Mathematical Model of the On-Board Antenna of Reentry Spacecraft Taking into Account Surface Waves

Introduction. The onboard antennas of the returned hypersonic aircraft are weakly directional, which is achieved by radiation from the open end of the waveguide. When passing through dense layers of the atmosphere, they are exposed to aerodynamic heating, for protection from which a heat-resistant radio-transparent thermal protection is used. The case of uniform thermal protection of the antenna can be interpreted as the absence of heating or heating uniform in the thickness of the thermal protection.Aim. The problem of obtaining an analytical description of the radiation characteristics of a circular waveguide closed by a flat homogeneous dielectric plate is solved. Since in such a formulation it is necessary to consider the resonant domain, a strict solution of Maxwell's equations is required.Materials and methods. Of the known analytical methods of solution, it is possible to use the method of integral transformations and the method of eigen functions. Both of these methods are used in the work. In this case, the assumption is used that the electrical parameters of the dielectric plate (thermal protection) and the geometric dimensions do not depend on time.Results. The relations describing the directional pattern of a circular waveguide with dielectric thermal protection and taking into account the electrical parameters of thermal protection and its thickness are obtained. Expressions are also obtained for the fields of lateral, surface and outflow waves, from which it is possible to calculate the power output by these fields. Relations for the separation of singular points of integrand expressions into poles corresponding to surface, outflow and lateral waves are obtained. Surface, outflow and lateral waves can have a certain effect on the radiation pattern. To determine this conclusion, analytical relations are obtained for determining the poles of integrand expressions that fully describe surface, outflow and side waves. All the analytical results obtained correspond to Numerical calculations were carried out on some of the obtained ratios.Conclusion. The results showed that the power of the side waves is zero. It also follows from the calculations carried out that there is no radiation field of surface and outgoing waves, i.e. there is no contribution of them to the radiation pattern.