The impact force acting on a flat plate exposed normally to a rarefied plasma plume issuing from an annular or circular nozzle

Abstract

With the indirect thrust measurement of electric thrusters working at a low vacuum chamber pressure as the research background, this paper analyses the impact force acting on a flat plate exposed normally to a rarefied plasma plume issuing from a thruster with an annular or circular exit section for the free-molecule flow regime (at large Knudsen numbers). The constraint relation proposed by Cai and Boyd (2007 J. Spacecr. Rockets 44 619, 1326) about the velocity components of gas particles leaving a location on the nozzle exit section and arriving at a given spatial point outside the nozzle has been employed here to derive the analytical expressions for calculating the impact force. Sample calculation results show that if the flat plate is sufficiently large, the impact force acting on the flat plate calculated for the case without accounting for gas particle reflection at the plate surface agrees well with the axial momentum flux calculated at the thruster exit or the theoretical thrust force of the studied thruster, while accounting for the contribution of gas particles reflected from the plate surface to the impact force production may significantly increase the calculated impact force acting on the flat plate. For a Hall-effect thruster in which the thrust force is dominantly produced by the ions with high directional kinetic energy and the ions are not directly reflected from the plate surface, the contribution to the impact force production of atom species and of gas particles reflected from the plate surface is negligibly small and thus the measured axial impact force acting on a sufficiently large plate can well represent the thrust force of the thruster. On the other hand, if the contribution of the gas particles reflected from the plate surface to the impact force production cannot be neglected (e.g. for the electric thrusters with comparatively low thruster exit temperatures), appreciable error would appear in the indirect thrust measurement.