The magnet system design, shown in Fig. 1, includes three major components: the superconducting coil with a total current of 123 MA turns that creates the central magnetic flux density of 6 T, two superconducting dipole magnets with a central magnetic flux density of ±1.67 T, and conventional toroid magnets with an averaged magnetic flux density in the steel disks of 2 T. The superconducting solenoid coil is enclosed in a central steel magnetic flux return yoke.
The superconducting solenoid coil has an inner diameter of 6.19 m at room temperature and a length of 23.468 m, keeping about the same diameter-to-length ratio as that used in the CMS magnet [2, 4]. The coil consists of seven modules of 3.35 m long with 3-mm-thick insulation between the modules.
To wind six layers of the coil inside the quench back cylinder of 12 mm thickness, made of the copper alloy, a Cu-stabilized conductor with a cross section of 22 × 68 mm 2 and NbTi superconducting insert of 2.34 × 20.63 mm 2 could be used. With a thickness of the insulation around the conductor of 0.5 mm, the additional insulation between six coil layers of 0.4 mm, and the insulation at the inner and outer radii of 1 mm, the coil radial thickness with the quench back cylinder is 0.43 m and the conductor mass is not less than 3.39 kt.
The total number of turns is 6090, and the current corresponding to the central magnetic flux density of 6 T is 20.2 kA. The stored energy in the coil (41.8 GJ) gives a ratio of the stored energy to the coil mass of 12.3 kJ/kg that is about the CMS value of this ratio [2, 4]. The axial pressure in the coil central plane is 84.4 MPa; the average radial pressure is 13.5 ±1.1 MPa, and the hoop strain is 1.89 ⋅10 −3 giving a tangential stress of 221.4 MPa.
Central Flux Return Yoke
The steel return yoke around the solenoid coil consists of five barrel wheels of 4.64 m width comprising two 0.5-m-thick layers separated by a radial distance of 0.35 m as shown in Figs. 2 and 3. This gives the integral of the magnetic flux density bending component in the coil central plane of 3.86 T ⋅m at the radial distance from 7.15 to 12 m. To provide the sufficient value of this integral with the minimum barrel yoke thickness is the main reason of the thickness choice. The stray field is discussed in Section 3. The air gaps between the barrel wheels needed to feed out the pipes, cables, and fibers from the sub-detectors are 0.175 m wide.
To extend the homogenous region of the magnetic flux inside the coil, the steel nose disks with a thickness of 0.7 m and an outer diameter of 11 m are located on both sides of the coil. The distance available between the nose disks for the sub-detectors is 23.7 m.
Four steel endcap disks of 0.6 m thickness connected by steel rings of 0.35 m thickness follow the nose disks at each coil side. The air gaps of 0.35 m between the barrel layers and between the endcap disks will allow the installation of the muon chambers covering the pseudorapidity  region of ±2.7. The air gaps between the barrel wheels and the first endcap disks to provide routes for the cabling, cooling, and gas supply are 0.6 m wide. The axial force on each endcap is 450 MN toward the solenoid coil center. The steel rings between the endcap disks overshadow the absolute pseudorapidity region from 2.7 to 3, and measuring the muon momenta with the endcap muon chambers in this region is not possible.
Superconducting Dipole Magnets
The dipole magnets allow the charged particle momenta to be measured for absolute pseudorapidity greater than 3. Two superconducting dipole magnets one at each end of the yoke consist of a cylindrical yoke of 0.5 m thickness with an inner diameter of 3.1 m and a length of 4.9 m and a dipole coil split in halves with a shape of constant perimeter end with 2.25-m inner radius. The dipole coil could be made of the same conductor as the solenoid with a cross section of 22 × 68 mm 2 and be operated with the same current of 20.2 kA that gives a total current of 12.12 MA turns. Each coil half consists of 6 pancakes of 50 turns each. The width and the thickness of the coil at room temperature are 0.418 and 1.15 m, respectively.
The direction of the magnetic flux density is horizontal and opposite in the two dipole magnets, and the central value of the horizontal magnetic flux density is ±1.67 T. In this case, both colliding proton beams will be deflected up. The stored energy in the dipole coil is 0.243 GJ.
The axial force on each dipole magnet is 14 MN toward the solenoid coil center, while the horizontal force on each magnet is −7.5 MN. The torques around the vertical axis through the dipole centers are −76 MN ⋅m at the negative end and 76 MN ⋅m at the positive end of the central yoke.
Conventional Toroid Magnets
The toroid magnets provide measurements of the muons in the absolute pseudorapidity region from 2.7 to 5. Two forward muon spectrometers are positioned starting 27.5 m off the solenoid coil center at both ends of the yoke. Each spectrometer consists of three steel toroid disks of 0.8 m thickness with an inner diameter of 0.732 m and an outer diameter of 8.8 m. There are four conventional copper coils carrying a current of 907.6 A around each toroid disk, to magnetize the steel. Each coil consists of 34 turns of 17.5 × 17.5 mm 2 copper conductor wound in two layers. A 10-mm-diameter hole in the conductor cross section serves for water cooling.
Still tubes with an inner diameter of 0.3 m and an outer diameter of 0.54 m keep the toroids in position, providing a gap of 0.4 m between the disks. The axial force on each toroid is 0.53 MN toward the solenoid coil center. The torques around the vertical axis through the centers of three toroids are 44 MN ⋅m at the negative end and −0.44 MN ⋅m at the positive end of the central yoke.
The total mass of steel in the magnetic system is 22.59 kt, and the outer diameter of central yoke is 17.7 m. The full length of the magnetic system including both forward muon spectrometers is 62.6 m.