## 3 The Method of Electron Density and Temperature by Langmuir Probes  
For low-temperature plasmas (<10 eV), the Langmuir probes are generally used to measure the plasma density and electron temperature. A Langmuir probe consists of a bare wire or metal disk, immersed in the plasma, with a sweep voltage to collect electron and ions [5]. In this study, the probe had a 1.0 mm diameter and was 20 mm long, suspended in a 12 mm tube with the vacuum seal at the upper end. The probe tip was a tungsten rod 1 mm in diameter and 8 mm long. When a probe is immersed in plasmas, the current is dependent on the ions current and the electron current. By loading a sweeping voltage on the probe, the I-V curve of the probe is obtained. According to the different current composition, the I-V curve can be divided into three regions [5]:  
Figure 3: Coaxial line plasma driven by 800 W microwave at fill pressure of 80 Pa.  
Figure 2: The structure of the coaxial reaction cavity and the Langmuir probe. (1) Ion saturation region. (2) Transition region. (3) Electron saturation region where ions are repelled, but electrons are attracted to the probe. When a negative voltage is applied on the probe, the positive ions approach to the probe. However, there is an electronic shield on the probe surface, which is the electron Debye length. The ion saturation region means the probe voltage (Vp) on the probe is sufficiently negative to collect all the ions with the Bohm velocity. The ions are accelerated through a \"pre-sheath\" to the required energy. When \(T_{e}\gg T_{i}\), the ion saturation current is determined by the electron temperature. Therefore, ion saturation current is, approximately, [7; 14; 15; 16]:  
\[\mathrm{I_{sat}}=0.605\mathrm{A_{probe}}\mathrm{n}\mathrm{e}\sqrt{\frac{kT_{e}} {mi}} \tag{1}\]  
Here, e is the electron charge, k is Boltzmann constant, Te is electron temperature, \(\mathrm{A_{probe}}\) is the surface area of the probe, mi is the ion mass. n is the plasma density in this paper, and we only consider the case where electron density and ion density are equal. In the transition region, the current consists of both electron current and ions current. Compared to electron current, the ion current is negligible. The electron current is expressed as follows:  
\[\mathrm{I_{e}}=\mathrm{I_{e0}}\exp\left[\frac{e(V_{p}-V_{s})}{kT_{e}}\right] \tag{2}\]  
\[\mathrm{I_{e0}}=\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{\left(\frac{ kT_{e}}{2\pi m_{e}}\right)}^{1/2}\mathrm{A_{probe}} \tag{3}\]  
Here, Vs is the space potential, \(\mathrm{I_{e}}\) is the electron current, \(\mathrm{I_{e0}}\) is the saturation electron current. Equation (4) can be achieved by transforming Equation (2). Equation (4) shows that the slope of the (In I)-Vp curve is exactly 1/TeV (which is convenient to write KTe/e as Te/V, the electron temperature in eV) and is a good measure of the electron temperature [5; 7]. \[\mathrm{ln}\mathrm{I_{e}}=\frac{1}{T_{ev}}\mathrm{\left(V_{p}-V_{s}\right)}+ \mathrm{ln}\mathrm{I_{e0}} \tag{4}\]  
Bring the result of _Tev_ into Equation (1), the plasma density (n) can be obtained. When the plasma is just charged, the I-V curve of the Langmuir probes immersed in coaxial microwave driven plasma is shown in Figure 4, which is measured under the argon fill pressure Pa = 80 Pa and microwave power Mpower = 800 W. The applied voltage on Langmuir probes is AC 60 V-50 Hz. As shown in Figure 4, when the voltage is positive, the voltage curve is consistent with the current curve. When the voltage is negative, the current curve first decreases with the voltage and then becomes smooth at around about \(-\)20 V. This is because +60 V does not make the probe current reach the electron saturation region. Therefore, when the voltage increases from 0 V to 60 V, the current also increases exponentially. When the voltage is less than \(-\)20 V, the ion current variation is very small (less than 0.005 mA), and it enters the ion saturation region.