Y. Ohnishi / KEK

Upgrade plan of KEKB

from 2012 to 20XX

Y. Ohnishi / KEK2008 January 24-26

Atami, Izu, Japan

2

Y. Ohnishi / KEK

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.

is a cross section of an interesting physics process. We can do nothing. 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.

€

N = σ L dt0

T

∫

3

Y. Ohnishi / KEK

What is luminosity ? (cont'd) Luminosity is defined by:

N+(N-) is a number of particles per bunch for positron (electron).

x*(y

*) is a beam size in the horizontal(vertical) plane. Usually, flat-beam, y

* << x*

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

€

L =N+N− f

4πσ x*σ y

*RL

4

Y. Ohnishi / KEK

Reductions to luminosity

Crossing angle

Hour-glass effecty

beam envelope

s

IP

bunch length

y*

focusing defocusing

y > y*

overlapregion

Beam

5

Y. Ohnishi / KEK

What limit the luminosity ?

☞ This might be true !

Reduction from the geometrical loss ?

Bunch length, z < y*, where y

* = (yy*)1/2.

Larger impedance in a ring makes bunch length longer. Head-on collision is preferable.

Money ?

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

Y. Ohnishi / KEK

Beam-beam force

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.

z

e-e+

v

v

r

a

l

€

E r =λ

2πε0rBϕ = −

μ0λv

2πr= −

β

cE r

€

Fr = −e E r − cβBϕ( ) = −e 1+ β 2( )E r ≅ −2eE r v ≈ c

Fr

is a longitudinal linecharge density.

cylindrical beam

ErB

e-

7

Y. Ohnishi / KEK

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

€

Δpr

p= −

1

mcγFrdt = −

e

mc 2γ−∞

∞

∫ E rdz−∞

∞

∫ Δt =Δz

2c

€

Δpx,y

p= −

N+re

γ−

Fx,y x, y,σ x*,σ y

*( )

€

iFx (x, y,σ x*,σ y

*) + Fy (x,y,σ x*,σ y

*) =2π

σ x*2 −σ y

*2w

x + iy

2(σ x*2 −σ y

*2)

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟− exp −

x 2

σ x*2

−y 2

σ y*2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟w

σ y*2

σ x*2

x + iσ x

*2

σ y*2

y

2(σ x*2 −σ y

*2)

⎛

⎝

⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟

⎧

⎨

⎪ ⎪

⎩

⎪ ⎪

⎫

⎬

⎪ ⎪

⎭

⎪ ⎪

w(z): complex error function

re: classical electron radius

ppr

kick angle

8

Y. Ohnishi / KEK

Beam-beam force (cont'd)

Δpx/p Δpy/p

Horizontal Vertical

This region is almost linear.

x*=200 m

y*=3 m

We call this slope(x,y) a beam-beam parameter.

€

Δpx,y

p−

4πξ x,y

β x,y*

x,y

€

x,y ± =reNmβ x,y

*

2πγ ±σ x,y* (σ x

* + σ y*)

Rξx,y

char

ge d

ensi

ty

Beam-beam force is nonlinear.

9

Y. Ohnishi / KEK

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 y*, beam-beam parameter y, eliminating the explicit dependence on beam size. €

L =γ ±

2ere

1+σ y

*

σ x*

⎛

⎝ ⎜

⎞

⎠ ⎟I±ξ y ±

β y*

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟RL

Rξ y

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

∝I±ξ y ±

β y* (flat-beam case)

€

L =N+N− f

4πσ x*σ y

*RL * means value at IP

10

Y. Ohnishi / KEK

Improvement of luminosity at KEKB upgrade

If small y* while keeping y

*/y constant, larger L can be realized. However, y

* > z to suppress the hour-glass effect. Crab-crossing and x→0.5 to mitigate nonlinear effects makes larger

y,max with increasing I.€

y ∝I−β y

*

σ x*σ y

*=

I−

σ x*

β y*

εy

≤ ξ y,max

L∝I−I+

σ x*σ y

*=

I+ξ y

β y*

≤I+ξ y,max

β y*

11

Y. Ohnishi / KEK

How large can we achieve beam-beam parameter ?

