Nano-Beam Scheme for SuperKEKB
Andrew Hutton
Slides taken from talks by
Haruyo Koiso, Yukiyoshi Ohnishi & Masafumi Tawada
Nano-beam Scheme
•
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 intrabeam scattering in LER.
Parameter Optimization
Main parameters can be quickly optimized with this panel.
Beam Parameters
KEKB
Design
KEKB Achieved
: with crab
SuperKEKB
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
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
1
2.11
53
80
xy
Luminosity
(1034 cm-2 s-1)
Colliding bunches
Belle II
New IR
e- 2.6 A
New beam pipe
& bellows
SuperKEKB
New superconducting
/permanent final focusing
quads near the IP
e+ 3.6 A
Replace long TRISTAN dipoles
with shorter ones (HER)
Add / modify RF systems
for higher beam current
Low emittance positrons
to inject
Redesign the HER arcs to
squeeze the emittance
TiN-coated beam pipe with
antechambers
Positron source
Damping ring
New positron target /
capture section
Low emittance gun
Low emittance electrons
to inject
x 40 Gain in Luminosity
Comparison of Parameters
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
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
1
2.11
80
xy
Luminosity (1034 cm-2 s-1)
SuperKEKB
6
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
I x  R
 y
L
L
S  


* 
2ere 

 y   Rxy 

If sx* = sx+* = sx-* and sy* = sy+* = sy-*,
S = 1+sy*/sx*
(aspect ratio of the beam size at IP).
Three fundamental parameters to determine the luminosity.
where
xy  
re N m
*
y
2 s
s
*
ym
*
xm
s

*
ym
Rxy 
Target Luminosity is 8x1035 cm-2s-1 in SuperKEKB.

SuperKEKB
8
Beam-Beam Parameter
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
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
1
2.11
80
xy
Luminosity (1034 cm-2 s-1)
SuperKEKB
9
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.
W-S
W-S
L = 8x1035
LER
LER
SuperKEKB
11
Vertical Beta Function at IP
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
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
1
2.11
80
xy
Luminosity (1034 cm-2 s-1)
SuperKEKB
12
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
Natural chromaticity LER: xx/xy = -104/-789
HER: xx/xy = -187/-853
SuperKEKB
KEKB
LER: xx/xy = -72/-123
HER: xx/xy = -70/-124
13
Collision Scheme
High Current Scheme
s
Nano-Beam Scheme
sz
*
x
sx*
d
2f
sz
Half crossing angle: f
Head-on
overlap region = bunch length
overlap region (≠ bunch length)
s *x
d
f
Hourglass requirement
  sz
*
y
Hourglass requirement
~5 mm

SuperKEKB
*
s
 y*  x
f
~200-300 mm
14
Hourglass Effect for Nano-Beam
 y*
LER waist
e-
e+
2s x 
d1 
sin 2f
2f 
d1
d2
2sx-
2s
d2   x 
tan 2f
2sx+
There are two kinds of
hourglass requirements.
With crab-waist, this term is zero
Hourglass (H.G)
requirement without crab-waist:

 2s x  2s x 
  max 
,

sin 2f tan 2f 
*
y
 2s x 2s x  
  max 
,

sin 2f tan 2f 
*
y
SuperKEKB
15
Beta Function at IP
• Machine parameters are chosen to be insensitive to
the HG effect.
• The vertical beta function:
 2s x  2s x 
  410  max 
,
 max 244,186 mm
sin 2f tan 2f 
*
y

*
y
 2s x 2s x  
 270  max 
,
 max 187,243 mm
sin 2f tan 2f 
• The vertical beta functions in both rings satisfy the HG
requirement.

• To squeeze y*, low emittance and low x* are needed.
*
s
 y*  x
f
SuperKEKB
16
Nonlinear Terms around IP
K
y
*2
Jy 0 
 2 * 2  *
1 KL L
 3

A(my )
L*
Phys. Rev. E47, 2010 (1993)
KEKB
L
LER
KEKB
R
SuperKEKB
L
SuperKEKB
R
y*
(mm)
K
(1/m2)
-1.777
-1.778
-4.425
-6.003
L*
(m)
1.332
1.762
0.7269
0.7680
Jy0 / A
(mm)
8.425
4.221
0.03919
0.02825
5.9
0.27
Beam Current
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
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
1
2.11
80
xy
Luminosity (1034 cm-2 s-1)
SuperKEKB
18
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.
Luminosity gain is 1(xy) x 20(1/y*) x 2(I) = 40 times of KEKB.
Then, we get 8x1035 cm-2s-1
SuperKEKB
19
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
c 
1
ex 
2
Jx 20
2
s
*
y 
f
*
x
 Hds
Bend
x:dispersion)
H   xx  2 xx'x x'x
2
• Redesign of arc cells to make low emittance

