Some mathematical questions of plasma ionization

A number of mathematical problems of the theory of ionization in relation to processes in stationary plasma thrusters (SPT) are solved in this work. Two main one-dimensional mathematical models of ionization are considered – hydrodynamic and kinetic. The main question is the existence of ionization oscillations (breathing modes). On the basis of a hydrodynamic model, a boundary value problem for stationary ionization equations is solved. Its unique solvability and the absence of breathing modes are proved. In the case when the ion velocity in the flow region has a single zero with a positive derivative, it is proved that the stationary boundary value problem has a countable number of solutions, and a necessary and sufficient condition for the existence of breathing modes is formulated. Finally, an analytical solution of the ionization equations is given in the case of constant velocities of atoms and ions, and the formulas obtained are applied to the solution of the Cauchy problem, boundary value and mixed problems in the simplest regions. In the case of the kinetic model of ionization, the existence of breathing modes is numerically shown and the results obtained are compared with the hydrodynamic case.

ПРОФІЛОМЕТРІЮВАННЯ КРОМОК РОЗРЯДНОЇ КАМЕРИ СТАЦІОНАРНОГО ПЛАЗМОВОГО ДВИГУНА

The effectiveness of stationary plasma thrusters was proved by many years of experience of their on board operation on various spacecraft especially on geostationary orbits. One of the main factors that affects the duration of the SPT operation time is the lifetime of the edges of the discharge chamber walls. One of the factors affecting the discharge chamber lifetime is the erosion of the edges of the insulators. Ceramic wear is cause by the destruction of the high-energy ion flow that takes place in thruster plasma.Theoretical study of the processes of discharge chamber insulators sputtering still does not allow mathematically determining the rate of development of the ceramic edges erosion processes with the necessary accuracy that is required for the SPT lifetime forecast. That is why all the researches require a full-scale testing of the thruster on a long time trial basis with subsequent measurements of the insulators value of erosion.In this paper, several methods for measuring the degree of insulators wear are considered. The analysis of the method for measuring the thickness of the ends of discharge chamber insulators was carried out, followed by the determination of radial erosion. It has been shown that this method is the most suitable for non-separable constructions of SPT due to the high accuracy of the measurements and its simplicity.A method for noncontact profilometry of the edges of thruster discharge chamber insulators was proposed. The use of a non-contact method allows measurements to be carried out, excluding the possibility of any deformations to the surface of insulators. Measurements were provided with the help of modern metallographic microscope. Advantages and disadvantages of the methodology are shown. The analysis of the factors that influences the error during measurements of the ceramic profile is carried out.A method is proposed for contact profilometry of the edges of thruster discharge chamber insulators. Advantages and disadvantages of the methodology are shown. The results of measurements of the profile of the two thrusters with the construction differences are provided.

Experimental Investigations of a Krypton Stationary Plasma Thruster

Stationary plasma thrusters are attractive electric propulsion systems for spacecrafts. The usual propellant is xenon. Among the other suggested propellants, krypton could be one of the best candidates. Most studies have been carried out with a Hall effect thruster previously designed for xenon. The ATON A-3 developed by MSTU MIREA (Moscow) initially defined for xenon has been optimized for krypton. The stable high-performance ATON A-3 operation in Kr has been achieved after optimization of its magnetic field configuration and its optimization in different parameters: length and width of the channel, buffer volume dimensions, mode of the cathode operation, and input parameters. For a voltage of 400 V and the anode mass flow rate of 2.5 mg/s the anode efficiency reaches 60% and the specific impulse reaches 2900 s under A-3 operating with Kr. The achieved performances under operation A-3 with Kr are presented and compared with performances obtained with Xe.