Mathematical modeling of determining the kinetic parameters of charged plasma particles using an insulated probe system in the ionospheric conditions

The goal of this article is to theoretically substantiate the possibility of determining the kinetic parameters of charged particles of the ionospheric plasma by measuring the currents of an insulated probe system in the electron saturation region. Methods of physical modeling, numerical integration of nonlinear differential equations, measurement uncertainty analysis, and computer modeling were used. The probe system consists of cylindrical electrodes: a probe and a reference electrode. The ratio of the reference electrode and the probe areas can be significantly smaller than required by the single cylindrical probe theory. The electrodes are placed transversely in a supersonic free-molecular plasma flow. The charged particle composition of the ionospheric plasma is modeled by positive ions of atomic oxygen and atomic hydrogen and by electrons, which ensure plasma quasi-neutrality. Along with a mathematical model of plasma with two ion species, a model of a one-component plasma is considered with the ion mass selected so that the ion saturation current to the cylinder may be the same for both models. Based on an earlier asymptotic solution for the electron saturation current in a one-component plasma, the kinetic parameters of charged particles (the ion temperature and directed velocity and the electron temperature) were related to the measured probe currents. A numerical and an analytical study of this relationship within the framework of the mathematical model of a plasma with two ion species resulted in analytical expressions for determining the kinetic parameters of charged particles from the measured currents of the insulated probe system in the electron saturation region. The errors of the analytical expressions in determining the kinetic parameters of a plasma with two ion species were estimated numerically and analytically as a function of the probe system’s electrode area ratio and the probe current measurement accuracy. The ranges of the probe system parameters that maximize the measurement reliability in the ionospheric conditions were determined