Nano-Beam Scheme for SuperKEKB

Andrew Hutton

Slides taken from talks by

Haruyo Koiso, Yukiyoshi Ohnishi & Masafumi Tawada

• The scheme proposed by P. Raimondi and SuperB Group.

• Squeeze y* as small as possible: 0.27/0.41 mm.

• Assume beam-beam parameter = 0.09 which has been already achieved at KEKB.

• Change beam energies 3.5 / 8 -> 4 /7 GeV to achieve longer Touschek lifetime and mitigate the effect of intra-beam scattering in LER.

Nano-beam Scheme

Parameter Optimization

Main parameters can be quickly optimized with this panel.

Beam Parameters KEKB

DesignKEKB Achieved

: with crabSuperKEKB

High-Current SuperKEKB

Nano-Beam

Energy (GeV) (LER/HER) 3.5/8.0 3.5/8.0 3.5/8.0 4.0/7.0

y* (mm) 10/10 5.9/5.9 3/6 0.27/0.42

ex (nm) 18/18 18/24 24/18 3.2/2.4

sy(mm) 1.9 0.94 0.85/0.73 0.059

xy 0.052 0.129/0.090 0.3/0.51 0.09/0.09

sz (mm) 4 ~ 6 5/3 6/5

Ibeam (A) 2.6/1.1 1.64/1.19 9.4/4.1 3.6/2.6

Nbunches 5000 1584 5000 2503

Luminosity (1034 cm-2 s-1) 1 2.11 53 80

e- 2.6 A

e+ 3.6 A

x 40 Gain in Luminosity

SuperKEKB

Colliding bunches

Damping ring

Low emittance gun

Positron source

New beam pipe& bellows

Belle II

New IR

Replace long TRISTAN dipoles with shorter ones (HER)

TiN-coated beam pipe with antechambers

Redesign the HER arcs to squeeze the emittance

Add / modify RF systems for higher beam current

New positron target / capture section

New superconducting /permanent final focusing quads near the IP

Low emittance electrons to inject

Low emittance positrons to inject

Comparison of Parameters

SuperKEKB 6

KEKB Design

KEKB Achieved: with crab

SuperKEKB Nano-Beam

Energy (GeV) (LER/HER) 3.5/8.0 3.5/8.0 4.0/7.0

y* (mm) 10/10 5.9/5.9 0.27/0.41

ex (nm) 18/18 18/24 3.2/2.4

sy(mm) 1.9 0.94 0.059

xy 0.052 0.129/0.090 0.09/0.09

sz (mm) 4 ~ 6 6/5

Ibeam (A) 2.6/1.1 1.64/1.19 3.6/2.62

Nbunches 5000 1584 2503

Luminosity (1034 cm-2 s-1) 1 2.11 80

Beam Energy

• In SuperKEKB, the beam energy is changed to decrease the effect of the intra-beam scattering in LER, especially to make longer Touschek lifetime.

• LER: 3.5 GeV → 4 GeV• HER: 8 GeV → 7 GeV• In HER, the lower beam energy makes lower

emittance.

SuperKEKB 7

Luminosity

SuperKEKB 8

€

L = γ ±

2ere

S ⋅I±ξ y ±

β y ±*

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟⋅

RL

Rξy ±

If sx* = sx+* = sx-* and sy* = sy+* = sy-*,S = 1+sy*/sx* (aspect ratio of the beam size at IP).

€

xy ± =reβ y±

* Nm

2πγ ±σ y m* σ x m

* + σ y m*( )

Rξy ±where

Three fundamental parameters to determine the luminosity.

Target Luminosity is 8x1035 cm-2s-1 in SuperKEKB.

Beam-Beam Parameter

SuperKEKB 9

KEKB Design

KEKB Achieved: with crab

SuperKEKB Nano-Beam

Energy (GeV) (LER/HER) 3.5/8.0 3.5/8.0 4.0/7.0

y* (mm) 10/10 5.9/5.9 0.27/0.41

ex (nm) 18/18 18/24 3.2/2.4

sy(mm) 1.9 0.94 0.059

xy 0.052 0.129/0.090 0.09/0.09

sz (mm) 4 ~ 6 6/5

Ibeam (A) 2.6/1.1 1.64/1.19 3.6/2.62

Nbunches 5000 1584 2503

Luminosity (1034 cm-2 s-1) 1 2.11 80

Beam-Beam Parameter

• The maximum value of the beam-beam parameter is assumed to be 0.09 in SuperKEKB.

• The beam-beam parameter of 0.09 has been achieved in KEKB.

• The horizontal beam-beam parameter becomes very small in the nano-beam scheme. xx~0.0028

• Dynamic effects is also small since the small horizontal beam-beam parameter and the horizontal betatron tune is far from 0.5.