Luminosity is proportional to a beam-beam parameter.

Beam-beam limit ?

KEKB(crab)

mitigate nonlinear effects

12

Y. Ohnishi / KEK

Crab crossing

Input Coupler

Liq. Helium Vessel

Stub Support

Coaxial Coupler

Copper Bellows

80 K Liq. Nitrogen Shield

Notch Filter

RF Absorber

Aluminum End

Plate

Aluminum End

Plate

SUS Support

Pipe

Crossing angle 22 mrad

Head-on(crab)(Strong-strong simulation)

Crab crossing will increase the beam-beam parameter by a factor of 2.

Superconducting crab cavities have beenproduced, and under beam test at KEKB.

(at the optimum tune)

Vert

ical beam

-beam

K. Hosoyama, et al.

K. Ohmi, et al.

(mA)

KEKB(exp. with crab)

KEKB

13

Y. Ohnishi / KEK

Beam-beam effect and “Chaos”

y=0.02

y=0.053

y=0.10

Lar

ge b

eam

-bea

m p

aram

eter

y

y

y

py

py

py

y

py

y

py

y

py

x0 = 0 x0 = 5% x x

1-dimensional 2-dimensional

"chaos"Particles are confined in KAM*.

KAM is destroyed.Beam size growth

*near-integrable surface

14

Y. Ohnishi / KEK

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(x→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 2N+N

N+N+N2N+N

3N (x-y-z)

(x-y+z)

(x+y+z)

z

x

€

xn ∝ cos 2πν xn +ψ 0( )

n = 0,1,2,L turns

y

x

15

Y. Ohnishi / KEK

Tune Scan with Beam-beam Simulation

Tune Survey in upgraded KEKBwithout parasitic collision effect.

x=24 nm case:Lpeak=4.0x1035 cm-2s-1 (L/bunch=8.0X1031, Nb=5000)

0.60

0.58

0.56

0.54

0.52

0.5200.5150.5100.5050.500x

5e+31

1.5e+31

1.5e+31 1e+31

1e+31

5e+30

Simulation by K. Ohmi and M. Tawada

(.503, .550)

Head-on

} y ~0.2

Better working point isvery close to the half integer !

Betatron tunes

Beam-beamparameter

Crab-crossing collision

16

Y. Ohnishi / KEK

Experiences at KEKB

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 ?

Crab crossing3.06 spnb=1548

Crab crossing49 spnb=50

22 mrad crossing3.5 spnb=1388

1.7x1035

€

Lsp =L

I+I−

I is bunch current.

what is a slope ?

9.4/4.1 Anb=5018

x=24 nm

17

Y. Ohnishi / KEK

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

Y. Ohnishi / KEK

Beam-beam simulation(Strong-Strong )

L/#

bunc

hes

(cm

-2s-1

)

#turns

x=84/47 msec

x=84/84 msec

x=47/47 msec

y/x=0.5%, z=3 mm

#turns

L/#

bunc

hes

(cm

-2s-1

)

x=12 nm

x=24 nm

30%

y/x=0.5%, z=3 mm

#turns

L/#

bunc

hes

(cm

-2s-1

)

z=3 mm

z=4 mm

16%

y/x=0.5%, x=12 nm

HER(13 nm, 47 msec)

LER(12 nm, 84 msec)<y2 >

(m

)

#turns

y/x=0.5%, z=3 mm

19

Y. Ohnishi / KEK

Luminosity upgrade (cont'd) Luminosity gain and upgrade items (preliminary)

Item Gain Purpose

beam pipe x 1.5high current, short bunch, electron cloud

IR(*x/y=20cm/3 mm) x 1.5 small beam size at IP

low emittance(12 nm) x → 0.5

x 1.3mitigate nonlinear effects with beam-beam

crab crossing x 2mitigate nonlinear effects with beam-beam

RF/infrastructure x 3 high current

DR/e+ source x 1.5low * injection, improve e+ injection

charge switch x ? electron cloud, lower e+ current

3 ye

ars

shu

tdow

n

20

Y. Ohnishi / KEK

Projected luminosity (preliminary)

