SuperKEKB IR Over View and
SC Magnets(The 16th KEKB Accelerator Review Committee)

Norihito Ohuchi

2011/02/08

SuperKEKB‐MAC (2011)1

Outline
1. IR overview
2. IR SC magnets– SC quadrupoles, correctors– Leak field cancel coils– Compensation solenoids

3. Cryostat and support mechanism
4. Construction schedule

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SuperKEKB‐MAC (2011)2

1. IR overview(Status of IR design)• Beam optics– Touschek Lifetime: LER=410 sec, HER=511 sec• LER/HER lifetimes are expected to be 577 sec/724 sec by improving the cancellation ofleak field by QC1E/P.

– Beam sizes of both beam lines are re‐defined for designing the hardware.
• Beam pipe and some SC coils have been re‐designed.
• Beam background noise is being studied with the new pipe design.

• IR magnet design– All magnets and correctors are designed to be superconducting.
– Iteration of design work of SC magnets is in progress by the requirement of thebeam optics.

• Cryostat and support design– The QCS cryostats and supports in the 1st version have been designed.
– The vibration analysis was performed for these designed cryostats and supports.

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SuperKEKB‐MAC (2011)3

IR SC magnets, cryostat and Belle

IP

HER

Beam crossing angle=83mrad

LER

8 SC main qadrupoles (QC1RP, QC1RE, QC2RP, QC2RE, QC1LP, QC1LE, QC2LP, QC2LE)
2 SC compensation solenoids
52 SC correction coils
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SuperKEKB‐MAC (2011)4

IR magnets
QC2LP

QC2RE

QC1RE

QC1LP

QC1RP
QC2LE

IRON IRON

QC1LE

QC2RP

IRON

Integral field gradient(T/m)・mPositionfrom IPmm

Magnet type

Corrector

QC2RE

12.91

2925

S.C. + Iron Yokea1, b1, a2, b4

QC2RP

10.92 [31.21T/m×0.350m]

1956

S.C.

a1, b1, a2, b4

b3, b4, b5, b6

QC1RE

26.22 [79.03×0.360]

1410

S.C.

a1, b1, a2, b4

b3, b4, b5, b6

QC1RP

22.43 [66.52×0.3372]

932

S.C.

a1, b1, a2, b4

b3, b4, b5, b6

QC1LP

22.91 [67.94×0.3372]

‐932

S.C.

a1, b1, a2, b4

b3, b4, b5, b6

QC1LE

26.03 [82.75×0.360]

‐1410

S.C.

a1, b1, a2, b4

b3, b4, b5, b6

QC2LP

10.96

‐1930

S.C. + Iron Yokea1, b1, a2, b4

QC2LE

14.13

‐2700

S.C. + Iron Yokea1, b1, a2, b4

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SuperKEKB‐MAC (2011)

Leak field cancel
coil

5No Aperture limit
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SuperKEKB‐MAC (2011)

737.8
6

Requirement on beam pipe from beam size
LER

NX=26 (Touschek Lifetime=737.8 s)
NX=17

QC1RE leak fieldcancel coil

Horizontal

HER

Vertical

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SuperKEKB‐MAC (2011)7

2. IR SC magnets
Design of QC1P
QC1P
e+
e‐

SC correctors
a2, b1, a1, b4
QC1P magnet design (QC1RP, QC1LP)
•

•
•
•
•
•

Same cross section and longitudinal design for
QC1RP and QC1LP
2 layer coils [double pancake]
Designed SC cable––

SC cancel correctors
b3, b4, b5, b6
SC cancel coils against the leak field from QC1P
• b5, b6, b4 , b3 from the inside• Cryostat inner bore radius=18.0 mm• Beam pipe(warm tube)

Cable size : 2.5 mm in height, and 0.93 mm in width
SC strand cable : φ 0.5 mm, 10 wires in the cable–inner radius=10.5 mm, outer radius=14.5 mm

SC correctors inside of the magnet bore–

a2, b1, a1, b4 from the inside, single layer coil

Cryostat inner bore radius=18.0 mm
Beam pipe (warm tube)– inner radius=10.5 mm, outer radius=14.5 mm
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SuperKEKB‐MAC (2011)8

QC1RP, QC1LP Magnet Parameters
QC1RP

QC1LP

Coil inner radius, mm

25.00

Coil outer radius, mm

30.485

Turns in one pole

12 (1st layer), 13 (2nd layer)

