## 6 Conclusions  
In plasma diagnosis experiments, when measuring the ion current collected by a cylindrical Langmuir probe, it is found that sometimes the orbital theories correctly predict the ion current and, at other times, the radial theories are found to be valid. Therefore, a transition from the validity of the orbital theories towards the validity of the radial theories is expected, depending on the experimental conditions of the plasma--that is, the ion temperature to electron temperature ratio, \(\beta\), and the ion mean free path to Debye length ratio, \(\Lambda\).  
The transition has been theoretically justified in the context of INCEC, so that positive ions lose their translation kinetic energy in collisions with the neutral atoms of the background gas. Therefore, for small \(\beta\) and \(\Lambda\) values, after the last collision, the ions lose their orbital motion and the OML model is no longer valid to describe the ion current collected by the probe. This way, when collisions are included, the OML model provides higher positive ion current collected by the probe, i.e., approaching the values predicted by the ABR model. Alternatively, for higher \(\Lambda\) values, after the last collision, the ions are far away from the probe, and the orbital component of the ion thermal motion is high enough for those ions to fall towards the probe, following an orbital trajectory, diminishing the ion current collected by probe, i.e., approaching the OML model.  
The aforementioned transition has been experimentally observed only for helium plasmas and not for argon and neon plasmas, and it has been justified due to the lower mass of the helium ions, which makes the helium thermal velocity higher for the same ion temperature. Therefore, only for higher \(\Lambda\) and \(\beta\) values in helium plasmas, the transition has been observed. Moreover, as an extreme case comparison, for electrons of even lower mass, the OML theory always predicts well the electron current collected when the probe is positively biased with respect to the plasma potential. Although it has been proven that the positive ion to electron temperature ratio, \(\beta\), is a more relevant parameter than the INCEC mean free path to Debye length ratio \(\Lambda\) in the transition between radial and orbital behavior of the ions, the ion mass is crucial, since it determines the existence of the transition.  
In view of these experimental results and theoretical arguments, the positive ion thermal motion and the collisions must be included in the sheath models, since they influence the radial or orbital behavior of the positive ion current to the substrate/probe, even though the collisions included in this article mainly take place outside of the sheath. This fact also explains that the \(\beta\) parameter has a more definite influence on the transition than the \(\Lambda\) one, as shown in Figures 4 and 5, but the influence of the ion mean free path to Debye length ratio \(\Lambda\) cannot be altogether ignored.  
Conceptualization, J.M.D.-C. and J.B.; methodology, J.M.D.-C. and J.B.; software, G.F.R. and J.M.D.-C.; validation, J.I.F.P. and J.B.; formal analysis, J.B.; investigation, G.F.R. and J.M.D.-C.; resources, J.I.F.P and J.B.; data curation, G.F.R. and J.M.D.-C.; writing--original draft preparation, J.B.; writing--review and editing, G.F.R., J.M.D.-C., J.I.F.P. and J.B.; visualization, J.I.F.P. and J.B.; supervision, J.I.F.P. and J.B.; project administration, J.M.D.-C.; funding acquisition, G.F.R. and J.I.F.P. All authors have read and agreed to the published version of the manuscript.  
This research has been partially funded by the Spanish Ministry of Science and Innovation, ref. no FIS2010-19951, which is partially financed with FEDER funds, and the FPU Program of the Spanish Ministry of Education (ref. FPU17/01387).  
The authors declare no conflict of interest.