## 3 Results
### Standard Target Window
Multiple simulations runs were realized with different values of power, namely 250, 500, 750, and 1000 W, to simulate distinct target currents. These runs were made for two different values of the mass flow rate of the cooling water, of 1 and 3 L/min. Figure 12 shows that the maximum temperatures reached in the liquid target, target window, and niobium insert increase linearly with the target current for both mass flow rates. As expected, the temperature increments in the niobium insert are small, when compared to  
Figure 11: Temperature of the target window on its surface in contact with the liquid target for helium cooling fluxes of 0.1 and 3 L/s. Figure 10: Temperature of the liquid target at the axis of the cavity, along the beam patch. the increments verified in the target window and liquid target. This fact is explained as the beam deposits its energy on the target window and the liquid target. Concerning the mass flow rate, it is possible to conclude that it has relevant influence on the temperatures of the niobium insert and liquid target. On the other hand, it has almost no influence on the maximum temperature achieved in the target window, as expected, considering that the cooling water flows at a greater distance from the window. As shown in Figure 13, the temperature of the cooling water at the outlet also increases linearly with the target current/deposited power, due to the increasing heat transferred to the cooling water. Figure 13 also indicates that the increment in temperature of the cooling water at the outlet is quantitatively dependent on the water mass flow rates. Such results are in agreement with experimental data collected by [PERSON] et al. [16], not only because a linear temperature increment in the cooling water of about 1 \({}^{\circ}\)C per 10 \(\mu\)A was experimentally measured, but also because such empirical value (achieved with a mass flow rate known to be around 1-2 L/min) is quantitatively in agreement with the results presented in Figure 13 for the simulated flows of 1 and 3 L/min (corresponding to increments of about 1.5 and 0.5 \({}^{\circ}\)C per 10 \(\mu\)A respectively). Simulations runs were also conducted with different mass flow rates of the cooling water, to test the influence of the cooling water on the temperatures of the several components of the liquid target system. Figure 14 shows that decreasing the mass flow rate of the cooling water below about 3 L/s results in a significant increase of the maximum temperatures of the liquid target, the niobium insert, and, even further away, the target window. This result confirms the importance of the cooling water in removing heat from the target system. Figure 14 also shows that increasing the mass flow rate beyond the standard established of 3 L/s only allows a slight reduction in the maximum temperatures in the niobium insert and liquid target temperatures, whereas almost no improvement is then observed in the maximum temperature reached in the target window. This result is expected, since the cooling water flows in contact with the external surface of the niobium insert, which, in turn, is in contact with the liquid target, but away from the window. These simulations also enable to confirm that the outlet temperature of the cooling water increases significantly as its mass flow rate decreases, as illustrated in Figure 4:0  
Figure 4:1 Maximum temperature of the target window, liquid target, and niobium insert, as a function of the beam power (and corresponding target current), for two flow rates of the cooling water of 1 (open symbols) and 3 L/min (full symbols). Simulations runs were also conducted to study the influence of the initial temperature of the cooling water in removing the heat from the target system. As shown in Figure 16, the initial temperature of the cooling water presents almost no influence in the maximum temperatures of the target components. The behavior is identical for the two mass flow rates simulated.