Design of New IR Quads(The 1st consideration for the updated IR)

Norihito Ohuchi, Masafumi Tawada

2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

1SuperKEKB IR Design
QC1RE
Vert. f

QC2LP
Horz. fPositrons
Off axis of QCSLD
S-L
Detector solenoid axis

Electrons
Off axis of QCSRD
Vert. fS-R

IP
30mradQCSLFE
Horz. f
QC1LE
Vert. fQC2LE
Horz. f2009/2/9‐11

QC2RE
Horz. fElectrons
Off axis of the solenoid
On axis of QCSLD
Vert. fIP chamber axis

Positrons
Off axis of the solenoid
Off axis of QCSRDVert. f

QC2RP
Horz. f

QCS[L,R]D are overlapped with anti-solenoids

SuperKEKB‐MAC (Ohuchi Tawada)

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IR Beam Envelops based on the beam optics by Koiso
HER
QC2REH
17.49 T/m, 10.49 T

QC1RES
15.87 T/m, 12.69 T

QCSRD
36.38 T/m, 12.11 T

QCSLD
53.01 T/m, 23.33 T

QCSLF
44.34 T/m, 23.06 T

QC1LES
34.79 T/m, 22.27 T

QC2LEH
5.13 T/m, 10.26 T

LER
QC2RP
3.06 T/m, 3.10 T

QCSRD
36.38 T/m, 12.11 T

QCSLD
53.01 T/m, 23.33 T

QC2LP
The space for the magnet design is defined by the area of 5 σ of beam size + 5 mm
for the design margin of beam pipe + 3mm thickness of beam pipe.
2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

10.58 T/m, 6.49 T

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Final focus quadrupole (QCSRD and QCSLD)• QCSRD
Design parameters of QCSRD••••

6 layer coils (3‐double pane cake coils)
Inner coil radius : 90.0 mm
Outer coil radius : 116.8 mm
Cable size : 1.1 mm × 4.1 mm•Number of turns : 271 in one pole

¾ 1.1 mm × 7.0 mm (KEKB)

1st layer = 38, 2nd layer = 39
3rd layer = 46, 4th layer = 47
5th layer = 50, 6th layer = 51••••••••

Field gradient : 40.49 T/mMagnet current : 1197.6 A
Magnetic length : 0.299m
Inductance : 69.98 mH
Stored energy : 49.3 kJ
Operation temperature : 4.5 K
Operation point w.r.t. SC limit : 76%
Magnet bore : room temp.

Cross section of QCSRD
2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

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QCSRD R&D Magnet and Cryostat Design
The R&D magnet was successfullyenergized over the design currentwithout quench.

QCSR(QCSR center from IP = 1.163 m)
KEKB=1.92 m

IP
The cryostats were designed with keeping theKEKB boundary conditions with Belle detector.
2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

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QCSLD cooled at 1.9 K
Design parameters ofQCSLD
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6 layer coils
Inner coil radius : 67.5 mm
Outer coil radius : 92.7 mm
Cable size : 1.1 mm × 4.1 mm– Cu ratio = 1.3
Number of turns : 208 in one pole
1st layer = 29, 2nd layer = 31
3rd layer = 35, 4th layer = 37
5th layer = 37, 6th layer = 39•
••
•
•
•

G by 2D cross section : 121.1 T/m
Magnet current : 2834.8 A
Magnetic length : 192.6 mm
Estimated physical magnet length: 435 mm
Operation temperature : 1.9 K
Max. field in the magnet : 7.62 T–

S.C. correctors••(without Belle and compensation solenoidfields)

Operation point w.r.t. SC limit : 74%
Magnet bore : room temp.

Cross section of magnet cryostat
2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

6Cable performance at 1.9 K for QCSLD
NbTi
NbTi cable for QCSRD
I c = 3495 A @ 5T and 4.2 K
Cu ratio = 1.8
Cable size = 1.1 mm × 4.1 mm

By decreasing temperature from
4.2 K to 1.9 K
The conductor can transfer thecurrent of 0.9 × Ic @ 5T and 4.2 K

I c = 3145.5 A @ 8T and 1.9 K
From LHC‐Project Report 358

2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

Cu ratio = 1.3
I c = 4253 A @ 8T and 1.9 K
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QCSLD cryostat

IPSLQCSLDConnection area of flanges between QCSbeam pipe and IP beam pipe
The connection between the QCS beam pipe and the IP beam pipe are very difficult.
•In the left side of IP, the QCS cryostat is considered to be inserted into Belle detector withconnecting to IP beam pipe and holding SVD and the beam pipe.

•The QCS cryostat bore works as the beam pipe (warm bore).

2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

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QCSLF (Permanent magnet)
Distances between two beams are assumed to be 29.85mm (IP side), 58.2mm(Arc side).

••

Magnet bore= 23 mm
Outer radius of the magnet– IP side = 35 mm, magnet center = 50 mm, Arc side = 65 mm– Total magnet length = 520 mm

2009/2/9‐11

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Magnetic Design of QCSLF
R32HS (SmCo) by Shin‐Etsu chemical Co., Ltd is used for the field calculation of QCSLF.
• Br = 1.13 T

SLAC used the material of
R26HS for the final focus
quadrupole of PEPII.