Inte

grat

e lu

min

osit

y (a

b-1)

Pea

k lu

min

osit

y (

cm-2s-1

)

Year

3 yearsshutdown

DampingRing

RF upgrade

KEKroadmap

operation time : 200 days/year

Target forroadmap

Target forroadmap

21

Y. Ohnishi / KEK

Machine parameters (preliminary)

LoI (updated) Upgrade (LER/HER)

Emittancex 24 12/13 nm

y 0.18 0.060/0.066 nm

Beta at IPx* 200 200 mm

y* 3 3 mm

Beam size at IP*1x* 50.0 37.5/39.8 m

y* 1.0 2.11/2.28 m

Bunch length z 3 3 mm

Transverse damping time x 47 84/47 msec

Betatron/synchrotron tune xysM+0.506/N+0.545/-0.0

31*1M+0.505/N+0.550/-0.0

25M,N:intege

r

Beam Energy E+/E- 3.5/8.0 3.5/8.0

Beam current I+/I- 9.4/4.1 9.4/4.1 A

#bunches Nb 5018 5018

Crossing angle x 30 → 0 (crab crossing) 30 → 0 (crab crossing) mrad

Beam-beam*2x 0.135 0.153

y 0.215 0.296

Beam-beamreduction*3

Rx 0.99 0.99

Ry 1.11 1.11

Luminosity reduction*3 RL 0.86 0.86

Luminosity L 4.0x1035 5.5x1035 cm-2s-1

*1 include beam-beam effects *2 calculated from luminosity *3 nominal values

22

Y. Ohnishi / KEK

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 decrea

sed. 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 (3S) and (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

€

PSR ∝E 4

ρ B2 B=106 m (HER) >> 16 m (LER)

Y. Ohnishi / KEK

Backup slides

24

Y. Ohnishi / KEK

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.

Tajima

B→Ks

B→J/Ks

25

Y. Ohnishi / KEK

Synchrotron Radiation LossP r

ad (M

W)

total

LER

HER

LER wiggler

LER wiggler

LER E (GeV)

€

m4S2 = 4 ELER E HER

€

ELERILER = 3.5 × 9.4 GeV A

E HERIHER = 8.0 × 4.1 GeV A

€

Prad = U0I

€

L∝ E ⋅ I

*E=3.8 GeV in LER is maximum to perform Y(5S) experiment.

26

Y. Ohnishi / KEK

No. ARES cavities

LER E (GeV)

No.

AR

ES

cav

itie

s

No. SCC in HER = 8 (fixed)

LER

HER

LER+HER

No wiggler in LER / #SCC is 8.#RF cavities = ~40 → constant LoI: ARES/SCC=16/12

27

Y. Ohnishi / KEK

Power consumption (RF only)

AC

plu

g po

wer

(M

W)

[RF

onl

y]

LER E (GeV)

LER

HER

LER+HER

No wiggler in LER / #SCC = 8 in HERTotal power consumption is 60~66 MW less dependent of energy asymmetry.

28

Y. Ohnishi / KEK

Horizontal Tune close to Half Integer x=0.5

In the collision of two beams, particles interact with fixed beam at either x or -x for x=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

€

x n( ) = 2Jxβ x cos 2πν xn +ψ x0( )

3 DOF 2+1 DOF 1+1+1 DOFCrab-crossing(resolve xz coupling)

x=0.5(resolve xy coupling)

n: turn number (integer)

29

Y. Ohnishi / KEK

Beam-beam simulation

L(x1035)=6.6295-0.021747*

Trans. damping time (msec)

Lum

inos

ity

(x10

35 c

m-2s-1

)

Lum

inos

ity

(x10

35 c

m-2s-1

)

Number of turns

47/47 msec

57/57 msec

84/84 msec

57/47 msec

LER/HER trans. damping time

I+/I- = 9.4/4.1 AE+/E- = 3.5/8.0 GeVNb = 5018x = 12 nmy/x = 0.5 %x/y = .505/.550

~10%