angle (z/x~1, z~y)• Good region is only (x, y)~(0.51,0.55).

5

10

15

20

nux

510

1520

nuy

00.00050.001

0.00150.002

5

10

15

20

nux0

0.00050.001

0.00150.002

2.5 5 7.5 10 12.5 15 17.5 20

2.5

5

7.5

10

12.5

15

17.5

20

(0.51,0.51)

(0.7,0.51)

(0.51,0.7)

Page 35: Crab crossing and crab waist at super KEKB

Reduction of the degree of freedom.

• For x~0.5, x-motion is integrable. (work with E. Perevedentsev)

if zero-crossing angle and no error.

• Dynamic beta, and emittance

• Choice of optimum x

,0.5

lim 0x

C yD

2 2,0

0.5limx

xx

2

0.5limx

xp

1

(crossing angle)+(coupling)+(fast noise)x

L

Page 36: Crab crossing and crab waist at super KEKB

Crab waist for KEKB• H=25 x py

2.

• Crab waist works even for short bunch.

Page 37: Crab crossing and crab waist at super KEKB

Sextupole strength and diffusion rate            K2=20

          25             

  30

5

10

15

20

nux

510

1520

nuy

00.00050.001

0.00150.002

5

10

15

20

nux0

0.00050.001

0.00150.002

5

10

15

20

nux

510

1520

nuy

00.00050.001

0.00150.002

5

10

15

20

nux0

0.00050.001

0.00150.002

5

10

15

20

nux

510

1520

nuy

00.00050.001

0.00150.002

5

10

15

20

nux0

0.00050.001

0.00150.002

Page 38: Crab crossing and crab waist at super KEKB

Why the sextupole works?

• Nonlinear term induced by the crossing angle may be cancelled by the sextupole.

• Crab cavity

• Crab waist

Need study

22exp( : :) exp( : :) exp( : :) ...x yF p z K xp

exp(: :) exp( : :)BBF M F

exp( : :) exp( : :) exp(: :) 1x xF p z p z

Page 39: Crab crossing and crab waist at super KEKB

Conclusion• Crab-headon Lpeak=8x1035. Bunch length 2.5mm is required for

L=1036.

• Small beam size (superbunch) without crab-waist. Hard parameters are required x=0.4nm x=1cm y

=0.1mm.

• Small beam size (superbunch) with crab-waist. If a possible sextupole configuration can be found,

L=1036 may be possible.• Crab waist scheme is efficient even for shot bunc

h scheme.