## 3 Plasma Sources
### Microwave (Non-ECR) Plasma Source
In the case of a plasma system operating at a frequency of 2.45 GHz, the critical electron density value is 7.6 \(\times\) 10\({}^{16}\) m\({}^{-3}\). The critical electron density is determined by Equation (4) [37]. \[\mathrm{n_{e}}=\frac{\varepsilon_{0}\mathrm{m_{e}}\omega^{2}}{\mathrm{q^{2}}} \tag{4}\]  
where  
\(\varepsilon_{0}\) is the permittivity of free space;  
\(\mathrm{m_{e}}\) is the electron mass;  
\(\mathrm{q}\) is the electron charge;  
\(\omega\) is the angular frequency. Once the plasma reaches the critical electron density, the microwave electromagnetic waves can no longer propagate and instead become evanescent [38]. A system operating at higher frequency will achieve higher critical density in the plasma, which means that higher levels of power will be absorbed before the incoming microwave power is reflected out by the plasma. The literature includes studies comparing two plasma systems operating at different microwave frequencies, one at 2.45 GHz and the other at 5.8 GHz. It was determined that the absorbed power in the system operating at the higher frequency was nearly twice as high. Higher-density plasmas can be created with lasers operating at optical frequencies or even gamma rays, which generate the highest-density plasmas of all [36]. These two sources are not considered in this field and hence will not be explored further here. It is also important to note that plasma density is not uniform throughout the plasma, with a higher plasma density at the area in which the electromagnetic radiation is incident with a significant reduction in density toward the plasma bulk. By increasing the power, the microwaves can be pushed into the critically dense plasma, thus achieving even higher densities; however, the efficiency of the system is reduced. For this reason, regimes such as Landau damping or electron cyclotron resonance (ECR) are used to achieve anisotropic plasmas with plasma densities that are significantly overcritical [36]. ECR systems will be studied in the next section. As mentioned earlier, microwave frequencies are significantly higher than radio frequencies; therefore, more electrons are produced in microwave systems. It is also important to note that the higher the source frequency, the higher the kinetic energy of the electrons that are produced [3; 39]. In the case of low-frequency systems operating up to 3 MHz, the power can be transferred through cables; however, in this case, since the frequency of operation is in the GHz range, transfer through lines suffers substantial power loss. Therefore, in the case of such high-frequency microwave systems, power transfer is conducted through the use of hollow conductive structures called waveguides, which enables the creation of a high radical density [40]. Microwave plasmas, especially those generated in low-pressure conditions tend to have very low sheath voltages compared with plasmas created by DC or RF sources. This minimizes ion-induced surface damage and makes them well-suited for applications requiring precise and non-destructive cleaning [40]. In a microwave plasma system, the sheath would be around 3 to 14 times the Debye length [41; 42; 43]. Thus, for a plasma with electrons having an energy of 5 eV and an electron density of \(10^{16}\) m\({}^{-3}\), the Debye length would be around 0.2 mm, with a sheath being 0.6 to 2.8 mm thick [36]. On the negative side, it is reported that, although microwave devices have improved in the achievable power levels, such an increase has been coupled with a reduction in microwave pulse length. This pulse shortening means that an increase in power would still see the radiated energy remaining at the same power level [37]. Table 5 presents the parametric grading achieved for microwave (non-ECR) plasma sources.