Spec. of integral field, T

22.43

22.91

Field gradient, T/m

66.52

67.94

Effective magnetic length, m

0.3372Magnet current, A

1575.58

1609.30

Current density of the cable (SC area), A/mm2

1685.01721.0Current density of the cable (overall), A/mm2

802.4

819.6

Magnetic field by Belle and comp. sol., T

3.0

3.2

Max. field in the coil without solenoid field, T

2.28

2.28

Max. field in the coil with solenoid field, T

3.79

3.93

Operating point with respect to Bc at 4.7 K

76%

79%

Magnet physical length, mm

416

Error field at r=1 cm (2D calculation)b6 = 2.55 × 10‐5b10 = ‐2.04 × 10‐6
b14 = 6.07 × 10‐7Error field at r=1 cm (3D calculation)b6 = 1.96 × 10‐6b10 = 3.93 × 10‐6

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9

QC1RP, QC1LP SC corrector coils
b4

a2

b1

a1

Coil inner radius, mm

23.4

21.3

22.0

22.7

Coil outer radius, mm

24.1

22.0

22.7

23.4

Turns on one pole

8

16

31

31

Design current, A

50

50

50

50

3398 T/m3

2.284 T/m

0.045 T

0.043 T

Bias magnetic field by QC1R/LP and Solenoids, T

3.59

3.53

3.55

3.57

Operating point with respect to Jc at 4.7 K< 65 %< 65 %< 65 %< 65 %

Capacity for magnetic alignment for QC1RP at R= 1 cm

NA

± 17.17 mrad

± 0.676 mm± 0.646 mm

Capacity for magnetic alignment for QC1LP at R= 1 cm

NA

± 16.81 mrad

± 0.662 mm± 0.633 mm

Magnetic field at R=1cm

SC octupole coil (R&D coil) for QC1RPSC Corrector Coil Operation Points

Direct winding method
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SuperKEKB‐MAC (2011)10

Design of QC1E
QC1E

SC cancel correctors
b3, b4, b5, b6

SC correctors
a2, b1, a1, b4
SC cancel coils against the leak field from QC1E
• b5, b6, b4 , b3 from the inside• Cryostat inner bore radius=30.5 mm• Beam pipe(warm tube)–

inner radius=22.0 mm, outer radius=26.0 mm

QC1E magnet design (QC1RE, QC1LE)
•

•
•
•

Same cross section and longitudinal design for QC1RE
and QC1LE
4 layer coils [double pancake]
Cryostat inner bore radius=25.0 mm
Beam pipe (warm tube)–••
2011/02/08

inner radius=17.0 mm, outer radius=21.0 mm

GR = 79.03 T/m at Iop=1242.1 A, Iop/Ic= 72.7 %GL = 82.75 T/m at Iop=1300.6 A, Iop/Ic= 75.8 %SuperKEKB‐MAC (2011)11

Cancel coils for the leak field of QC1P/E and QC2RP•••

The leak field profiles along the opposite lines are calculated.
The leak magnetic fields of the main quadrupoles on the opposite beams are designed to becanceled with the SC correctors of b3, b4, b5 and b6.
B1 and B2 components in the leak field are not canceled, and they are included in the optics
calculation.
–

B2 component is used for focusing and defocusing e‐/e+ beams.

QC1RP leak field profile along the e‐ beam line

2011/02/08

QC1RE leak field profile along the e+ beam line

SuperKEKB‐MAC (2011)12

Design of SC cancel coils
QC1RE leak field cancel sextupole coil
Coil parameters•
Double pancake coil•
Turn/pole = 44•
Inner radius = 38.4 mm•
Outer radius = 39.8 mm•
Coil current = 53.0 A•
SC wire= φ 0.4mm–

B3

Jc > 85 A @5T, 4.2 K

Old design of sextupole coil

B9

Improvement
1.

Improved B9 profile
Integral B9 is 8% of the old model.

2011/02/08

SuperKEKB‐MAC (2011)

Change of location in the coil package–
Rin = 21.2 mm→ Rin = 38.4 mm
2. Modification of 2D cross section
design of the sextupole coil–B9 < 013

Leak field by SC cancel coils
In the 15th KEKB Accelerator Committee, the followings
were pointed:••

The cancel coils produce the leak fields in the quadrupole
bore.
These leak fields should be studied carefully.

In the first design of the coil package, the b1, b3 and b4
coils were designed for cancelling.