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SuperKEKB‐MAC (Ohuchi Tawada)

10Field calculation of QCSLF
At the magnet center••

Rin = 23mm, Rout = 50mm
Field gradient = 48.61 T/m

IP side••Rin = 23mm, Rout = 35 mm
Field gradient = 30.61 T/m

Arc side• Rin = 23mm, Rout = 65 mm• Field gradient = 58.15 T/mAverage = 45.79 T/mRequirement of QCSLF from beam optics•

2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

44.34 T/m, 23.06 T11

QC1RE, QC2RE & QC2RP• The magnets are designed by the S.C. wiring technique.
• The magnets are in shape of a circular truncated cone in order not to be
exposed to the SR light from QCSRD.

R&D of winding of S.C. wireon the QC1RE bobbin inshape of the circulartruncated cone.
Diameter of S.C. wire = 0.781ｍｍ

2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

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QC1RE magnet design
QC1RE design parameters•••

Average field gradient = 12T/m
Effective magnetic length = 0.75m
Inner radius of beam pipe bore = 51mm–••

Inner radius of LHe vessel bore =60mm
Coil(Circular Truncated Cone )
––––

•
•

Beam pipe temperature=80K

2 layer coils by S.C. wire
Rin of the coil=65mm (IP side)
Rin of the coil＝73.6mm (magnet center)
Turns/pole＝34

Outer radius of Iron Yoke = 170mm
Required field gradient at IP side
–GIP= 12×（73.6/65）2＝15.39T/m

Cross section design of QC1RE at IP side
The cryostat bore functions as a beam pipe, andit is cooled at 80 K by LN2.
2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

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QC1RE magnetic field calculation

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2009/2/9‐11

Design current of the magnet = 384.7 A
Field gradient = 15.39 T/mCurrent density of S.C. wire = 733.8 A/mm2– Cu/NbTi = 1.4, current density at NbTi = 1761.2 A/mm2
Maximum field in the coil =1.432T
Leak field at the positron area ＜0.2Gauss
SuperKEKB‐MAC (Ohuchi Tawada)

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QC2RE & QC2RP magnet design
QC2RE design parameters•••••

Average field gradient = 8.8 T/m
Effective magnetic length = 0.8 m
Inner radius of beam pipe bore = 85 mm (T=80K)
Inner radius of LHe vessel bore =95 mm
Coil (Circular Truncated Cone )
––––

QC2RE

QC2RP

••

2 layer coils by S.C. wire
Rin of the coil=100 mm (IP side)
Rin of the coil＝106.5 mm (magnet center)
Turns/pole＝ 52× 2

Outer radius of Iron Yoke = 240mm
Required field gradient at IP side–GIP= 8.8×（106.5/100）2＝9.98T/m

QC2RP design parameters•••••

Cross section design of QC2RE and QC2RPat IP side. The cryostat bores function as beampipes, and they are cooled at 80 K by LN2.
2009/2/9‐11

Average field gradient = 3.4 T/m
Effective magnetic length = 1.0 m
Inner radius of beam pipe bore = 67 mm (T=80K)
Inner radius of LHe vessel bore =75 mm
Coil (Circular Truncated Cone )––––•1 layer coil by S.C. wire
Rin of the coil=80 mm (IP side)
Rin of the coil＝85 mm (magnet center)Turns/pole＝ 42

Required field gradient at IP side–

SuperKEKB‐MAC (Ohuchi Tawada)

GIP= 3.4 ×（85/80）2＝3.86T/m
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QC2RE & QC2RP magnetic field calculation

QC2RE• Design magnet current = 377.5 A• Field gradient = 9.98 T/m• Current density of S.C. wire = 720.1 A/mm2–•QC2RP• Design magnet current = 227.2 A• Field gradient = 3.86 T/m• Current density of S.C. wire = 433.4 A/mm2

Cu/NbTi = 1.4, current density at NbTi =1728.2 A/mm2

Maximum field in the coil =1.453T
2009/2/9‐11–•

Cu/NbTi = 1.4, current density at NbTi =1040.1 A/mm2

Maximum field in the coil =0.425 T

SuperKEKB‐MAC (Ohuchi Tawada)

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Operation condition for QC1RE, QC2RP, QC2RE

Operation temperature= 4.5 K

2009/2/9‐11

SuperKEKB‐MAC (Ohuchi Tawada)

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QC1LE & QC2LP (preliminary calculation)
QC1LE [34.79 T/m, 22.27 T]
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Coil inner radius = 45 mm
Coil outer radius = 49 mm
Iron Yoke inner radius = 59 mm
Current density in the coil = 421.5 A/mm2– Cu ratio = 1.5; J = 1054 A/mm2
G = 34.8 T/mMagnetic field in the coil = 1.6 T

QC2LP [10.58 T/m, 6.49 T]••••

Coil inner radius = 66 mm
Coil outer radius = 67 mm
Iron Yoke inner radius = 69 mm
Magnet parameters close to QC1RE

Magnet cross section

2009/2/9‐11

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Summary• For the updated IR beam optics, various types ofquadrupoles are designed including the permanent
magnet for QC1LE.
• QCSLD is designed to be operated at 1.9K, and themagnetic calculation with the compensation solenoid
is necessary in order to confirm the operation margin.
• The circular truncated cone shape quadrupoles areproposed for QC1RE, QC2RE and QC2RP.
• These magnets need R&D in order to confirm theelectric and magnetic performances.
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