## 3 Slotted Waveguide Antenna Design  
With the aim to improve the microwave-to-cavity coupling and at the same time to have a more uniform and symmetric axial electric field distribution, a radically new microwave injection system has been employed. A slotted waveguide antenna operating in free space has firstly been studied, to explore its behavior as a function of the fundamental project parameters. A first preliminary antenna design is described in Reference [12]. Slotted waveguide antennas find many applications in radar and communication systems due to their low-profile design requirements, mechanical robustness, good efficiency, relative ease of realization and wide operational frequency bandwidth [13; 14; 15]. The guided wavelength for the TE\({}_{10}\) mode of the rectangular waveguide is given as \(\lambda_{g}=\frac{\varepsilon}{\sqrt{1-\varepsilon/(2\varepsilon f)}}\), where \(f\) is the operational frequency and \(a\) is the waveguide large side. The guidelines for the design of a slotted waveguide antenna can be easily found in literature [16; 17]. The main design parameters of the simulated slotted waveguide antenna are listed in Table 1. Among these, some critical ones can be highlighted, particularly the width and length of the slots, w\({}_{slot}\) and l\({}_{slot}\), respectively, and the distance between the last slot center and the closing short wall or d\({}_{short}\). The number of employed slots is also a critical parameter that needs to be taken into account during the antenna project. In fact, the impedance bandwidth is inversely proportional to the slot number. On the contrary, the antenna efficiency increases with the slot number. In general, a trade-off for this parameters is chosen depending on the required performances. The slotted waveguide antenna, shown in Figure 5, has been optimized through the use of CST Studio Suite. The operational bandwidth is 14.2-15.25 GHz with central frequency 14.7 GHz. Eight slots have been employed in order to maximize the \(|S_{11}|\) impedance bandwidth and at the same time to preserve the radiation efficiency (near 100% in the numerical simulations). The slot number has also been chosen considering the available space along the cavity outer wall, equal to 150 mm. A tuning of the previously reported critical parameters (w\({}_{slot}\), l\({}_{slot}\), d\({}_{short}\)) has been  
Figure 4: Electric field module plot on side and front slices for: (**a**) cylindrical cavity (\(f_{0}=14.457\) GHz) and (**b**) “plasma-shaped” cavity (\(f_{0}=14.304\) GHz). Electric field has been normalized to the maximum value of 10 kV/m. performed through a cycle of parametric steps in order to observe their effect on the antenna impedance bandwidth [18]. The calculated \(|S_{11}|\) curves are shown in Figure 6. After an optimization phase, a good compromise between impedance bandwidth and efficiency has been found by setting \(\text{w}_{slot}=1.75\) mm, \(\text{l}_{slot}=9.92\) mm and \(\text{d}_{short}=6.455\) mm. It is worth to point out that, when the ECRIS is operated at a frequency \(<18\) GHz, a wide operational bandwidth is desirable in order to employ the frequency tuning effect to boost the source performances in terms of charge states and extracted currents [19]. When the slot number is increased, the antenna directivity increases at the cost of a narrow operational bandwidth: such a characteristic could be an advantage exploitable in the future generation of ECRIS operating at higher frequencies and powered through narrow bandwidth amplifiers. As a final step, in order to employ the slotted waveguide as microwave launcher for the \"plasma-shaped\" chamber, a twisted version of the antenna has been created and simulated. The slotted-twisted waveguide antenna is visible in Figure 7a: starting from the WR62 attach flange, a 45-deg twist has been applied to the waveguide body. The structure retains the same project parameters listed in Table 1, except from \(\text{d}_{short}\), in which value has been set to 7.954 mm for optimization reasons.