MCBX DesignFirst approaches

J. García, F. Toral, J. Munilla – CIEMAT

MCBX Requirements. Strand & Cable. Different approaches to shorten magnet length

◦ 18 vs 36 strands alternative Cable.◦ Coil ends: First Tests with 18 strands.◦ One vs Two layers at each coil.

Mechanical Issues◦ Torque analytical expression and estimated stress◦ First 2D FEA analysis

Manufacturing options Open issues

Index

Combined Dipole (Operation in X-Y plane) Aperture diameter = 150 mm Integrated field = 2.5 Tm Working temperature = 1.9 K Magnetic length ≅ 1.2 m Working Point = 65% Field Quality = Multipoles below 10 units.

Desirable features:◦ Larger operational field (up to 3T).◦ Shorter coil ends

MCBX Requirements

Strand & Cable

Strand parameters

Cu:Sc 1.75 -

Strand diameter 0.48 mm

Metal section 0.181 mm2

Nº of filaments 2300 -

Filament diam. 6.0 µm

I(5T,4.2K) 203* A

Jc 3085* A/mm2

Cable Parameters

No of strands 18 -

Metal area 3.257 mm2

Cable thickness 0.845 mm

Cable width 4.370 mm

Cable area 3.692 mm2

Metal fraction 0.882

Key-stone angle 0.67 deg

Inner Thickness 0.819 mm

Outer Thickness 0.870 mm* Extracted from strand March -09Waiting for better estimates from Amalia

275 km SC-strand in stock at CERN Polyimide Insulation: 2 x 25µm + 55 µm (in stock at CERN)

At these approaches:

Inner and Outer Coil (IC&OC) were optimized for a good field quality without iron (few units).

Iron Yoke◦ 4 Holes of Ø90mm at 190mm from the center◦ Outer diameter = 540mm

Different approaches to shorten magnet length

1- A 36 strand alternative cable was considered◦ No optimization (same block design than in the 18 strand case

was used, only for comparative analysis)◦ CABLE04 from Roxie repository:

Same strand. Known geometry and properties.

2- Coil ends: First 3-D models evaluated in order to consider the possibility of shorter coil ends.

3– One vs Two layers for each coil: In order to increase field and additionally decrease current.

Different approaches to shorten magnet length

1- 18 vs 36 strands comparative

Inner coil (IC) & Outer Coil (OC) parameters

Units 18 Strands 36 Strands

Nominal field 100% (B1,IC) T 2.13 2.73

Nominal field 10% (B1,IC) T 0.214 0.2805

Nominal field 100% (A1,OC) T 2.11 2.71

Nominal field 10% (A1,OC) T 0.212 0.284

Nominal current (IC) A 2450 3400

Nominal current OC) A 2150 3100

Working point % 60% 60%

Torque (IC) Nm/m -9.16∙104 -1.684∙105

Torque (OC) Nm/m 9.02∙104 1.677∙105

Aperture (IC) mm Ø150 Ø150

Aperture (OC) mm Ø180 Ø190

Iron yoke Inner Diam. mm Ø230 Ø250

Iron yoke Outer Diam. mm Ø540 Ø540

Currents above 2500A give bad side effects on powering, so the high currents required for the 36 strands cable case discarded this design

First 3-D models in order to consider the possibility of shorter coil ends.

Tests carried out with IIC=3000A and IOC=0 (60% Load) using previous 2D design (18-strand cable)

Straight section length ≅ 0.86 m

The goal is that peak field at coil ends would not be greater than in the straight section.

2- Coil ends: First Tests

2- Coil ends: First Tests

≅175mm

Parameters UnitsLong Coil End(Iron covered)

Long Coil End(Without Iron covered)

Shorter Coil End(Iron covered)

Integrated field Tm 2.736 2.627 2.617

Total Length m 1.215 1.215 1.125

Multipoles Units < 8 < 12 < 12

Peak field(R=75.1mm)

T 3.79 3.64 4.07

Peak field(Straight section)

T 3.553 3.553 3.553

≅130mm

Warning! Mechanical behavior of the cables was not considered at this pointInteresting option?

