Compromise kinetic-fluid model of electrons dynamics in electric propulsion devices with closed electrons drift as an alternative to the hybrid PIC-Fluid method

Abstract

Electric propulsion devices with closed electron drift include Hall effect thrusters, plasma-ion thrusters with a radial magnetic field, and helicon thrusters, which are sources of plasma, ions, and electrons. Within the framework of the hybrid PIC-Fluid method for calculating a Hall effect thruster, which has been actively replicated in recent decades, the level of detail in the PIC unit does not correspond to the criterion of substance continuity, and the fragmentary set of equations in the Fluid unit does not contain several terms necessary for the calculation and indicates a profound misunderstanding of the origin and limits of applicability of the equations and the true nature of the processes. The calculation of ionization characteristics, the height of the potential barrier at the plasma boundary, the electrons and ions, and their energy fluxes to the surface of the thruster chamber is carried out using a Maxwell distribution, the conditions for the formation of which did not correspond to the realities in the rarefied plasma of electric propulsion devices. The closeness of the calculated integral characteristics to the measured ones is achieved using empirical coefficients with a difference of tens of times in different publications with a complete inability to predict the characteristics of samples of electric propulsion devices that have not yet been developed and tested. In this paper, a compromise method is proposed, the possibility of which is due to the closeness of the electron velocity distribution to isotropic due to the influence of a strong magnetic field and non-specular reflection of electrons from the potential barrier at the plasma boundary. The method operates with the angular moments of the distribution function without integrating the components of the kinetic equation by the velocity module. To calculate the densities of mass, momentum, energy, and their fluxes considering dissipative processes, it is sufficient to determine the angular moments of the second and third orders, the traces of which include the moments of the zero and first orders, respectively. Equations of angular moments are given as intermediates between the kinetic equation and the velocity distribution function moments equations. The expansion of the velocity distribution function in a series of angular moments is recorded. Calculations have been performed that show sufficient agreement with the known measurement results and a significant difference in the characteristics of the Langmuir layer and plasma at the boundary with it from those found using the Maxwell distribution. The use of the obtained results allows us to significantly increase the accuracy of predicting the thruster parameters and thereby reduce the volume of costly experiments to optimize their characteristics.