Dipole coil

Sextupole coil

Octupole coilb3, b4, b5 and b6 coils are selected for cancelling the quadrupole leak field.
2011/02/08

SuperKEKB‐MAC (2011)14

QC1RE leak field profile and cancellation along LER beam line
No cancellation of dipole and quadrupole fields
B3

Calculation by M. Iwasaki
B5

B4

x10-3

Leak field (T)After cancellation

Corrector field
Leak field
Distance from IP (m)B6 x10-3

B9

B9 (OLD)

x10-3

x10-3

After cancellation
Leak field
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SuperKEKB‐MAC (2011)15

Parameters of cancel coils for QC1RE leak field(2D cross section)
b5

b6

b4

b3

Coil inner radius, mm

34.2

35.6

37.0

38.4

Coil outer radius, mm

35.6

37.0

38.4

39.8

Turns /pole

21

10

28

8

Design current, A

12.17

12.17

30.42

52.35

Magnetic field @R=1.5 cm, Gauss

8.24

1.66

37.8

157.0

Bias magnetic field by Solenoids, T

0.5

0.5

0.5

0.5

< 50 %< 50 %< 50 %< 50 %

Operating point with respect to Jc at 4.7 K

Cancelling QC1P and QC2RP leak fields for HER beam••

Coil design works are now in progress.
For QC1P:–––•

Sextupole coil design was completed.
Integral octupole field is canceled, but local field is not canceled. → The coil should be redesigned for cancelling the local field.
Decapole and dodecapole coils are not designed at present. → These coils will be designed.

For QC2RP:––

2011/02/08

Integral sextupole and octupole fields are canceled, but local field is not canceled. → These
coils should be re-designed for cancelling the local field.
Decapole and dodecapole coils are not designed at present. → These coils will be designed.
SuperKEKB‐MAC (2011)

16

QC2
• QC2RP– Design concept of magnet as same as QC1RP. SC quadrupole without iron yoke.
– Magnetic designs of the quadrupole and the correctors were completed.
– Cancelling coils of QC2RP leak field: b3, b4, b5 and b6.
– In the optics calculation, the field profile and the leak field are included.

• QC2RE, QC2LP, QC2LE– SC quadrupole with iron yoke.
– Leak fields on the opposite beam line are negligible.
• No cancelling coils.

– Correctors of a1, b1, a2 and b4 are assembled in the qudrupole bore.
– Calculation of quadrupoles are in progress.
• 3D calculation of quadrupoles with iron yoke
• Mutual Influence between Belle and compensation solenoid fields and the iron yoke.

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SuperKEKB‐MAC (2011)17

Magnetic field calculation of QC2LP

Calculation by M. Tawada

QC2LP
I=1170A
1. No iron yoke
G=26.3 T/m
2. With iron yoke
G=36.0 T/m
Leak field along e‐ beam line<1 Gauss

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SuperKEKB‐MAC (2011)18

Compensation solenoids

V.9
Calculation
by M. Tawada•

Compensation solenoids••

Compensation solenoids are designed to contain QC1, QC2RP, correctors and cancel coils in the solenoid bores.
Solenoids are divided into small coils to produce the field profiles to make the Vertical Emittance within the
optics requirement.
–•

HER = 4.0 pm, LER = 2.0 pm

Electro‐magnetic forces （Fz）––

ESR = 39.6 kN、QC2RE = ‐12.9 kN → Total＝26.7 kN
ESL =‐21.3 kN、QC2LP = 13.6 kN → Total ＝－7.7 kN

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Solenoid field profile and magnet parameters
Front coil of ESL

Bmax=4.34 T

Front coil of ESR

Bmax=3.5 T

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SuperKEKB‐MAC (2011)

ESR

ESL

Current

411.7 A

382.2 ASC cable

1.63mm (W)× 0.67mm(H)Cu ratio＝1.0

Current density( SC area)

754.0 A/mm2

700.0 A/mm2

Current density( in the cable)

377.0 A/mm2

350.0 A/mm2

Maximum fieldin the coil

3.50 T

4.34 T

Operating pointwith respect to Jc
at 4.7 K

68 %

75 %

20

3. Cryostat and support mechanism• The problem that need to be overcome：vibration of cryostat andsupport• The front positions of SuperKEKB QCS cryostats are almost same as
the KEKB cryostats– Front positions from IP and lengths of cryostats• KEKB：QCSR＝ 765mm [1850mm], QCSL＝ 580mm [1720mm]• Super KEKB：QCSR＝ 633.5mm [2884mm], QCSL＝ 627mm [2534mm]– EMF• KEKB：QCSR＝ 2.8 kN 、QCSL＝22 kN• Super KEKB：QCSR＝ 26.7 kN、QCSL＝7.7 kN• Understanding the mechanical characteristics of KEKB‐QCS cryostat
and support mechanism– Vibration measurement of the KEKB QCS cryostats and supports– Mechanical analysis by ANSYS• Comparison of calculation and measurement of KEKB QCS cryostats and supports• Vibration study of SuperKEKB QCS cryostats and supports

