# Effect of Terahertz Antenna Radiation in Hypersonic Plasma Sheaths with Different Vehicle Shapes
## 2 The Plasma Sheath and the THz Array Antenna
### The Plasma Sheaths Corresponding to Blunt-Coned Vehicle and Sharp-Coned Vehicles  
The models were used to simulate the hypersonic flying process of blunt-coned vehicles and sharp-coned vehicles in the atmosphere. Since the air in the atmosphere can be considered as a compressible fluid, the finite volume method (FVM) [16] was used to solve the hypersonic hydrodynamic models. In such a case, the plasma flow fields are obtained by numerically solving the models. Moreover, the model is reliable since the simulation results agree well with the RAM experiments results. This study uses the plasma sheath model to explore the antenna performance with different vehicle shapes, which is original and different from our previous works [8; 12; 13; 16]. The size of the blunt-coned vehicle is the same as the reentry vehicle involved in the RAMs [17]. The length and the bottom size of the sharp-coned vehicle are equal to that of the blunt-coned vehicle. The two vehicles are set to fly at the speed of 6550 m/s with a 0\({}^{\circ}\) attack angle. The flight altitude of the vehicles is 30 km. The mass density of the neutral atmosphere at this altitude is \(1.566\times 10^{2}\) kg/m\({}^{3}\). Figure 1a,b illustrates the simulation result of the plasma sheaths corresponding to the two vehicle shapes at the speed of 6550 m/s. Figure 1a,b are the electron density distributions of the blunt-coned vehicle and sharp-coned vehicle, respectively. Figure 1a is flipped along Y-axis to be compared with Figure 1b. As seen in the figure, the plasma sheath distributions are quite heterogenous. The vehicle shape has an enormous influence on the plasma sheath distribution. Compared with the blunt-coned vehicle, the electron density (\(N_{e}\)) is higher near the vehicle wall of the sharp-coned vehicle. Meanwhile, the thickness of the sharp-coned vehicle's plasma sheath is obviously smaller than that of the blunt-coned vehicle. According to Figure 1a, the electron density near the blunt-coned vehicle nose is the highest and the electron density near the vehicle wall becomes much lower due to the evolvement of plasma. However, the situation is different in the sharp-coned vehicle plasma sheath. In Figure 1b, the electron density is almost the same from the vehicle nose to the tail. In addition, the plasma layers of the same color are not perpendicular to the antenna radiation path according to the left zoom area of Figure 1a. In the right zoom area of Figure 1b, the antenna radiation path is perpendicular to the plasma  
layers. The difference may result in different radiation directions of the antennae mounted on the two vehicle shapes, since plasma is dispersive. Additionally, regardless of the vehicle shape, the plasma distribution in the wake region is much more complex than the plasma distribution near the wall. The complex and unstable area is not suitable for electromagnetic wave propagation. In such cases, the vehicle sidewall would be a better choice for mounting the communication antenna. In this study, the antenna is mounted at a position nearly 0.5 m away from the vehicle nose (see the red line in Figure 1a,c). In order to investigate the impacts of the plasma sheath on antenna radiation, the electron densities and electron collision frequencies along the antenna transmission path (see gray arrows in Figure 1a-c) are illustrated in Figure 2a,b, respectively. The plasma sheath structures enveloping the blunt-coned vehicle and sharp-coned vehicle are clearly presented by the figure. It can be seen that the peak electron density position is 5 cm away from the blunt-coned vehicle wall. The peak electron density for the sharp-coned vehicle is at about 0.5 cm. In addition, the thicknesses of the plasma sheaths are about 20 cm and 4.5 cm. The average electron density for the sharp-coned vehicle is much higher than that for the blunt-coned vehicle. Meanwhile, the order of electron collision frequency magnitude of the plasma sheaths is almost the same, despite there being three peaks in Figure 2a and only one peak in Figure 2b.