Modelling Electrostatic Sheath Effects on Swarm Electric Field Instrument Measurements

The Electric Field Instrument (EFI) was designed to measure ionospheric ion flow velocities, temperatures and distribution functions at the ram face of the European Space Agency’s Swarm spacecraft. These flow velocities, combined with the known orbital velocity of the satellite and local magnetic field, will be used to infer local electric fields from the relation E=?v×B. EFI is among a class of many particle sensors and flow meters mounted on satellites to monitor in situ plasma conditions. The interpretation of the measurements made with EFI and similar sensors relies on a spacecraft sheath model. A common approach, valid in the relatively cold and dense ionospheric plasma, is to assume a potential drop in a thin sheath through which particle deflection and energisation can be calculated analytically. In such models, sheath effects only depend on the spacecraft floating potential, and on the angle of incidence of particles with respect to the normal to the surface. Corrections to measurements are therefore local as they do not depend on the geometry of nearby objects. In an actual plasma, satellites are surrounded by electrostatic sheaths with a finite thickness. As a result, local corrections to particle distribution functions can only be seen as an approximation. A correct interpretation of measured particle fluxes or particle distribution functions must, at least in principle, account for the extent and shape of the sheath in the vicinity of the measuring instrument. This in turn requires a careful analysis of the interaction of the satellite with the surrounding plasma, while accounting for detailed aspects of the geometry, as well as for several physical effects. In this paper, the validity of the thin sheath model is tested by comparing its predictions with detailed PIC (Particle In Cell) calculations of satellite-plasma interaction. Deviations attributed to sheath finite thickness effects are calculated for EFI measurements, with representative plasma parameters encountered along the planned Swarm orbit. Finite thickness effects of the plasma sheaths are found to induce EFI velocity measurement errors not exceeding 37 m/s, with larger errors occurring in plasmas that are simultaneously tenuous (10⁹ m^?3 or lower) and warm (0.5 eV or higher).