## 3 Interaction between Plasma Sheath and HPM
### Particle Model in Thermodynamic Non-Equilibrium State  
Because the masses of electrons, ions, and neutral particles are so dissimilar in the HPM irradiating plasma process, the electric field force has a limited driving impact on heavier particles in comparison to electrons. As a result, it is safe to infer that the electric field forces only affect the electrons but not the heavier particles. In other words, the velocity of heavy particles remains unaltered due to the impact of the electric field force, but electrons accelerate and collide with heavy particles continuously for energy exchange, resulting in a rise in the internal energy and temperature of heavy particles. The electrons in the plasma travel under the influence of an electric field in a directed motion, according to [PERSON]'s law, and the electric field does work on the electron motion. The electron accelerates initially as a result of the electric field and then collides with the surrounding heavier particles as a result of the collision, resulting in the formation of a polarization current at a specific speed. The electrons transmit kinetic energy to heavy particles, causing the internal energy of the heavy particles to increase. As previously stated, Figure 6 depicts the particle motion law under the HPM. Figure 4: The distribution of plasma EM parameters on stagnation line. Figure 5: The transmission, reflection, and absorption of plasma sheath are in the frequency range of 0.1-100 GHz. The polarization current value at each time step can be computed using the iterative ADE-FDTD algorithm. The Joule power of the plasma is the product of the polarization current and the electric field value of the plasma, and the Joule power at this time represents the energy that the plasma absorbs from the HPM. The following is the formula:  
\[Q_{em}=\mathbf{J}\cdot\mathbf{E}. \tag{9}\]  
The polarization current value excited at each time step can be determined using the ADE-FDTD technique to mimic the propagation of EM waves in the plasma [34; 35; 36; 37; 38; 39; 40; 41; 42]. There is current flow in the weakly ionized plasma when it is exposed to an external electric field. The effect of ions' mobility on the electrical characteristics of plasma can be overlooked. As a result, the principal source of internal current is electrons moving in a specific direction. The plasma's polarization current can be written as  
\[\mathbf{J}=-en_{e}v_{e}, \tag{10}\]  
where \(e\) is the electron charge, \(n_{e}\) is the electron density, and \(v_{e}\) is the electron velocity. The electron velocity \(v_{e}\) creating the polarization current \(\mathbf{J}\) is derived by incorporating the ADE-FDTD algorithm into (10). It can be observed from (6) of the ADE-FDTD to compute the polarization current, and when particle collisions are taken into account, the polarization current emerges. As a consequence, the polarization current's electron velocity \(v_{e}\) is the velocity following an electron collision. The total amount of energy received by plasma, comprising the kinetic energy following electron impact and the increase in a particle's internal energy, is computed by (9) as plasma absorption energy \(Q_{em}\). As an outcome, a rise in the internal energy of a particle equals the plasma absorbed energy \(Q_{em}\) minus the electron's kinetic energy \(\frac{1}{2}\rho v_{e}^{2}\) at this time. The ADE-FDTD determines the energy absorbed by an electron \(Q_{em}\) as well as its kinetic energy \(\frac{1}{2}\rho v_{e}^{2}\). We can calculate the increase in the particle's internal energy. According to the control unit's energy conservation law, total energy \(E\) per unit volume equals the sum of internal and kinetic energy stated as  
\[E=\rho[\mathbf{e}+\frac{1}{2}(u^{2}+v^{2}+w^{2})], \tag{11}\]  
where \(\rho\) is the density per unit volume; \(\mathbf{e}\) is the internal energy per unit volume; and \(u\), \(v\), and \(w\) are the velocity of the particle in the \(x\), \(y\), and \(z\) directions, respectively.