SuperKEKB 10

Beam-Beam Simulation

• Beam-beam simulation gives 8x1035 cm-2s-1

• Difference between with and without the crab-waist is not so large.

SuperKEKB 11

L = 8x1035

LER LER

W-S W-S

Vertical Beta Function at IP

SuperKEKB 12

KEKB Design

KEKB Achieved: with crab

SuperKEKB Nano-Beam

Energy (GeV) (LER/HER) 3.5/8.0 3.5/8.0 4.0/7.0

y* (mm) 10/10 5.9/5.9 0.27/0.41

ex (nm) 18/18 18/24 3.2/2.4

sy(mm) 1.9 0.94 0.059

xy 0.052 0.129/0.090 0.09/0.09

sz (mm) 4 ~ 6 6/5

Ibeam (A) 2.6/1.1 1.64/1.19 3.6/2.62

Nbunches 5000 1584 2503

Luminosity (1034 cm-2 s-1) 1 2.11 80

Vertical Beta Function at IP• By using the modern technique, the vertical beta function can

be squeezed to be a few hundred micron at most. – y

* ~ 1/20 of KEKB• Hourglass effect (HG) is a serious problem to squeeze the beta

function in the head-on collision.• In order to satisfy HG, a collision of narrow beams with a large

crossing angle is adopted. This is “nano-beam scheme”. • However, dynamic aperture (DA) will be reduced because of the

nonlinear fringe, and kinematic terms in the interaction region (IR), and also strong sextupoles.

SuperKEKB 13

Natural chromaticity LER: xx/xy = -104/-789 HER: xx/xy = -187/-853

LER: xx/xy = -72/-123HER: xx/xy = -70/-124

SuperKEKB KEKB

d

Collision SchemeHigh Current Scheme Nano-Beam Scheme

Half crossing angle: f

14

2f

sz sx*

€

s x*

€

s z

€

d = σ x*

φ

overlap region (≠ bunch length)

Hourglass requirementHourglass requirement

€

y* ≥ σ z

overlap region = bunch length

SuperKEKB

Head-on

€

y* ≥ σ x

*

φ~5 mm ~200-300 mm

Hourglass Effect for Nano-Beam

15SuperKEKB

€

y−* ≥ max 2σ x +

sin2φ, 2σ x−

tan2φ ⎛ ⎝ ⎜

⎞ ⎠ ⎟

β y+* ≥ max 2σ x−

sin2φ, 2σ x+

tan2φ ⎛ ⎝ ⎜

⎞ ⎠ ⎟

Hourglass (H.G)requirement without crab-waist:

2f

2sx- 2sx+

d1

d2

€

d1 = 2σ x+

sin2φ

€

d2 = 2σ x+

tan2φ

€

y +* LER waist

e+ e-

There are two kinds ofhourglass requirements.

With crab-waist, this term is zero

Beta Function at IP• Machine parameters are chosen to be insensitive to

the HG effect.• The vertical beta function:

• The vertical beta functions in both rings satisfy the HG requirement.

• To squeeze y*, low emittance and low x

* are needed.

SuperKEKB 16

€

y−* = 410 ≥ max 2σ x +

sin2φ, 2σ x−

tan2φ ⎛ ⎝ ⎜

⎞ ⎠ ⎟= max 244,186( ) μm

β y+* = 270 ≥ max 2σ x−

sin2φ, 2σ x+

tan2φ ⎛ ⎝ ⎜

⎞ ⎠ ⎟= max 187,243( ) μm

€

y* ≥ σ x

*

φ

Nonlinear Terms around IP

€

Jy0 =β y

*2

1− 23

KL*2 ⎛ ⎝ ⎜

⎞ ⎠ ⎟L*

A(μ y )

LER KEKBL

KEKBR

SuperKEKBL

SuperKEKBR

y* (mm) 5.9 0.27

K (1/m2) -1.777 -1.778 -4.425 -6.003

L* (m) 1.332 1.762 0.7269 0.7680Jy0 / A (mm) 8.425 4.221 0.03919 0.02825

L*

K

Phys. Rev. E47, 2010 (1993)

Beam Current

SuperKEKB 18

KEKB Design

KEKB Achieved: with crab

SuperKEKB Nano-Beam

Energy (GeV) (LER/HER) 3.5/8.0 3.5/8.0 4.0/7.0

y* (mm) 10/10 5.9/5.9 0.27/0.41

ex (nm) 18/18 18/24 3.2/2.4

sy(mm) 1.9 0.94 0.059

xy 0.052 0.129/0.090 0.09/0.09

sz (mm) 4 ~ 6 6/5

Ibeam (A) 2.6/1.1 1.64/1.19 3.6/2.62

Nbunches 5000 1584 2503

Luminosity (1034 cm-2 s-1) 1 2.11 80

Beam Current• In order to achieve the target luminosity, the beam current in

nano-beam scheme becomes twice of KEKB.• The highest beam current is 2 A in LER and 1.4 A in HER at the

KEKB operation.– 1.8 A in LER / 1.35 A in HER at physics run

• In SuperKEKB, the design beam currents are 3.6 A for LER and 2.62 A for HER.

