## 3 FEM Model of the Rotating Target
### Numerical Investigations on the Presence of Internal Stiffeners  
The influence of internal stiffeners (inserted inside the evaporator) on the mechanical behaviour of the rotating target, subject to the actions listed in Section 3.1, was evaluated by means of FEM (finite element method) analysis. Two configurations of evaporator were investigated: the first was characterised by the absence of internal stiffeners, case (a), as depicted in Figure 9a, and the second one by their presence, case (b), as depicted in Figure 9b. The internal stiffeners had a rectangular shape with dimensions of 190 mm width, 225 mm height, and 5 mm thickness. The internal stiffeners were placed every 15\({}^{\circ}\) for a total of 24 elements. Furthermore, the presence of an internal hole is due to fluid dynamics. Figure 10 shows numerical results for the configuration without internal stiffeners. In particular, Figure 10a shows the temperature field, while Figure 10b the von Mises stress distribution, respectively. Figure 10a shows the hot spot due to the ion beam power deposition (supposed uniform) where the maximum temperature reached was 113 \({}^{\circ}\)C. The temperature moving towards the condenser was significantly lower due to the presence of the cooling system. The von Mises criteria [19] were adopted to define the higher value of stress equal to 62 MPa inside the impact area of the evaporator. In Figure 11a,b, the same calculations are reported for the case of an evaporator with internal stiffeners. Differently from the previous case, the temperature field does not appear uniform over the ion beam impact area (Figure 10a) but assumes higher values in correspondence with the internal stiffeners' positions. Figure 9: Internal view of the evaporator: (a) absence of internal stiffeners; (b) presence of internal stiffeners. Figure 11: (**a**) Temperature field in \({}^{\circ}\)C on the evaporator, case (b) with internal stiffeners. (**b**) Von Mises stress field in MPa of the evaporator, case (b) with internal stiffeners. Figure 10: (**a**) Temperature field in \({}^{\circ}\)C on the evaporator, case (a) without internal stiffeners. (**b**) Von Mises stress field in MPa of the evaporator, case (a) without internal stiffeners. The temperature field reached the highest value of 236 \({}^{\circ}\)C in the proximity of stiffeners. In the region between two stiffeners, under the application of ion beam thermal load, the temperature assumed a lower value, equal to 113 \({}^{\circ}\)C. Following the von Mises stress criteria, the maximum stress reached was 120 MPa. The internal stiffeners were anchored to the mantle of the evaporator, therefore representing a constraint that limits the possibility of displacements. As a consequence, the increment of temperatures and mechanical stress occurred in correspondence with stiffeners. In Figure 12, the comparison of the temperature field between the two cases was made in terms of temperature under the hot spot for the two analysed typologies and for a different number of cycles. Each cycle represents a complete rotation of the target. As already explained, the presence of internal stiffeners, provides hyperstatic constraints on the lateral mantle, thus also producing a higher temperature rise, when the surface is hit by the ion beam. The larger increase in temperature is due to the inability of the surface to freely deform out of the plane. On the other hand, the presence of internal stiffeners for their geometrical dimension increases the inertia in the plane leading to an improvement of the rigidity of the system and thus enhancing the instability safety factor. In case (a), the temperature increase occurred when the reference point of the outer shell of the evaporator passed under the ion beam. However, this phenomenon is much less relevant concerning the previous case. Figure 13 shows the comparison in terms of von Mises stresses as a function of the number of cycles for the two cases considered.