## 4 Strong Interaction Analysis
### Description of the Devices  
Figure 8 shows a snapshot of the graphical interface of EN4 EM showing a 3D view of the whole system taken at the instant of firing. Figure 9 focuses on the discretization of the rail launchers; for the sake of readability, only a limited number of the branches used to model the sliding contacts (i.e., those related to elements in effective contact) are shown.  
Figure 6: Time waveforms of the \(z\)-axis component of current density in the rail at the feeding end. Uneven distribution occurs for about 80% of the launch time.  
Figure 7: Basic equivalent lumped parameter circuit of a rail launcher. The presence of f (frequency) among the independent variables means that the circuit parameters are function of the rate of change of the electromagnetic phenomena.  
The details of the geometries of both the devices are reported in Table 2. The compulsator is a two-poles, single-phase machine. The stationary exciting coils have 25 turns each; they are fed with a direct current of 36 kA, capable to produce a magnetic flux density of 3T in correspondence of the armature coils. The discontinuous stationary shield is aluminum made. The axial length of the compulsator is 50 cm. The two armature coils are copper made, series connected and constituted of four turns each. They are positioned on the rotor. All the active components (field coils, armature coils, and shield) span an angle of 150\({}^{\circ}\).  
The snapshots of the 3D views of the active parts of the compulsator are shown in Figure 10. The whole device is built by arranging two items of each of the shown components according to the layout in Figure 3b.  
Figure 8: Snapshot of 3D view of the complete launch system: compulsator plus launcher at the instant of firing.  
Figure 10: Screenshots of a the active parts of the compulsator: (**a**) field coil (stationary inner part); (**b**) compensating shield (stationary part just outside the field coils); (**c**) rotating armature (outer part).  
Figure 9: Screenshot of a planar lateral view of the launcher showing the discretization adopted for the strong interaction analysis. Only the active auxiliary branches used to model the sliding contacts are shown. The leftmost segments represent the connections to the compulsator terminals.  
At the instant of firing the magnetic axis of the field and of the armature coils are aligned, while the center of the shield is rotated (with respect to the scheme shown in Figure 3 of 60\({}^{\circ}\) in the direction of the motion of the rotor [29]. The launcher has copper rectangular rails and a C-shaped armature. The oblique side of the armature forms an angle of 45\({}^{\circ}\) with the direction of the rails as shown in Figure 9.  
In the light of the discussion in Section 2, the numerical model is able to take into account the relevant components and phenomena in both the compulsator and the rail.  
In particular, for the air-core compulsator: (1) the complex armature winding scheme; (2) the presence of excitation/control circuits; (3) the eddy currents in all the conducting parts of the machine (the shield, the shaft, and so forth); (4) the compensating windings of different shapes and arrangements (aluminum sheet, single shorted turns, and so forth.); (5) real winding turns connections; (6) end-turn effects; (7) relative angular velocity between conductors [29]. For the rail launcher: (8) the sliding contacts and the related the velocity skin effect; (9) the current distribution in the solid armature and in the rails [20].  
Finally, the numerical formulation can model centrifugal forces and vibrations acting on the shaft of the compulsator due to electric and mechanical unbalances or to misalignments of the shaft from its centered position, as well as the full 3D electromechanical transient behavior of the machine during the real operating conditions.