## 4 The Method of Electron Temperature by OES  
Because this coaxial line plasma is discharged in the enclosed cavity, and the gas flow rate is relatively low, it is usually considered to work at local thermodynamic equilibrium (LTE) [20]. In this case, electron temperature \(\rm T_{e}\) can be determined by the relative intensity of two or more spectral lines of the atoms, which have the same ionized stage. In LTE condition, the radiation energy density can be expressed as [21]:  
\[\rm\varepsilon_{mn}=\frac{1}{4\pi}N_{m}A_{mn}hv_{mn} \tag{5}\]  
where the subscripts m and n denotes the upper level and the lower energy level of the particles, respectively. \(\rm\varepsilon_{mn}\) is the emission coefficients, \(\rm N_{m}\) is the particles density of upper level, \(\rm A_{mn}\) is the transition probability. \(\rm hv_{mn}\) is the energy of the transition, where \(\rm v_{mn}\) is the frequency of the radiant wave. Using the speed of the light c, the wavelength of the emission light \(\rm\lambda_{mn}\) is given by  
\[\rm\lambda_{mn}=\frac{c}{v_{mn}} \tag{6}\]  
This leads immediately to  
\[\rm\varepsilon_{mn}=\frac{1}{4\pi}N_{m}A_{mn}hc/\rm\lambda_{mn} \tag{7}\]  
In complete LTE at the temperature \(\rm T_{e}\) (eV), Maxwell-Boltzmann statistics must be applied. \[\rm\frac{N_{m}}{N_{n}}=\frac{g_{m}}{g_{n}}\exp\left(-\frac{E_{m}-E_{n}}{kT_{e} }\right) \tag{8}\]  
where g is the statistical weight of the level, E is the energy of the level in eV, k is the Boltzmann constant factor. The emission intensity measured by spectrometer can be written as  
\[\rm I_{i}=\rm\varepsilon_{i}V\Omega T_{i}^{\rm\tau}\eta_{  
Since multiple spectral lines are used to improve accuracy, taking only one spectral line, Equation (11) can be written as:  
\[\ln\left(\frac{\lambda_{\mathrm{i}}\mathrm{I}_{\mathrm{i}}}{\mathrm{A}_{\mathrm{i }}\mathrm{g}_{\mathrm{i}}}\right)=-\frac{1}{\mathrm{KT}_{\mathrm{e}}}\mathrm{E }_{\mathrm{i}}+\mathrm{C} \tag{12}\]  
where C is a constant. Through measurements and NIST atomic spectra database [23], all values except Te.oes are known. Substituting the adopted spectral lines into Equation (12), by fitting the curve's slope, the electron temperature Tev.oes can be calculated. The spectrum of this coaxial line plasma is shown in Figure 8, which is measured under the argon fill pressure Pa = 80 Pa and the microwave power Mpower = 800 W.  
The spectrum indicates two kinds of particles, nitrogen molecule (N\({}_{2}\)) and Ar. N\({}_{2}\) comes from air residue. The air residue is also one of the important causes of probe contamination. Compared with the nitrogen molecule, the peak of this spectrum of Ar I is very obvious with high intensity, which improves the accuracy of measurement of Tev.oes. Although there are many spectral lines of Ar, this does not mean that all spectral lines are suitable for calculating electron temperature, because some spectral lines have a superposition of other spectral lines with a different wavelength, which is very close; besides, the presence of Stark broadening and Doppler broadening would decrease accuracy. Therefore, those spectral lines with a smaller FWHM should be selected. The parameters required by the selected spectrum lines in this article are given in Table 2.  
Using the peak value of the normalized intensity in Figure 9 and the parameters in Table 2, the value of the specified spectral line can be calculated. Draw multiple points and perform linear regression; the line's slope can be used to calculate the electron temperature. The result is presented in Figure 10 and is determined to be 1.452 eV in this configuration. If the electron temperature _Tev.oes_ = 1.452 eV obtained by OES and the ion saturation current _Isat_ = 0.0601 mA obtained by the probe with contamination is taken into Equation (4), the electron density can be obtained, which is \(n=1.2839\times 10^{16}\) m\({}^{-3}\).