– 2.5  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.
SuperKEKB
21
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
Crossing angle = LER angle + HER angle = 83 mrad
proportional to q4
Solenoid axis
= angle bisector
Energy ratio
4/(4+7)
We choose 41.5 mrad and the contribution of solenoid fringe is ~4 pm.
SuperKEKB
24
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
Head-on Frame
narrow and long bunch
with large crossing angle
˜z
2s
2s *x


˜  fsz
s

s*x
˜z 
s
f
*
x
short bunch with head-on
= 2s˜
2s z
*
x
f
L
n b N xy  
xy  
˜z
2s
y*
re
Nm
2  fs z
y*

ey
Y. Ohnishi / KEK
26
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 RFgun are considered.
Y. Ohnishi / KEK
27
IR design
LER
QC2LP
Horz. F
PM
QC2RE
Horz. F
PM
HER
QC1RE
Vert. f
QC1LP
Vert. f
41.5 mrad
Detector solenoid axis
IP
QC2LE
Horz. F
PM
41.5 mrad
QC1RP
Vert. f
QC1LE
Vert. f
QC2RP
Horz. F
LER and HER beam are focused by separated quadrupole doublet, respectively
2010.2.15
SuperKEKB
28
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
•
•
2010.2.15
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
SuperKEKB
29
IR design with PM version
Anti solenoid-R
QC2LP
PM
QC1LE
+corr. coil
Cryostat
Cryostat
QC1RE
+corr coil
IP
QC2LE
PM
2010.2.15
QC1LP
+corr. coil
QC1RP
+corr. coil
Anti solenoid-L
SuperKEKB
N. Ohuchi
QC2RE
PM
QC2RP
+corr. coil
QC1RE
30
The magnet design of QC1R/L-P
N. Ohuchi
Vac ch ID 20mm
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 Beam envelop
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
Coolant path
SC correctors:
Normal Octupole
Skew
Quadrupole
Normal Dipole
Skew Dipole
Cross section of QC1
RP1.123
SC correctors:
Normal Sextupole
Normal
Quadrupole
Normal Dipole
1.013
0.93
7.0
3.9
Designed new SC
cable for main
quadrupole
2.5
Leakage fields are canceled by the correction
windings on the other beam pipe
1.057
KEKB
QCS
0.967
S-KEKB
H-Current
0.9
S-KEKB
NanoBeam
31
○ Belle Detector
8m(W)×8m(L)×10m(H)
Total weight: 1300tons
650tons (Barrel Yoke)
600tons (End Yoke)
50tons (Others)
H. Yamaoka
32
2010.2.15
15th KEKB Review
32
Anti solenoid
H. Koiso
Vertical emittance degradation depends on the anti-solenoid field profile
Anti-solenoid Ver.2
HER:53mrad
ey
B
z

2010.2.15
SuperKEKB
33
IR vacuum chamber
K. Kanazawa
Positron
• 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
2010.2.15
SuperKEKB
34
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
QC1LP
QC1RP
QC1LE
QC1RE
QC2LP
QC2RP
QC2LE
QC2RE
Physical 20
Aperture
(mm)
20
30
30
60
60
70
70
Required 11.2
Aperture
(Horz.)(
mm)
10.0
16.4
17.2
25.6
28.4
47.6
48.4
Vert.
(mm)
14.8
18.2
18.2
9.4
9.6
15.4
10.6
2010.2.15
15.8
SuperKEKB
35
A. Morita
COD (Belle)
COD in Belle detector depends on the solenoid field profile
COD(LER 41.5 mrad)
COD(HER 41.5 mrad)
100um
200um
4mm
QC2LE
IP
QC1LE
SuperKEKB
QC1RE
QC2RE
QC2LP
QC1LP
QC1RP
QC2RP
2010.2.15
IP
1mm
36
Machine Parameters of SuperKEKB
(): zero current parameters
LER
HER
2010/Feb/08
Emittance
ex
3.2(2.7)
2.4(2.3)
nm
Coupling
ey/ex
0.40
0.35
%
x* / y*
32 / 0.27
25 / 0.41
mm
Horizontal Beam Size
s x*
10.2(10.1)
7.75(7.58)
mm
Vertical Beam Size
sy*
59
59
nm
Bunch Length
sz
6.0(4.9)
5.0(4.9)
mm
Half Crossing Angle
f
Beam Energy
E
4
7
GeV
Beam Current
I
3.60
2.62
A
Beta Function at IP
41.5
mrad
Number of Bunches
nb
2503
Energy Loss / turn
U0
2.15
2.50
MeV
Total Cavity Voltage
Vc
8.4
6.7
MV
Energy Spread
sd
8.14(7.96)x10-4
6.49(6.34) x10-4
Synchrotron Tune
ns
-0.0213
-0.0117
Momentum Compaction
p
2.74x10-4
1.88x10-4
Beam-Beam Parameter
xy
0.0900
0.0875
Luminosity
L
8x1035
cm-2s-1
37
http://www-kekb.kek.jp/MAC/2010/
SuperKEKB
38