# Propagation Characteristics of Modulated EHF Signal in the Wake Region of Plasma Sheath
## 2 Characteristics of EHF Wave in Plasma Sheath  
### Analysis Method  
In this paper, the propagation characteristics of EHF signals in the plasma sheath of a blunt-coned hypersonic vehicle were studied using a one-dimensional plate model. The plasma sheath model used here was the same as in the article [11]. For the shape and the size of the spacecraft, we adopted the parameters of the spacecraft in the RAM C-II experiment; that is, the radius of the sphere in the front of the aircraft is 15.24 cm, the half angle of the cone is 9\({}^{\circ}\), and the length is 1.295 m. RAM series flight experiments are one of the most important experiments with which to study the \"black out\" problem in the history of aerospace. The parameters and data of RAM C-I and RAM C-II experiments have been published for a long time and are frequently cited [1; 34]. The flying altitude of the spacecraft was set to 31 km, which is the most serious altitude of \"blackout\" in an RAM C-II test [13]. The flight speed was set to 6550 m/s, which was the same as that of RAM C-II reentry vehicle, at an altitude of 31 km. In addition, the plasma sheath is obviously influenced by the atmospheric conditions around the hypersonic vehicle. The atmospheric condition used in this paper was obtained from the NRLMSISE00 model, which is an empirical atmospheric model available online. In addition, for the antenna location, because there will be turbulent structures near the center of the wake or the edge of the bottom, which will seriously affect the communication stability, the antenna can only be placed between the wake center and the edge of the bottom. For the channel angle, if the inclination angle is too large, an increase in the transmission path will cause strong total signal attenuation, and if the inclination angle is too small, there will be large polarization loss on the antenna. Therefore, the selected channel angle must also be moderate. In general, the selection of the simulation parameters is used to obtain the optimal communication scheme. It is assumed that the antenna is installed at the tail of vehicle (see point A in Figure 1) and that the signal path is inclined outward. Point B represents the side signal incidence position. Figure 1 shows only half of the plasma sheath since the angle of attack is set to 0\({}^{\circ}\)and the plasma sheath is symmetrical. The symmetry axis of the vehicle is selected as the X axis and the vehicle vertex coordinates and antenna coordinates are set to (0, 0) and (\(-\)1.295, 0.27), respectively. The half cone angle of the blunt cone hypersonic vehicle is 9\({}^{\circ}\). The color axis represents the electron density. In Figure 1b, the channels in the wake region of the plasma sheath are identified as 1-6, respectively. The angles between channels 1 and 6 and the tail of the vehicle are: 32\({}^{\circ}\), 36\({}^{\circ}\), 44\({}^{\circ}\), 48\({}^{\circ}\), 56\({}^{\circ}\), and 58\({}^{\circ}\), respectively. The propagation characteristic parameters are obtained by the following method. First of all, it should be noted that it is very difficult to determine the optimal incidence angle because the signal can only adopt oblique incidence in tail communication. Here, we used the refraction law under approximate conditions to determine the incident angle before carrying out scattering matrix method (SMM) analysis. Assuming that the signal propagation path between point A and point B is a straight line, the refraction angle \(\gamma\) on the sheath boundary will be approximately 9\({}^{\circ}\) (half cone angle of the blunt cone hypersonic vehicle) greater than angle \(\alpha\) (angle between the channel and the tail of the vehicle). Then, the incident angle \(\beta\) on the sheath boundary can be deduced from the angle \(\gamma\) by using the refraction law. Moreover, the incident angle \(\theta_{\rm i}\) in the SMM calculation coordinate system can be obtained by Formula (1).