Force & Torque Neutral Dipole vs. Balanced Conical Solenoid

1. Force & Torque Neutral Dipole versus Balanced Conical Solenoid- FCC detector meeting, March 3, 2016 - Matthias Mentink on behalf of FCC detector magnet group

2. Motivation Twin Solenoid + Force & Torque Neutral Dipoles • Advantage: Full coverage, i.e. good field integral for η = 0 to ∞ • Disadvantage: Very large dipoles (stored energy: 1.5 GJ) in stray field (> 1 T) of twin solenoid, very large internal forces and torques, heavy & expensive. Is there a good alternative? Force & Torque Neutral Dipole: Challenging to build

3. Content • Twin Solenoid • Force & Torque Neutral Dipole • Balanced Conical Solenoid • Comparison of field integrals • Summary

4. 1. Twin Solenoid Counter-clockwise current 14 12 10 8 6 4 2 0 B [T] Clockwise current Radial position R [m] -12 -8 -4 0 4 8 12 Axial position Z [m] • Twin Solenoid: Combines two superconducting solenoids with opposite flowing currents: • Inner solenoid with 12 m free bore, 6 T in the center. • Outer solenoid returns flux and reduces stray field • (5 mT boundary: RZ=0 = 29 m, Rwidest = 40 m, ZR=0 = 62 m). • Minimum shaft diameter reduced to 27.5 m  Stored energy increased to 62 GJ.

5. 2. Force and Torque Neutral Dipole Twin Solenoid y x Main dipole coil Lateral dipole coil z • Combination of solenoidal + perpendicular dipole field  Force & Torque • Twin Solenoid + unbalanced forward dipole: Fy = 27 MN, Tx = 210 MNm. • Lateral dipole coils with opposite current provide counter torque and force •  Net zero force and torque, but large internal forces and torques inside cold mass. • Mechanical stability: • 0.1 m displacement  Fy = 42 kN, Tx = 0.5 MNm in worst case scenario. • Mechanical constraints required, in particular along y direction.

6. 3. New option: a Balanced Conical Solenoid (BCS) magnet 20 15 10 5 0 0.1 T B [T] 0.2 T 0.3 T 0.5 T Balancing coil (Counter clockwise) Radial position R [m] Conical coil (Clockwise) -25 -20 -15 -10 -5 0 5 10 15 20 25 Axial position Z [m] • Balanced Conical Solenoid • Conical solenoid augments bending power of twin solenoid for pseudo-rapidity η≥ 2.5 • Just conical solenoid, axial force: 280 MN toward TS • Addition of balancing coil: Makes not just cold mass, but each individual coil force and torque neutral • Mechanical stability: • Stable in axial direction, unstable in off-axis directions: dT/do=-2.9 MNm/o, dFz/dz=-1.9 MN/m, dFx/dx=+1.1 MN/m • Supports needed, in particular in off-axis direction

7. 4. Field integral ‘seen’ by tracker: TS, TS+BCS, dipole Inner tracker boundary, r = 2.5 m, z = 8 m Forward tracker boundary, z = 23 m Cross-over Cross-over • Comparison: • Addition of BCS: ≈2x field integral enhancement with respect to just TS. • TS + BCS versus dipole: Field integral of dipole better for η > 3.1, double field integral better for η > 4. • For η > 4, balanced conical solenoid may be augmented with low-angle dipole weighing tons, not hundreds of tons. • Is Balanced Conical Solenoid a valid alternative for the dipole?

8. 5. Summary Comparison of Balanced Conical Solenoid versus Force & Torque Neutral Dipole: Force and torque neutral configurations through balancing: • Force & Torque Neutral Dipole: Net force and torque are zero, but large forces and torques exist between coils. • Balanced Conical Solenoid: Each individual coil is in a net force and torque neutral configuration. Cold mass comparison: • Cold mass about 300-400 tons. • Balanced Conical Solenoid has more stored energy (~2x), but.; also a more homogeneous force distribution, reducing need for support structure. Field integrals of TS + BCS versus dipole: • Cross-over point of field integral at η = 3.1 • Cross-over point of double field integral at η = 4 • Balanced Conical Solenoid may be combined with a much smaller dipole for high η. Force & Torque Neutral Dipole TS + Balanced Conical Solenoid