• Number of bunches is 2503 to get the suitable density of the overlap region (alternate buckets filled).– Bunch current becomes 1.44 mA in LER and 1.05 mA in HER.

SuperKEKB 19

Luminosity gain is 1(xy) x 20(1/y*) x 2(I) = 40 times of KEKB.

Then, we get 8x1035 cm-2s-1

Crossing Angle

• The full crossing angle is 83 mrad in SuperKEKB.

• Separation of two beams is necessary to put final focusing magnets closer to IP as much as possible. This affects the magnet design and the dynamic aperture.

• The angle between the solenoid axis and the beam line is 41.5 mrad, respectively. This angle is determined by optimization of the vertical emittance generated by SR from the solenoid fringe.

SuperKEKB 20

Emittance

• Redesign of arc cells to make low emittance– 2.5 p non-interleaved sextupole cell (-I’ connection)

• chromaticity is corrected and nonlinear kick is cancelled.– LER (4 GeV)

• Longer bending radius is adopted.– HER (7 GeV)

• Number of cells increases to reduce dispersion.

€

H = γ xη x2 + 2α xη xη 'x +β xη 'x

(hx:dispersion)

€

ex =cγ γ

2

Jx

12πρ 0

2 HdsBend∫

21SuperKEKB

€

y* ≥ σ x

*

φ

Emittance• Local chromaticity correction (LCC) is necessary to

correct large chromaticity generated in the vicinity of IP.

• However, the LCC generates some emittance to make dispersion region.

• The emittance generation at the LCC should be reduced as much as possible. This is a trade-off between DA and emittance.

SuperKEKB 22

Emittance• In SuperKEKB, the horizontal emittance is 3.2 nm in

LER and 2.4 nm in HER, respectively. – 2.7 nm in LER and 2.3 nm in HER at the zero beam current

• Coupling parameter of 0.4 % in LER and 0.35 % in HER are assumed. (challenging!)

• Vertical emittance induced by SR from solenoid fringe field can not be ignored. (suggested by E. Perevedentev)

• In order to suppress it, rate of change of Bz should be reduced and/or decrease angle between the solenoid axis and the beam axis.

• Machine error also should be reduced and corrected. SuperKEKB 23

Vertical Emittance originated from Solenoid Fringe

SuperKEKB 24

Crossing angle = LER angle + HER angle = 83 mrad

Solenoid axis= angle bisector

We choose 41.5 mrad and the contribution of solenoid fringe is ~4 pm.

Energy ratio4/(4+7)

proportional to q4

Bunch Length

• In SuperKEKB, the bunch length is 6 mm in LER and 5 mm in HER which are similar to the present KEKB.

• The “bunch length” means a value includes intra-beam scattering and wake field from the ring impedance at the design beam current.

SuperKEKB 25

Nano-Beam Scheme

Y. Ohnishi / KEK 26

=

Head-on Frame

€

2σ x*

€

2σ z

€

2 ˜ σ z

€

2 ˜ σ z€

2 ˜ σ x*

€

φ

€

˜ σ x* = φσ z

˜ σ z =σ x

*

φ

€

L ∝nbN±ξy ±

βy*

ξy ± ≅re

2πγ ±

Nm

φσ z

βy*

ε y

narrow and long bunchwith large crossing angle short bunch with head-on

Parameter Consideration• In SuperKEKB, the luminosity performance depends on the

lattice performance significantly.

• Especially, Touschek lifetime becomes serious in the nano-beam scheme due to lack of DA.

• Target lifetime is 600 sec in both rings. The large DA in the momentum direction is necessary.

• Transverse aperture is also necessary for the “betatron injection”. If enough transverse aperture cannot be kept, “synchrotron injection” should be considered. The emittance of the injected beam should be small, therefore e+ damping ring (DR) and RF-gun are considered.

Y. Ohnishi / KEK 27

IR design

2010.2.15 SuperKEKB 28

Detector solenoid axis

QC1LPVert. f

QC1RPVert. f

QC2LPHorz. FPM

QC2RPHorz. F

QC1REVert. f

QC1LEVert. f

QC2LEHorz. FPM

QC2REHorz. FPM

41.5 mrad

41.5 mrad

HER

IP

LER and HER beam are focused by separated quadrupole doublet, respectively

LER

29

IR Magnets design

• Use both of superconducting magnets and permanent magnets

• Superconducting magnets• Leakage fields of superconducting magnets are canceled by correction

windings on the other beam pipe• Warm bore

• Permanent magnets for QC2LE, QC2LP, QC2RE• Pros.

