Target Magnets & Shielding Bob Weggel Particle Beam Lasers, Inc. Magnet Optimization Research Engineering, LLC. March 5, 2012 1.

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Target Magnets & Shielding

Bob WeggelParticle Beam Lasers, Inc.

Magnet Optimization Research Engineering, LLC.March 5, 2012

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Isometric View of Three Target-Magnet Designs

Design IDS120h (top), IDS120i (middle) & IDS120j (bottom) [courtesy Van Graves]

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Cross Sections of Target-Magnet Designs [courtesy Van Graves]

IDS120h: I.R.’s step down gradually from 120 cm to 45 cm; minimal gaps between coils IDS120i: Large gaps between cryostats; I.R.’s = [120, 100, 80, 60] cm; gaps at [3, 9, 15] mIDS120j: 3 coils per cryostat; I.R.’s = [120, 90, 70, 50] cm; gaps at [4,10,15] m; zmax = 20 m

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Cross section of Coils & Shielding Vessels of IDS120h

Tubes & flanges: = 7.85 g/cm3; shielding = 10 g/cm3; Outer ≈ 30 tons/m; Inner ≈ 8 tons/m.

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Isometric View of Meshed Shielding Vessels of IDS120h

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Sag of Shielding Vessel vs. Length L & Wall Thickness t

O.R.max = 114 cm; I.R.min = 60 cm; γ = 7.85 g/cm3; γshielding = 10 g/cm3; tin = ½tout; ~30 tons/m.

With tout = 4 cm, tin = 2 cm & L = [6, 7, 8, 9] m, sagFEM = [1.5, 2.5, 4.1, 6.4] mm Limit L to 8 m.

1

2

5

10

5 6 7 8 9

FEM

2-cm outer wall

2.5 cm

5 cm

4 cm

3 cm

Length of support tube [m]

Sa

g o

f su

pp

ort

tu

be

with

20

0 G

Pa

Yo

un

g's

mo

du

lus

[m

m]

Sag of Coaxial-Tube Beam: 1.14-m rmax

, 0.60-m rmin

; Tubes = 7.85 g/cm3; Annulus = 10 g/cm3

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Sag of Shielding Vessel vs. Length L & Wall Thickness t

O.R.max= 58 cm; I.R. min = 16 cm; tout = 4 cm; tin = 2 cm; γ = 7.85 g/cm3; γshielding = 10 g/cm3;

~8 tons/m. When L = [6, 6½, 7, 7½, 8] m, sag = [2.0, 2.9, 4.0, 5.4, 8.0] mm Limit L to 7 m.

2

3

4

5

6

7

6.0 6.5 7.0 7.5 8.0

FEM4-cm outer wall,2-cm inner wall

Length of shielding vessel [m]

Sag o

f sh

ield

ing v

ess

el w

ith 2

00 G

Pa Y

oung's

modulu

s [m

m]

Sag of Inner Shielding Vessel of IDS120h

8

500

1000

2000

200

300

400

600

800

1200

1600

5 6 7 8 9 10 11 12 13 14 15 16

Bob Weggel 5/9/2011

10 K 9 K 8 K 7 K 6 K 5 K 4.2 K

Ambient field [T]

Nb

3S

n-s

tra

nd

no

n-c

op

pe

r cu

rre

nt

de

nsi

ty

[A/m

m2]

Field and Temperature Dependence of Current Density of Nb3Sn Strands

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Normalized Maximum Hoop Stress σ* ≡ σmax / (B1 j1 a1)

a1 ≡ I.R. of coil; a2 ≡ O.R. of coil; B1 ≡ B(r=a1), B2 ≡ B(r=a2); j1 ≡ current density

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

3.53.02.52.01.51.0

Bob Weggel 5/8/2011

Radius ratio O.D./I.D.

Fie

ld r

atio

B2/B

1

Normalized Maximum Hoop Stress * max.

/(B1 j

1 a

1)

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On-Axis Field Profile B(z)of Target Magnet IDS120j

<B(z)> = 20 T over the 75-cm length centered at z = −37.5 cm. B(z=15 m) ≈ 1.5 T.

0.5

1

2

10

5

20

-450 -300 -150 0 150 300 450 600 750 900 1050 1200 1350 1500-75

Field error

103(B)2/B

Desired fieldTotal field

SC magnet

Resistive magnet

Distance along axis [cm]

On-a

xis

field

[T]

On-Axis Field Profile of Target Magnet "IDS120j"

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-0.45

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

-450 -300 -150 0 150 300 450 600 750 900 1050 1200 1350 1500-75

r = 5 cmr = 10 cmr = 15 cmr = 20 cmr = 25 cmr = 30 cm

Distance from plane z = 0 [cm]

Rad

ial c

ompo

nent

of m

agne

tic fi

eld

[T]

Radial Component of Off-Axis Field of Target Magnet IDS120j

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-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

-450 -300 -150 0 150 300 450 600 750 900 1050 1200 1350 1500-75

5 cm10 cm15 cm20 cm25 cm30 cm

Distance from plane z = 0 [cm]

Bz(z

,r)

- B

z(z,0

) [

T]

Bz(z,r) - B

z(z,0) of Off-Axis Field of Target Magnet IDS120j

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Field Magnitude |B| ≡ (Br2+Bz

2)½ of Target Magnet IDS120j

Maximum field = 20.4 T; contours at 1.5 T and integer values from 1 T through 20 T

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Hoop Strain σhoop in Magnet of Copper Hollow Conductor

700-MPa coil banding limits σhoop in each coil to 0.35%; contour interval = 0.02%.

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σhoop in Copper & Nb3Sn Magnets (Most-Upstream Cryostat)

Maximum hoop strain in each coil is 0.35%; contour interval = 0.02%.

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σhoop in Coils of Cryostat #2 (NbTi Conductor)

Maximum hoop strain in each coil is 0.35%; contour interval = 0.02%.

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σhoop in in Coils of Cryostat #3 (NbTi Conductor)

Maximum hoop strain in each coil is 0.35%.

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σhoop in Coils of Cryostat #4 (NbTi Conductor)

Maximum hoop strain in two upstream coils = 0.35%; max.(σhoop) in downstream coil also is 0.35% if one adds an identical set of coils downstream.

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Target Magnet “DS120j5”: Optimized I.R. of Flanking Coils

I.R.’s of coils in cryostats #2-#4 are [120, 90, 116] cm, [76, 70, 75] cm & [67, 50, 67] cm.

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On-Axis Field Profile B(z)of Target Magnet IDS120j5

Maximum field error is nearly 30% less than in design IDS120j.

0.5

1

2

10

5

20

-450 -300 -150 0 150 300 450 600 750 900 1050 1200 1350 1500-75

Field error

103(B)

2/B

Desired fieldTotal field

SC magnet

Resistive magnet

Distance along axis [cm]

On-

axis

fiel

d [T

]On-Axis Field Profile of Target Magnet IDS120j5