2011/02/08

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SuperKEKB‐MAC (2011)22

Mechanical analysis of KEKB cryostat and support
Calculationby H. Yamaoka

Measured integrated amplitude of vibration
QCS-R: 0.11 μm (>1Hz), 0.085 μm (>10Hz)
QCS-L : 0.11 μm (>1Hz), 0.055 μm (>10Hz)

Measurement
by M. Masuzawa
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SuperKEKB‐MAC (2011)23

Vibration analysis of KEKB QCS cryostat
QCS-s
14Hz

Coil-s17Hz
21Hz

Coil-tQCS-t

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Calculation model of SuperKEKB cryostats
FEM model

Coil:260kg

Coil:280kg

Fixed

Fixed

Left-side
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Right-side25

Vibration analysis of SuperKEKB cryostats
QCS-L

QCS-R
Input mode is sameas KEKB cryostat.

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SuperKEKB‐MAC (2011)26

Summary of vibration analysis
SuperKEKB QCSLeftKEKB QCS
Right

Right

> 1Hz

> 10Hz> 1Hz> 10Hz> 1Hz> 10HzHori. transverse

87

80

107

100

119

112

Hori. axial

37

9

37

8

40

11

Vertical

87

28

90

33

151

120

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SuperKEKB‐MAC (2011)27

Static mechanical analysis
KEKB QCS-R cryostat

SuperKEKB QCS-L/R cryostats
QCS-L

2.0 mm: Sag by the cryostat’s own weight
0.1 mm: Sag

QCS-R
0.8 mm: Lifting the cryostat’s head by theaxial force of 30 kN.
This axial force corresponds to the EMF
acting on the compensation solenoid.
0.3 mm: Sag
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SuperKEKB‐MAC (2011)28

IR magnet construction schedule

Field measurementson beam lines
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Summary• Beam optics (Touschek Lifetime)– The leak field by QC1P/E and the field performance of B3 cancelling coil are improved.
• LER/HER lifetimes are expected to be 577 / 724 sec, respectively.
• Optics calculation will be performed soon.

• SC magnet design– The magnetic designs of QC1E/P and QC2RP [no iron yoke] are almost completed.
• Need to complete the designs of cancelling coils for the leak fields and correctors.

– The magnetic designs of QC2LP and QC2R/LE [with iron yoke] are ongoingly pushed
through.
• Influence of the iron yokes on the field profile along the beam line.

• Cryostat and support mechanism design– Mechanical analysis of KEKB and SuperKEKB cryostats and supports have been
performed.
• Vibration of the cryostats is able to be reduced within an acceptable value.
• The calculation model will be brushed up by comparing the measured data of the KEKB cryostat.

– Vibration study will be performed by using the KEKB QCS cryostat.
• High vibration damping material for the support component. [MnCuNiFe Alloy]
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Back‐up

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Leak field from QC1RP
Leak field (T)2‐pole field (Normal)

No cancelation of B1 and B2

4‐poleLeak field

Distance from IP (m)6‐pole8‐poleLeak field
Corrector field

After cancellation
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SuperKEKB‐MAC (2011)32

Leak field from QC2RP
Leak field (T)2‐pole field (Normal)

No cancelation of B1 and B2

4‐poleLeak field

Distance from IP (m)6‐pole8‐poleLeak field
Corrector field

After cancellation
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33

QC1RP R&D
Development of small cross section SC Rutherford cable
Keystone angle needs
to be 2.6 degree

2.5mm

Cable Performance (Ic @5T, 4.2K)
before cabling：320A
after cabling (A=1.5 deg.)：297A
after cabling (B=2.0 deg.)：307A
after cabling (C=2.6 deg.)：305A
Average =303A (94.7%)

SC cable for
QC1,2 : possible
for production

Cross section of cable C (2.6 deg.)
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SuperKEKB‐MAC (2011)34

QC1RP R&D magnet

•
•
•
•
•

QC1RP R&D magnet components： completed.
Production of small cross section SC cable：completed.
Coil winding machine and cable tensioning device: being tuned for winding coil
Production of SC coils will start from April.
Cold test is scheduled at June.
– The R&D magnet will contain the corrector coils in the magnet bore.
2011/02/08

SuperKEKB‐MAC (2011)35