In this study, we developed three computational techniques for the ECE radiation analysis of the Hall thruster.

The first one is the single particle approximation analysis. This is the simplest one among the approaches. We modeled the plasma region of the Hall thruster with three parameters, the magnetic field, electron temperature, and electron density distributions. These parameters are constant in a cell. We calculated the radiation with the parameter distributions according to the observation angle. The frequency of a cell is determined by the magnetic field of the cell. This analysis is easy to approach and does not require a high computing performance. However, the results of this analysis don't have detail results. The radiated electric field is derived from the power, so there is no polarization information on the electric field. We moved on more sophisticated analysis.

The next one is the Particle-In-Cell (PIC) analysis. PIC is for analysis of microscopic phenomena. Particle motions in the thruster channel region is simulated with the PIC method. We selected electrons from the Maxwell-Boltzmann distribution for the speed of electrons. The Monte Carlo method was adopted in this selection. We solved the Lorentz force equation to get the motion data of the electrons and analyzed the radiated electric field with the particle motions. Then, we took the Fourier transform of the electric field to consider the radiation in the frequency domain. This approach is from definition, the radiation is from charge acceleration. It is more realistic approach to the plasma. It uses same parameter distributions, but the parameters in a cell is not constant any more because of adoping the Monte Carlo method. It also shows the polarization information of the radiation. However, we assume in this analysis that the radiation is in free space. The channel plasma is considered as current sources for radiation. The material constants of the plasma is concerned as free space.

The last approach adopted is to consider the non free space and inhomogeneous media. The hybrid FEM/MoM (hybrid element method) was suggested to exploit advantages of finite element method (FEM) and method of moment (MoM), the representative methods for the radiation analysis, and to compensate their disadvantages. The hybrid element method was introduced to analyze the ECE radiation by using EMAP5. In this analysis, the plasma was considered as dielectrics, and the source currents were from the plasma parameters.