# Comparison of Two Detector Magnetic Systems for the Future Circular Hadron-Hadron Collider
## 3 Comparison of the Magnetic Systems  
### General Comparisons  
In Figures 5 and 6, the magnetic flux density distribution is displayed in a vertical \(YZ\) plane of the baseline and minimal steel yoke magnetic systems, respectively. The magnetic flux density in the center of the main coil is 4 T in the baseline and 4.24 T in the minimal steel yoke designs, accordingly. Figure 5: Magnetic flux density distribution in a vertical \(YZ\) plane of the FCC-hh detector baseline magnetic system. The color magnetic field map plotted with the cell size of 0.05 m has a width of 50 m and height of 23 m. The color scale unit is 0.5 T. The minimum and maximum magnetic flux density values are 0.0142 and 4.1595 T. The quarter of the tracking system used in this analysis is drawn with the white rectangles. Figure 6: Magnetic flux density distribution in a vertical plane of the FCC-hh detector minimal steel yoke magnetic system. The color magnetic field map plotted with the cell size of 0.05 m has a width of 50 m and height of 23 m. The color scale unit is 0.5 T. The minimum and maximum magnetic flux density values are 0.0002 and 4.3623 T. The maximum magnetic flux density in the barrel wheel layers is 2.3 T. The magnetic flux density in the first endcap disks at the radius of 6 m is 2.4 T. The quarter of the tracking system used in the present analysis is drawn with the white rectangles. The larger central magnetic flux density value in the minimal steel yoke option reflects the contribution of the yoke to the coil's inner magnetic field. In both figures, the color scales for the magnetic flux density are the same: from 0 to 4.5 T. The same color in both figures corresponds to the same magnetic flux density value. The magnetic flux distributions in these figures are somewhat different, and some areas of the systems are described with slightly different colors. Comparison of the magnetic flux distribution in Figures 5 and 6 displays that the magnetic flux inside the coils is very similar for both options except in the transition areas between the main and forward coils, where the magnetic flux density in the minimal steel yoke option is lower than in the baseline design by 9.3%. The presence of an inner steel disk with a thickness of 1 m and a bore diameter of 3.47 m causes this effect. As displayed in Figure 7, the 6% increase in the central magnetic flux density, caused by the steel yoke contribution, is compensated by a decrease in the magnetic flux density at the axes of the forward coils. At distances of \(\pm\)13.53 m from the main coil center along the coil axes, the magnetic flux density is 3.2 T in the baseline design and 3.04 T (5% lower) in the minimal steel yoke magnetic system. Figure 8 presents the stray magnetic flux density variation vs. radius in the middle plane of the main coil, and vs. distance from the main coil center along the coil axes. The stray magnetic flux density drops to the safe level of 5 mT at a radius of 59.4 m (52.2 m) from the coil axis in the baseline (minimal steel yoke) design. The stray field drops to 5 mT at 64.9 m (60.2 m) from the main coil center along the coil axes in the baseline (minimal steel yoke) design. In the minimal steel yoke magnetic systems, the compression axial force onto the central barrel wheel is 236.9 MN from each side including the attractive axial force onto the endcap assembly of 164 MN. These values are 2.92 and 2.42 times larger than the corresponding axial forces in the CMS magnet yoke at the 3.81 T central field [11]. The axial force on each forward coil in the minimal steel yoke magnetic system is 62.4 MN against of 61.8 MN in the baseline design. The compression axial force in the main coil middle plane is 529.8 MN (against of 610.7 MN) that creates a pressure of 29.6 MPa (against of 34.1 MPa). The radial pressure in the main coil is 2.5 MPa (against of 1.55 MPa), and in each forward coil is of 2.23 MPa (against of 2.66 MPa).