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 is considered, bypassing the calculation of the main plasma processes in SPT. It turns out that under certain conditions – setting the output parameters along the SPT axis and plasma incompressibility, this is possible. 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. The convergence of successive approximations, the uniqueness theorem are proven and the matrix Green function is constructed. The results of calculations are presented, demonstrating the operability of the mathematical model.