Nano-beam Scheme
description
Transcript of Nano-beam Scheme
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
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
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2f
sz sx*
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s x*
€
s z
€
d = σ x*
φ
overlap region (≠ bunch length)
Hourglass requirementHourglass requirement
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y* ≥ σ z
overlap region = bunch length
SuperKEKB
Head-on
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y* ≥ σ x
*
φ~5 mm ~200-300 mm
Hourglass Effect for Nano-Beam
15SuperKEKB
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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
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d1 = 2σ x+
sin2φ
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d2 = 2σ x+
tan2φ
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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
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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
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y* ≥ σ x
*
φ
Nonlinear Terms around IP
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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
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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
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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
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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
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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
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○ Belle Detector 8m(W)×8m(L)×10m(H)Total weight: 1300tons 650tons (Barrel Yoke) 600tons (End Yoke) 50tons (Others)
H. Yamaoka
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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
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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
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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
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