# Effect of Terahertz Antenna Radiation in Hypersonic Plasma Sheaths with Different Vehicle Shapes
## 5 Analysis and Discussion  
Previous research has revealed that the plasma sheath can impact the electromagnetic wave propagation, which can result in antenna performance changes. In this study, the coupling of the antenna and plasma shows that radiation performance is worsened compared with performance in vacuum. However, the study focuses on the radiation performance in plasma sheaths of two different vehicle shapes: the blunt-coned shape and the sharp-coned shape. Different vehicle shapes lead to different plasma sheath distributions. The antenna mounted on the sharp-coned vehicle has better radiation performance than the same antenna mounted on the blunt-coned vehicle. According to the results in Figures 1 and 2, the main differences between the two plasma sheaths are plasma thickness, electron distribution, and electron collision frequency distribution. The three parameters reflect different relative permittivity distributions.  
It can be seen from Equation (1) that plasma relative permittivity consists of the real part and the imaginary part. The real part of relative permittivity is related to refraction and reflection. The ratio of the real part to the imaginary part is related to plasma dielectric loss. In this study, according to Equation (1), the imaginary part of relative permittivity is small. Compared with the influence of refraction and reflection, dielectric loss in plasma can be ignored. According to Figure 2, in the two plasma sheath distributions, the real part of the relative permittivity along the transmission path decreases from an initial value to a minimum, and then increases to 1 (the relative permittivity of neutral air). The minimum value difference of relative permittivity in the two situations, which is mainly decided by peak electron density, is small. Therefore, the main character that influences the antenna gain should be plasma thickness, and larger plasma thickness leads to lower antenna performance. This can explain the phenomenon that antenna mainlobe gain in the blunt-coned vehicle plasma is much lower than in the sharp-coned vehicle plasma.  
In addition, it should be noticed that the plasma layers corresponding to different orders of magnitude of electron density are not parallel to the vehicle wall in Figure 1a. Since plasma is a dispersive medium, the plasma distribution can form a lens-like structure and refract the antenna radiation lobe. However, the layers for the sharp-coned vehicle are parallel to the wall. In such a case, the radiation direction shift in the blunt-coned vehicle plasma can be explained.  
The results reveal that the sharper vehicle can lead to a smaller plasma sheath thickness and less impact on antenna performance. However, the sharper nose result in higher plasma electron density, which leads to a higher plasma cut-off frequency. The antenna can  
Figure 5: **(a)**: The signal attenuation in the plasma sheath of the blunt coned vehicle and the electron density distribution for blunt coned vehicle along the propagation path. **(b)**: The signal attenuation in the plasma sheath of the sharp coned vehicle and electron density distribution for the sharp coned vehicle along the propagation path.  
only perform well when the operating frequency is higher than the plasma sheath cut-off frequency. In such cases, the antenna should be designed to operate at a higher frequency. Nevertheless, for a specific communication system, the maximum operation frequency is fixed. Overall, the shape of the vehicle should be designed based on the actual demand. The shape of the vehicle should be as sharp as possible with the condition that the onboard antenna operation frequency is higher than the plasma sheath cut-off frequency.