## 3 Experimental Measurement Conditions and Methodology  
The high-voltage DC power supply has an upper limit of 2000 V and 100 mA. The discharge currents are typically much lower, so that the voltage limitation is the relevant one. For argon, neon and helium plasmas, the discharge DC current is always lower than 12.5 mA. The pressure range for the argon plasma is \(p(\mathrm{Pa})\in[2,10]\); for the neon plasma, it is \(p(\mathrm{Pa})\in[10,35]\), and for the helium plasma, it is \(p(\mathrm{Pa})\in[13,37]\). Given that the transition in the validity of the orbital and radial theories is found in the helium plasma, a total of 448 current-voltage characteristics were measured, while in argon and neon plasmas, for which no transition was found, a total of 171 and 111 current-voltage characteristics, respectively, were measured. This set of measurements includes the measurements already published [26; 28] together with additional measurements in which we explored the higher electron temperature range in the three kinds of plasmas, although no new insight was gained, as the measurements followed the same trend as the rest of the measurements, albeit extending the range in which the trend was observed. The measured electron density, \(n_{e}\), gives values in the range from \(9\times 10^{14}\) to \(7\times 10^{15}\) m\({}^{-3}\), while the electron temperature, \(T_{e}\), ranges from 1000 to 4400 K, corresponding to \(\beta\) values which vary from 0.08 to 0.35. The \(\Lambda=\lambda_{+}/\lambda_{D}\) parameter is obtained from the following expression. \[\lambda_{+}=\frac{1}{n_{+}\sigma_{+-n}}, \tag{1}\]  
with \(\sigma_{+-n}\) being the cross-section for positive ion-neutral collision [10; 42], and \(\lambda_{D}=\sqrt{\frac{\sigma_{0}k_{B}T_{e}}{e^{2}n_{e}}}\)[10]. For each of the plasmas, the following apply. * For argon plasmas, the cross-section for positive ion-neutral collision, under our experimental conditions, is \(\sigma_{+-n}=7.84\times 10^{-15}\) cm\({}^{2}\)[10; 42]. Therefore, the ion mean free path for argon is the following: \[\lambda_{+}=\frac{133}{218\cdot p(\mathrm{Pa})}(\mathrm{cm}).\] (2) Therefore, the \(\Lambda\) values vary from 3.98 to 29.71 for the argon discharges studied in this article. * For neon plasmas, the cross-section for the ion-neutral collision is \(\sigma_{+-n}=4.25\times 10^{-15}\) cm\({}^{2}\)[10; 42]. Therefore, the ion mean free path for neon is the following: \[\lambda_{+}=\frac{133}{118\cdot p(\mathrm{Pa})}(\mathrm{cm}).\] (3) Therefore, the \(\Lambda\) values vary from 1.52 to 24.27 for the neon discharges studied in this article. * For helium plasmas, the cross-section for the ion-neutral collision is \(\sigma_{+-n}=3.99\times 10^{-15}\) cm\({}^{2}\)[10; 42]. Therefore, the ion mean free path for helium is the following: \[\lambda_{+}=\frac{133}{111\cdot p(\mathrm{Pa})}(\mathrm{cm}).\] (4) Therefore, the \(\Lambda\) values vary from 2.27 to 14.29 for the helium discharges studied in this article. Note that the upper limit for the ion mean free path to Debye length ratio \(\Lambda\) for the three gases decreases with decreasing ion mass, such that for argon, the upper limit is \(\Lambda_{max,Ar}=29.31\), close to the double the helium \(\Lambda\) upper limit, \(\Lambda_{max,He}=14.29\). It is also interesting to compare these \(\Lambda\) ranges with the sheath edge, which has values always lower than \(k\cdot\lambda_{D}\). The \(k\) value depends on the sheath edge criteria used, usually considered to be \(4<k<8\)[20; 34; 36], but regardless of the criteria used, there is a range in which the ion mean free path is comparable to the size of the sheath. Two novel series of measurements were performed in the helium plasma, one for constant background pressure \(P=20.2\) Pa and one for constant discharge current \(I_{d}=5.0\) mA.