different magnetic fields and discharge currents are shown in Figure 2. To examine the performance of the HCL-FADOF more clearly, we focus on peak transmittances and check them under different discharge currents (maximum of 20 mA as allowed for our HCL) and magnetic fields, as shown in Figure 3. It is clear that with the discharge current increasing until 18 mA, the peak transmittances at different magnetic fields increase. The maximum transmittance can reach 29 % at the discharge current of 18 mA and the magnetic field of 260 G. It is obvious that the higher discharge current leads to the higher atomic density and the higher transmittance. However, when the discharge current increases to 20 mA, transmittances slightly decrease. The performance of this HCL-FADOF at 18 mA discharge current in detail is further studied. The transmittance spectra at different magnetic fields and the discharge current of 18 mA in contour form are shown in Figure 4. With the magnetic field increasing, the center frequency of the transmittance spectrum decreases. Figure 3: The peak transmittances at different magnetic fields versus various the discharge current of the HCL. The maximum transmittance is 29% at the discharge current of 18 mA and the magnetic field of 260 G.  
Figure 2: Some typical transmittance spectra of the HCL-FADOF. (**a**) The transmittance spectrum at the magnetic field of 225 G and the discharge current of 14 mA; (**b**) the transmittance spectrum at the magnetic field of 475 G and the discharge current of 14 mA; (**c**) the transmittance spectrum at the magnetic field of 225 G and the discharge current of 6 mA; (**d**) the transmittance spectrum at the magnetic field of 475 G and the discharge current of 6 mA. To compare the performance of the HCL-FADOF and the VC-FADOF, all transmittance spectra have been fitted in ElecSus software, using its own fitting function. Several fitted transmittance spectra are shown in Figure 5 and the fitted parameters (the equivalent temperature and the magnetic field) are listed in each subfigure. All the fitted temperatures at different discharge currents are shown in Figure 6. The fitted results show that the atomic density in the rubidium HCL of this experiment corresponds to that of a rubidium saturated vapor cell at the temperature of more than 60 \({}^{\circ}\)C when the discharge current exceeds 15 mA. It is straightforward to think that the equivalent temperature, which is determined by the atomic density as we mentioned at the beginning, is decided by the discharge current of the HCL. The atomic density can be calculated according to the equivalent temperature using Equation (1) [25,26]:  
\[\rho_{N}=\frac{10^{A+\frac{B}{T}}}{kT} \tag{1}\]  
in which \(k\) is [PERSON]'s constant, \(T\) is the temperature in K, \(\rho_{N}\) is the atomic density of rubidium in ground state in \(/\)m\({}^{3}\), \(A\) and \(B\) are constants that depend on the elements. For rubidium, \(A=9.316\), \(B=-4040\) below 321 K and \(A=9.861\), \(B=-4215\) above 321 K. Although the atomic density can be calculated according to the gas discharge theory [27], an empirical formula, which describes the relationship between the atomic density and the discharge current, is more useful and convenient in the experiment. To obtain the empirical formula, the relationship between the equivalent temperature and the discharge current is further fitted under the assumption that the empirical formula can be expressed by Equation (2):  
\[\rho_{N}=\frac{aI}{1+bI} \tag{2}\]  
in which \(I\) is the discharge current of the HCL in mA and \(a\), \(b\) are the coefficients to be fitted. \(a\) represents the conversion coefficient of the discharge current and the atomic density, and \(b\) is related to the saturated discharge current of the HCL. Please note that the \(I\) in Equation (2) must be no more than 20 mA.