Correcting moments of in situ particle distribution functions for spacecraft electrostatic charging

We first introduce previous works on spacecraft electrostatic charging and its effects on particle measurements and the calculation of moments from three‐dimensional distribution functions. We illustrate the fact that the lack of use, or misuse, of Liouville's theorem may lead to misinterpretations and inappropriate corrections to those effects. We emphasize in particular that its appropriate use naturally accounts for what is often called the “sheath focusing effect” in moment calculation. In the case of a “perfect” particle detector we show that there exists a trivial and essentially exact formulation for the calculation of moments of particle distribution functions that accounts for the spacecraft potential and that is particularly useful for onboard moment calculations. The main limitations, but that are not specific to this formulation, are inaccuracies in angle information (from blurring of acceptance angles at low energies or spacecraft‐skimming trajectory effects) and those arising from the detector properties (resolution, cutoffs, photoelectrons, etc.). We discuss this correction in the context of previous works and remind that it primarily affects low‐energy measurements and for populations whose temperature is comparable to the potential. Based on spacecraft observations, we show that this correction is most needed for regimes such as that of solar wind electrons but also for cold ions as often observed, for instance, in the magnetosphere near the Earth's magnetopause. Key Points Introduction of past work on spacecraft potential correction Description of proper method to correct particle moments from spacecraft charging Illustration of the impact of this correction from spacecraft data