Numerical mathematical model for calculating ion density in the gas-discharge chamber of a radio-frequency ion thruster

Abstract

The mathematical model for calculation of the ion density in the gas-discharge chamber of a radio-frequency ion thruster is developed. The model is based on the assumption of higher potential of the central plasma volume comparing to the chamber walls due to higher mobility of electrons. Firstly, the initial approximation for the plasma potential is set and parameters of the ion trajectories in quasistationary electric field are computed. Then, from the assumption of keeping the total ion flow for each trajectory, the ion density is computed as well as the next approximation for plasma potential. The computation is performed iteratively until the change in the ion density is less than the predefined small value. The model was verified by comparing the results of numerical simulation with the analytical solution for spherical volume. The high accuracy of the numerical model is shown. Also, the ion density in the discharge chamber of a radio-frequency ion thruster was calculated with the uniform distribution of neutral atom density and coefficient of ionization rate. It was shown that at such conditions the ion density has a maximum in central part of the discharge chamber and it decreases towards the walls.