18 StrandsDouble Layer, 10 mm between

coils

18 StrandsDouble Layer, 15 mm between

coils

3- One vs Two layers comparative

3- One vs Two layers comparative

Inner coil (IC) & Outer Coil (OC) parameters Units18 StrandsSingle layer

18 StrandsDouble Layer, 10 mm

between coils

18 StrandsDouble Layer, 15 mm

between coils

Nominal field 100% (B1,IC) T 2.13 2.89 2.85

Nominal field 10% (B1,IC) T 0.214 0.302 0.2995

Non-linearity (B1,IC) % -0.47% -4.30% -4.84%

Nominal field 100% (A1,OC) T 2.11 2.9 2.88

Nominal field 10% (A1,OC) T 0.212 0.3102 0.3118

Non-linearity (A1,IC) % -0.47% -6.51% -7.63%

Field Increment % 0 35.68% 33.8%

Nominal current (IC) A 2450 1725 1750

Nominal current OC) A 2150 1500 1500

Working point % 60% 61.23% 61.28%

Torque (IC) Nm/m -9.16∙104 -1.8615∙105 -1.8725∙105

Torque (OC) Nm/m 9.02∙104 1.801∙105 1.816∙105

Aperture (IC) mm Ø150 Ø150 Ø150

Aperture (OC) mm Ø180 Ø190 Ø200

Iron yoke Inner Diam. mm Ø230 Ø240 Ø250

Iron yoke Outer Diam. mm Ø540 Ø540 Ø540

Number of conductors used (1st quad) - 162 345 357

Mechanical issues - Analytical torque

𝐼𝑇=∫− 𝜋2

𝜋2

𝐽 dl=∫− 𝜋2

𝜋2

𝐽 0 cos𝜃𝑅 dθ=2 𝐽 0𝑅 𝐽 0=𝐼𝑇2𝑅

𝑇𝑙= �⃗�× �⃗�

𝑙=𝐵𝑙 ∫− 𝜋2

𝜋2

𝑆 ∙ 𝐼=𝐵∫− 𝜋2

𝜋2

2𝑅cos𝜃 𝐽 0 cos𝜃 𝑅dθ

dl

Rθ

d=2Rcosθ

IT-IT

BOC

J[A/m]=J0cosθ

�⃗�

𝑻𝒍

=𝝅𝟐𝑹𝑩𝑰𝑻

Dipole parameters Units18 StrandsSingle layer

18 StrandsDouble Layer, 15 mm

between coils

Old MCBX(Nominal condition)

Mean radius (IC) m 0.0775 0.08 0.0524

Nominal field 100% (OC) T 2.11 2.88 3.3

Number of conductors IC (1st quad) - 74 154 414

Nominal current (IC) A 2450 1750 511

Torque using Roxie forces (IC) 105 Nm/m 0.916 1.8725 -

Torque using Analytical Eq. (IC) 105 Nm/m 0.931 1.95 1.15

Difference Roxie vs Analytical Eq. % +1.68% +4.176% -

Estimated stress in the conductors

T

R

R

h F

F

𝜎 𝜃𝑐𝑜𝑛𝑑=𝐹𝐴

=𝑇 /2𝑅h𝑙

=𝑇 / 𝑙2 h𝑅

Dipole parameters Units18 StrandsSingle layer

18 StrandsDouble Layer, 15 mm

between coils

Old MCBX(Nominal condition)

Mean radius (IC) m 0.0775 0.08 0.0524

Nominal current (IC) A 2450 1750 511

Torque (IC) 105 Nm/m 0.916 1.8725 1.15

Conductors height (h) mm 4.37 2 x 4.37 14.85

Stress at the coil-collar interface MPa 135 134 74

Twice the stress at old MCBX anyway!!

(1 or 2 layers)

Approach to decrease the stressIntermediate support

Stress at coil-collar interface decreases to approximately 100 MPa

However this design has important drawbacks:- A good field quality is

difficult to achieve.- Difficult assembly

process.

First 2D FEA analysis: Magnetic model

Simplified model of a combined dipole

with 60 deg sectors that provides an equivalent field in order to obtain

similar stresses to those on…

2.88T

2.85T≅ 4T

18 StrandsDouble Layer

15 mm between coils

First 2D FEA analysis: Analytical resultsFirst of all, the analytical results were checked in order to:

- Asses them as design tools.- Provide an idea of the usefulness of the complete model.

Moment Reaction for all edges fixed at Inner coil:

TIC=1.7686•105 Nm/m(Reasonably close to the 1.8725•105 Nm/m of the Roxie model)

𝜎 𝜃𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑=𝑇 / 𝑙2 h𝑅

= 1.7686 ∙105

2 ∙0.08∙0.01110  MPa

Force reaction=1100N𝜎 𝜃 110  MPa 𝜎 𝜃 105  MPa

(Without taking stress concentration into account)

Reasonable results!

Only magnetic forces were considered

All contacts bonded unless those between coils and collars, Frictional with μ=0.2

Collars: E=200GPa

Coils: E=40GPa

Support = Remote displacement in the outer edge of the collars

First 2D FEA analysis: Complete model

First 2D FEA analysis: Coil Results

Stress Units Min Max

Azimuthal MPa -187 28

Radial MPa -69 25

Equivalent (Von Misses)

MPa 0.17 177

First 2D FEA analysis: Collar Results

Stress Units Min Max

Azimuthal MPa -482 433

Radial MPa -315 227

Equivalent (Von Misses)

MPa 0.13 590

First 2D FEA analysis: Displacements

Interference studies to providepre-compression to the coils.

Collar design to avoid stress concentration and coil inwards movement.

Cable mechanical and thermal properties for cryogenic temperatures.

Thermal load 300K->1,9K

First 2D FEA analysis: Next steps

One layer: ◦ More difficult connection.◦ Less conductors and easier winding◦ Less field with higher current.◦ Same stress at the coils.

Two layers: ◦ Easier connections.◦ Much more conductors.◦ More field with lower currents.◦ Same stress at the coils.

Manufacturing Options: One vs two layers

Kapton: ◦ Better cooling.◦ More difficult assembly.

Resin-impregnated glass fiber tape: ◦ Easier assembly.◦ More difficult tooling.

Manufacturing Options: Insulation

MCBX will come with two iron flavours◦ MQXF Iron holes

Open issues: Iron geometry

Round vs flat edgesat iron file??

MCBX will come with two iron flavours◦ D1 Iron holes

Open issues: Iron geometry

460.00

320.00

190.00

R 25.00

5.00

15.00 R 160.00

R 230.00190 mm

(Giovanni’s slides)VS

210 mm(MBXD & MBXE iron

files)

210 mm

Keypoints separated 0.0499 instead of 0.05 at iron files??

More accurate Jc-Fit is going to be provided. Last estimations suggest the margin is going to decrease with these new fit, compared to FIT1 (Roxie)

Open issues: Jc-Fit

Roxie FIT1Values provided by Ezio

Mechanical behaviour of the 3d Coil ends◦ De-keystoning modelling

Open issues: 3D coil ends

Thanks