## 5 Discussions
This model considers the populations of 21 energy levels, including the ground state (denoted as level 1); the 1s5 and 1s3 metastable levels; the 1s4 and 1s2 resonant levels; the 2p1 to 2p10 levels; and the 2 sd3, 3p, and high levels (hl), each grouped into a single level. Additionally, it accounts for the populations of argon excimers \((Ar2^{*})\) and ionized argon species \(\left(Ar^{+},Ar^{2+}\right)\). The primary processes included in the rate equations are the excitation and de-excitation mechanisms of the electronic states. The spectral lines for which intensities were estimated using the collisional radiative model includes data from Table 5. \begin{table}
\begin{tabular}{c c c} \hline
**Wavelength [nm]** & **Upper Level** & **Lower Level** \\ \hline  
\hline \end{tabular}
\end{table} 
Table 5: The argon plasma emission spectra peaks in the wavelength range of 750–950 nm at 500 W, 400 G magnetic field intensity, and 12 sccm propellant flow rate. Typically, the fitting parameters in such models include electron concentration and electron temperature. However, because the spectral lines are partially absorbed within the plasma (indicating that the plasma is optically thick for these lines), it was necessary to calculate the escape factor. This escape factor, which influences both line intensities and population levels, depends on several variables, such as gas temperature, pressure, path length through the plasma, and particle distribution. Spectral measurements were conducted longitudinally at a distance of 12 cm, a considerable distance that promotes the reabsorption of spectral lines within the plasma. These measurements were taken without the use of collimation optics, meaning that the optical signal was collected from the entire plasma, resulting in a highly averaged signal. These factors made the process of minimizing the chi-square function particularly challenging. The estimated plasma density and electron temperature for the 500 W RF supply power in pulsed mode, using the right helical antenna with a length of 78 mm, were \(n_{e}=5\cdot 10^{17}\) m\({}^{-3}\) and \(T_{e}=5\) eV. Considering the resulting electron temperature from the collisional radiative model (CRM), the Bohm velocity of ions \((C_{s})\) becomes 3460 m/s. Under the [PERSON] et al. (2017) approximation for the acceleration coefficient \((\alpha_{accel}\sim 3.2)\), the specific impulse under ideal conditions becomes approximately 1100 s \(\left(I_{spideal}=\alpha_{accel}C_{s}/g_{0}\right)\). Correspondingly, the ideal thrust force is estimated to be above 3 mN \((\,T_{ideal}=M_{i}\Gamma_{i}A_{i}v_{i}\sim 3.21\) mN\()\). To advance the breakthrough of HPT operation, it is essential to correlate the heating mechanisms in both the Inductively Coupled Mode (normal waves, NW-H mode) and the helicon wave-sustained discharge (W mode). In Section 2, it was underlined that, in an MEICP reactor, both helicon and TG waves contribute to the plasma heating. At low operating pressures and high-density magnetic field RF discharges, the TG wave is strongly absorbed at the plasma edge \((\sim mm)\). Conversely, due to its low damping characteristics, the helicon wave penetrates deep into the core reactor region, where it is absorbed and drives on-axis plasma heating. As noted in ([PERSON], 2016; [PERSON], 2016), the helicon wave absorption may result from parametric decay instability, generating ion acoustic turbulence, that contributes to electron heating. According to ([PERSON], 2016), this turbulence can arise under the following particular conditions: at relatively high external magnetic fields \((\,B_{0}\sim 1000\) G), where the lower hybrid frequency closely matches the pump wave frequency (\(\sim\)13.56 MHz), or at very low magnetic fields in the range of 20 to 80 G.  
In the proposed Helicon Plasma Thruster, the wave frequency exceeds the lower hybrid frequency \((B_{0}<800\) G), indicating that parametric instability is unlikely to be the primary driving mechanism for plasma heating in this configuration.