## 2 Experimental Setup and Measurement Method  
A high-voltage DC discharge has been chosen for these experiments. The gas is introduced in a large Pyrex cylinder, 40 cm high and with an inner diameter of 31 cm, where two stainless steel electrodes are held 15 cm from each other, each electrode having a diameter of 8 cm. The anode is connected to the ground. The electrodes are supplied a high DC voltage by means of the low ripple/low noise-to-signal ratio KEPCO BHK 2000-0.1 MG high-voltage DC power supply. The DC power supply is configured as a current supply, given that the discharge current is related to the electron density and it better serves to characterize the discharge compared to the DC voltage or the discharge power. The entering gas flow is controlled by a mass gas flow controller, MKS 247. A tungsten cylindrical, 6 mm long, 0.1 mm diameter Langmuir probe is placed in the diffuse afterglow of the plasma discharge. In this zone, the plasma is spatially homogeneous and the electron temperature is found to be the lowest, so that the effect of the ion temperature cannot be neglected and the ion to electron temperature ratio, \(\beta\), is not negligible [1; 2; 4; 7; 26; 28]. The neutral and positive ions are supposed to be thermalized. As the electrodes are very hot during the measurements, the ion and neutral atom common temperature is estimated to be 350 K [1; 2; 5; 7; 24; 26; 28; 33; 34].  
The current-voltage characteristic of the cylindrical Langmuir probe can be used to obtain an indirect measurement of the parameters that characterize the plasma in the zone of the discharge where it is placed. The plasma potential, \(V_{plasma}\), the floating potential, \(V_{fluat}\), and the electron energy distribution function, EEDF, can be measured [1; 2; 4; 6; 26; 34; 35; 36; 37; 38; 39; 40; 41]. Regarding the measured EEDF, it is checked that, in every measurement, the EEDF can be considered as following the distribution of Maxwell-Boltzmann [1; 4; 6; 26; 28], which is essential since the assumption of a Maxwellian EEDF is made in both radial and orbital theories. The EEDF is used to perform the calculation of the electron temperature, \(T_{e}\), and the electron density, \(n_{e}\), which is equal to the ion density, \(n_{+}\), by means of the quasi-neutrality condition, \(n_{e}\approx n_{+}\). These values for \(n_{e}\) and \(T_{e}\) have been used as in all further calculations since they do not depend on the radial or orbital theory used to obtain the results. The discharge and the measurements are controlled, and the initial calculations are performed, using a LabView Virtual Instrument [1; 4; 6; 7].  
The experimental device has been designed with the objective of obtaining a low electron temperature plasma, so that the ion temperature, in the range of the ambient temperature, becomes non-negligible when compared to the electron one [1]. This property of the DC discharge allowed us to check the validity of the radial theory developed by the authors, which takes into account the temperature of the ions in argon and neon plasmas in the conditions of the discharge [1; 2; 19; 20; 21; 22; 23; 24]. On the other hand, the size of the probe was chosen to be small enough so that the small-radius OML theory would be of applicability in the cases in which the orbital theories are applicable, as was found in the helium plasma in some conditions of the discharge. The LabView-controlled measuring system makes fast measurements, each taking only 4 ms, so that the temperature of the probe does not change during the measurement of the current-voltage characteristic. In order to make sure that the measurements are quick enough, the current-voltage characteristics were measured, starting both in the electron saturation zone and in the ion saturation zone, making no difference to the results of the measurements.