– Cryostats are small– Assembly of vacuum chamber can be simple – Vacuum pump can be located near IP

• Cons.– Need to develop a permanent magnet– Fine temperature control is required – Extra magnets are required to change beam energies

2010.2.15 SuperKEKB

302010.2.15 SuperKEKB

IR design with PM version N. Ohuchi

QC1RE

QC1RP+corr. coil

QC1LP+corr. coil

QC1RE+corr coil

QC1LE+corr. coil

QC2LPPM

QC2RP+corr. coil

QC2LEPM

QC2REPM

Anti solenoid-L

Anti solenoid-R Cryostat

Cryostat

IP

31

The magnet design of QC1R/L-P

Cross section of QC1 RP

Magnet Parameters• Magnet inner radius=22 mm, outer radius=27.55

mm• Magnet current=1511 A• Field gradient=75.61 T/m• Current density, JSC= 1615.8 A/mm2

• Magnetic length Leff = 0.2967 m• Peak field w/o solenoids = 2.24 T• Operation temperature = 4.4 K

Cable Parameters• Size =2.5mm 0.93mm• Number of SC strand=10• Diameter of the strand=0.5mm• Cu ratio=1.8• Ic= 2000 A @ 5T and 4.2 K

7.0

1.123

1.057KEKBQCS

3.9

1.013

0.967S-KEKB

H-Current

0.93

2.5

0.9S-KEKB

NanoBeam

Designed new SC cable for main quadrupole

SC correctors:Normal OctupoleSkew QuadrupoleNormal DipoleSkew Dipole

SC correctors:Normal SextupoleNormal QuadrupoleNormal Dipole

N. OhuchiVac ch ID 20mm

Coolant path

Beam envelop

Leakage fields are canceled by the correction windings on the other beam pipe

15th KEKB Review 322010.2.15

32

○ Belle Detector 8m(W)×8m(L)×10m(H)Total weight: 1300tons 　 650tons (Barrel Yoke) 　 600tons (End Yoke)　 50tons (Others)

H. Yamaoka

33

Anti solenoid

2010.2.15 SuperKEKB

Vertical emittance degradation depends on the anti-solenoid field profile

Anti-solenoid Ver.2HER:53mrad

€

Δey

Bz

H. Koiso

342010.2.15 SuperKEKB

IR vacuum chamber K. Kanazawa

• Vacuum level will be worse due to poor vacuum conductance.• IR assembly is a big issue • BPM can’t be fixed rigidly on the quadrupole magnet

Positron

35

Physical Aperture• Required acceptance for injection

– 2Jx=5x10-7 (m), 2Jy=2x10-8(m), 4% coupling– Dynamic effects are ignored because nominal nx = 0.53

• Physical aperture is not enough for the design β-functions– COD is not taken into account– No margin for error

2010.2.15 SuperKEKB

QC1LP QC1RP QC1LE QC1RE QC2LP QC2RP QC2LE QC2RE

PhysicalAperture (mm)

20 20 30 30 60 60 70 70

RequiredAperture (Horz.)(mm)

11.2 10.0 16.4 17.2 25.6 28.4 47.6 48.4

Vert.(mm)

15.8 14.8 18.2 18.2 9.4 9.6 15.4 10.6

36

COD (Belle)

2010.2.15 SuperKEKB

COD(LER 41.5 mrad) COD(HER 41.5 mrad)

A. Morita

IPQC

1RP

QC

2RP

QC

1LP

QC

2LP

IPQC

2RE

QC

1RE

QC

1LE

QC

2LE

4mm1mm

200um

100um

COD in Belle detector depends on the solenoid field profile

Machine Parameters of SuperKEKBLER HER

Emittance ex3.2(2.7) 2.4(2.3) nm

Coupling ey/ex0.40 0.35 %

Beta Function at IP x* / y

* 32 / 0.27 25 / 0.41 mm

Horizontal Beam Size sx* 10.2(10.1) 7.75(7.58) mm

Vertical Beam Size sy* 59 59 nm

Bunch Length sz6.0(4.9) 5.0(4.9) mm

Half Crossing Angle f 41.5 mrad

Beam Energy E 4 7 GeV

Beam Current I 3.60 2.62 A

Number of Bunches nb2503

Energy Loss / turn U02.15 2.50 MeV

Total Cavity Voltage Vc8.4 6.7 MV

Energy Spread sd8.14(7.96)x10-4 6.49(6.34) x10-4

Synchrotron Tune ns-0.0213 -0.0117

Momentum Compaction ap2.74x10-4 1.88x10-4

Beam-Beam Parameter xy0.0900 0.0875

Luminosity L 8x1035 cm-2s-1

(): zero current parameters

2010/Feb/08

37

http://www-kekb.kek.jp/MAC/2010/

SuperKEKB 38