A simple mathematical model for calculating the output parameters of a stationary plasma thruster

The mathematical model allowing to calculate the output parameters of plasma in SPT – azimuthal and longitudinal currents and velocities, radial distribution of temperatures and pressures of electrons and ions, thrust force and magnetic field is considered. The model is constructed under certain conditions, namely the establishment of output parameters along the SPT axis and plasma incompressibility. The determining factors underlying the proposed approach are the two-fluid nature of plasma, including full consideration of the electron inertia, and dissipative processes – magnetic and hydrodynamic viscosities of electrons and ions, thermal conductivity of plasma and temperature relaxation. Mathematically, the calculation of the output diagrams is reduced to solving a boundary value problem for a certain linear system of ODE of the 8th order with variable coefficients on the segment. The paper proposes two methods of successive approximations for the numerical solution of the obtained boundary value problem. A sufficient condition for the convergence of successive approximations to the exact solution is given and the mathematical properties of the main system of equations (uniqueness theorem, Green's function, compactness of the inverse operator) are briefly analyzed. The results of calculations are presented, demonstrating the operability of the mathematical model.