## 3 Interaction between Plasma Sheath and HPM
### Particle Model in Thermodynamic Non-Equilibrium State
Figure 6: Diagram of electron collision and polarization current in plasma under HPM. The internal energy per unit volume is expressed as  
\[\textbf{e}=e_{tr}+e_{r}+e_{v}+e_{e1}+e^{0}, \tag{12}\]  
where \(e_{tr}\) is the translational energy, \(e_{r}\) is the rotational energy, \(e_{v}\) is the vibrational energy, \(e_{e1}\) is the electron excitation energy, and the formation energy is \(e_{0}\). There are four modes of gas components in the state of the thermodynamic system: the translational mode, rotational mode, vibrational mode, and electronic mode [43]. Only the translational and rotational energy of gas molecules are activated in the thermodynamic equilibrium state; hence, the aforementioned four energy modes can be characterized by temperature. In the thermodynamic non-equilibrium state, the translational energy, rotational energy, vibrational energy, and electronic energy are excited successively. Therefore, a single temperature can no longer accurately reflect the change of intramolecular energy. In ref. [43], [PERSON] proposed a dual temperature model. That is, the translational temperature and the rotational temperature of molecules can be described by temperature \(T\), and the vibration temperature of molecules and the electron excitation temperature is defined by another temperature \(T_{v}\). The model can describe the basic properties of the thermodynamic non-equilibrium state well. When studying thermochemical non-equilibrium relaxation at the molecular level, it should be emphasized that molecular vibrational energy and electron excitation have a far longer relaxation period than chemical reactions, while the relaxation time of molecular translational energy and rotational kinetic energy is much shorter [7; 44]. Therefore, the vibration energy and electron excitation energy can be frozen when computing the electrical properties of the flow field, leaving only the temperature of molecular translational energy and rotational kinetic energy to consider. Thermodynamics, in other words, can be said to be in equilibrium. The internal particle's energy in the system of thermodynamic equilibrium follows the Maxwell-Boltzmann distribution [45; 46]. The energy per unit mass component \(s\) can be represented as  
\[e_{s}=\int_{T_{ref}}^{T}c_{v}^{s}dT+e_{s}^{0}, \tag{13}\]  
where \(c_{v}^{s}\) is the heat capacities at constant volume of component \(s\) and \(e_{s}^{0}\) is the formation energy of component \(s\) at reference temperature \(T_{ref}\). The formation energy of dissociated ionized air components can be found in [46], which is not listed here. The gas component \(s\)'s translational energy is  
\[e_{tr}^{s}=\frac{3}{2}\frac{RT}{M_{s}},component\;s\;is\;atom, \tag{14}\]  
\[e_{tr}^{s}=\frac{5}{2}\frac{RT}{M_{s}},component\;s\;is\;\;molecule. \tag{15}\]  
The rotational energy of the gas component \(s\) is  
Figure 5:0  
According to (13)-(16), the rise in heavy particles' internal energy may be calculated using the translational and rotational modes of gas components, and the temperature \(T\) affects the rise of internal energy. As a corollary, the temperature increase \(\Delta T\) after the plasma absorbs HPM radiation may be estimated. The model of temperature increase is the result of the above processes for calculating the temperature increment \(\Delta T\) of heavy particles.