Non-uniform electron density estimation based on electromagnetic wave attenuation in plasma

The surface of a high-speed vehicle reentering the atmosphere is surrounded by plasma sheath. Due to the influence of the inhomogeneous flow field around the vehicle, understanding the electromagnetic properties of the plasma sheath can be challenging. Obtaining the electron density of the plasma sheath is crucial for understanding and achieving plasma stealth of vehicles. In this work, the relationship between electromagnetic wave attenuation and electron density is deduced theoretically. The attenuation distribution along the propagation path is found to be proportional to the integral of the plasma electron density. This result is used to predict the electron density profile. Furthermore, the average electron density is obtained using a back-propagation neural network algorithm. Finally, the spatial distribution of the electron density can be determined from the average electron density and the normalized derivative of attenuation with respect to the propagation depth. Compared to traditional probe measurement methods, the proposed approach not only improves efficiency but also preserves the integrity of the plasma environment.