## 4 Results  
The experimental points are plotted for the different plasmas in Figures 1-3. The experimental Sonin plot points are grouped in terms of the INCEC mean free path to Debye length ratio \(\Lambda\), which allows a comparison between the three plasmas in which the scale of the sheath varies with the Debye length. We show the Sonin plot that includes the theoretical curves that correspond to the orbital and the radial theories in Figures 1-3. The complete solution by [PERSON] [16] for the orbital theory is used, calculated from the fitting curves obtained by [PERSON] and [PERSON] [44]. The radial model developed by the authors for several \(\beta\) values, which converge to the Allen-Boyd-Reynolds model adaptation to cylindrical Langmuir probes by [PERSON] for negligible ion temperature with respect to the electron temperature [19; 21; 22]. In Figure 1, we also show the experimental Sonin plot points corresponding to different ranges in the \(\Lambda\) parameter for argon plasmas. The results of the measurements show that the radial theory describes appropriately the positive ion current collected by a cylindrical Langmuir probe immersed in an argon plasma, in the conditions of the DC discharge used in the measurements. Figure 2 shows the experimental Sonin plot points obtained from the different neon plasma discharge conditions measured. Figure 2 also includes the experimental points colored and symbolized as a function for the \(\Lambda\) parameter. As can be seen in Figures 1 and 2, the \(\Lambda\) parameter shows an evolution in the Sonin plot points--that is, the points for which the ion mean free path is longer are grouped to the right, while the points for which the ion mean free path is short are grouped to the left. These points are located over the radial model theoretical curves for \(\beta\
eq 0\) and fit well with the experimental \(\beta\) values for each point. Therefore, the influence of \(\Lambda\) is not very important in terms of the ions' behavior in this range for argon and neon plasmas. As in Figures 1 and 2, Figure 3 shows the Sonin plot for the experimental points colored and symbolized as a function of the \(\Lambda\) parameter. On one hand, those points corresponding to the lower \(\Lambda\) values (green circles for \(2.27\leq\Lambda\leq 6.69\)) are mainly placed in the radial zone or close to it, and none of them are placed in the orbital zone. On the other hand, those points corresponding to the higher \(\Lambda\) values (blue squares for \(11.11\leq\Lambda\leq 14.29\)) are mainly placed in the orbital zone or close to it, and none of them are placed in the radial zone. Finally, those points corresponding to intermediate \(\Lambda\) values (red crosses for \(6.72\leq\Lambda\leq 11.09\)) are mainly placed in the intermediate zone, where none of the theories  
Figure 1: Argon plasma Sonin plot for the normalized probe potential \(y_{SP}=25\). Experimental data for the argon plasma: green circles for \(3.98\leq\Lambda\leq 11.45\), red crosses for \(11.95\leq\Lambda\leq 17.68\) and blue squares for \(17.88\leq\Lambda\leq 29.71\). In solid lines, the orbital and radial theoretical curves are shown. Figure 3: Helium plasma Sonin plot for the normalized probe potential \(y_{SP}=25\). Experimental data for the helium plasma: green circles for \(2.27\leq\Lambda\leq 6.69\), red crosses for \(6.72\leq\Lambda\leq 11.09\) and blue squares for \(11.11\leq\Lambda\leq 14.29\). In solid lines, the orbital and radial theoretical curves are shown. In purple bold line, the fitting curve for the experimental helium plasma Sonin plot points is shown. Figure 2: Neon plasma Sonin plot for the normalized probe potential \(y_{SP}=25\). Experimental data for the neon plasma: green circles for \(1.52\leq\Lambda\leq 4.05\), red crosses for \(4.05\leq\Lambda\leq 6.32\) and blue squares for \(6.48\leq\Lambda\leq 24.27\). In solid lines, the orbital and radial theoretical curves are shown. are verified, and only a few of them are placed in the other zones.