First 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

 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

Strand parameters Cu:Sc1.75- Strand diameter0.48mm Metal section0.181mm 2 Nº of filaments2300- Filament diam.6.0µm I(5T,4.2K)203*A Jc3085*A/mm 2 Cable Parameters No of strands18- Metal area3.257mm 2 Cable thickness0.845mm Cable width4.370mm Cable area3.692mm 2 Metal fraction0.882 Key-stone angle0.67deg Inner Thickness0.819mm Outer Thickness0.870mm * Extracted from strand March -09 Waiting 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

 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.

Inner coil (IC) & Outer Coil (OC) parameters Units18 Strands36 Strands Nominal field 100% (B1,IC)T Nominal field 10% (B1,IC)T Nominal field 100% (A1,OC)T Nominal field 10% (A1,OC)T Nominal current (IC) A Nominal current OC)A Working point%60% Torque (IC)Nm/m-9.16∙ ∙10 5 Torque (OC)Nm/m9.02∙ ∙10 5 Aperture (IC)mmØ150 Aperture (OC)mmØ180Ø190 Iron yoke Inner Diam.mmØ230Ø250 Iron yoke Outer Diam.mmØ540 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 I IC =3000A and I OC =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.

≅175mm ParametersUnits Long Coil End (Iron covered) Long Coil End (Without Iron covered) Shorter Coil End (Iron covered) Integrated fieldTm Total Lengthm MultipolesUnits< 8< 12 Peak field (R=75.1mm) T Peak field (Straight section) T3.553 ≅130mm Warning! Mechanical behavior of the cables was not considered at this point Interesting option?

18 Strands Double Layer, 10 mm between coils 18 Strands Double Layer, 15 mm between coils

Inner coil (IC) & Outer Coil (OC) parametersUnits 18 Strands Single layer 18 Strands Double Layer, 10 mm between coils 18 Strands Double Layer, 15 mm between coils Nominal field 100% (B1,IC)T Nominal field 10% (B1,IC)T Non-linearity (B1,IC)% -0.47%-4.30%-4.84% Nominal field 100% (A1,OC)T Nominal field 10% (A1,OC)T Non-linearity (A1,IC)% -0.47%-6.51%-7.63% Field Increment%035.68%33.8% Nominal current (IC) A Nominal current OC)A Working point%60%61.23%61.28% Torque (IC)Nm/m-9.16∙ ∙ ∙10 5 Torque (OC)Nm/m9.02∙ ∙ ∙10 5 Aperture (IC)mmØ150 Aperture (OC)mmØ180Ø190Ø200 Iron yoke Inner Diam.mmØ230Ø240Ø250 Iron yoke Outer Diam.mmØ540 Number of conductors used (1 st quad)

dl R θ d=2Rcosθ ITIT -I T B OC J[A/m]=J 0 cosθ Dipole parametersUnits 18 Strands Single layer 18 Strands Double Layer, 15 mm between coils Old MCBX (Nominal condition) Mean radius (IC)m Nominal field 100% (OC)T Number of conductors IC (1 st quad) Nominal current (IC) A Torque using Roxie forces (IC)10 5 Nm/m Torque using Analytical Eq. (IC)10 5 Nm/m Difference Roxie vs Analytical Eq.%+1.68%+4.176%-

T R R h F F Dipole parametersUnits 18 Strands Single layer 18 Strands Double Layer, 15 mm between coils Old MCBX (Nominal condition) Mean radius (IC)m Nominal current (IC) A Torque (IC)10 5 Nm/m Conductors height (h)mm4.372 x Stress at the coil-collar interfaceMPa Twice the stress at old MCBX anyway!! (1 or 2 layers)

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.

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 Strands Double Layer 15 mm between coils

First 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: T IC = Nm/m (Reasonably close to the Nm/m of the Roxie model) Force reaction=1100N (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

StressUnitsMinMax AzimuthalMPa RadialMPa-6925 Equivalent (Von Misses) MPa

StressUnitsMinMax AzimuthalMPa RadialMPa Equivalent (Von Misses) MPa

 Interference studies to provide pre-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

 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.

 Kapton: ◦ Better cooling. ◦ More difficult assembly.  Resin-impregnated glass fiber tape: ◦ Easier assembly. ◦ More difficult tooling.

 MCBX will come with two iron flavours ◦ MQXF Iron holes Round vs flat edges at iron file??

 MCBX will come with two iron flavours ◦ D1 Iron holes 190 mm (Giovanni’s slides) VS 210 mm (MBXD & MBXE iron files) 210 mm Keypoints separated 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) Roxie FIT1 Values provided by Ezio

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