## 4 Simulation of Low-Frequency Communication in Plasma Sheath  
### Temperature Increment Model  
The change in particle temperature has a direct impact on the collision frequency for the plasma EM parameters. As a consequence, the impact of changing collision frequency on plasma EM characteristics is an important concern. Firstly, the polarization current \(\mathbf{J}\) is proportional to the frequency of collision frequency \(v_{c}\) and plasma frequency \(\omega_{p}\), as seen in the iterative diagram of Figure 7. Furthermore, the energy \(Q_{em}\) of the plasma absorption from the HPM can be obtained from the polarization current \(\mathbf{J}\). Secondly, the temperature increment model can convert the energy \(Q_{em}\) into the particle temperature increment \(\Delta T\) Thirdly, the temperature increase \(\Delta T\) has a direct impact on the collision frequency. Finally, the collision frequency is a polarization current parameter that has a direct impact on the plasma's EM characteristics. Because the plasma sheath continues to be irradiated by the HPM, the EM properties of the plasma are constantly changing. In the above process, it can be seen that the increment of temperature directly affects the collision frequency. However, the plasma fluid is constantly changing, and the temperature increment will also affect other fluid parameters, so the plasma frequency will also change as time goes by. When the EM parameters of two plasmas change simultaneously, it is difficult to clarify the effect of a single parameter. Therefore, we want to find a special period in which only the collision frequency changes while the plasma frequency remains unchanged. Fortunately, we found a time window to ensure that only the collision frequency changed and the plasma frequency remained unchanged. We know that the state of the plasma is chemical non-equilibrium. In this state, \(Da\approx 1\). \(Da\) is known as the Damkohler number [7], and it is written as  
\[Da=\tau_{f}/\tau_{c}, \tag{17}\]  
where \(\tau_{f}\) is the flow's characteristic duration (the flow field's characteristic length divided by the flying speed, \(l/V_{\infty}\)). \(\tau_{c}\) is the time it takes for a chemical reaction to take place. The RAM-C II model's major dimension is 1.295 m, and the speed of flight is 7650 m/s, as shown in Figure 1a. Therefore, the characteristic time of the flow field is determined as  
\[\tau_{f}=l/V_{\infty}=1.295/7650=1.69\times 10^{-4}~{}s. \tag{18}\]  
As a result of \(Da\approx 1\), a chemical process' characteristic time may be estimated using the characteristic time of a fluid. Chemical reactions in the area of flow have a typical duration of roughly \(1.69\times 10^{-4}\) s.  
The HPM has high frequency, short pulse, and high power, and it is an essential form of strong EM pulse. The maximum pulse width of the HPM added in this paper is 100 ns, the characteristic electrical time is calculated as \(1.0\times 10^{-7}\) s, and the chemical reaction characteristic time is about 1000 times that of the characteristic electrical time. Therefore, the parameters in the fluid are almost static when we calculate the flow field's electrical properties. This creates a distinct time window, which is the typical duration of a fluid's chemical reaction. During the characteristic time of the fluid's chemical reaction, the internal parameters of the flow field do not change. The internal temperature of the flow  
Figure 7: Iterative diagram of temperature increment \(\Delta T\) and collision frequency \(v_{c}\). field increases instantly with the addition of HPM, according to the temperature increment model. The collision frequency of plasma \(v_{c}\) increases instantaneously, but the plasma frequency remains unchanged.