Deriving plasma densities in tenuous plasma regions, with the spacecraft potential under active control

Variations of the floating potential on spacecraft are often used to derive plasma densities, complementing the plasma instrument measurements. All spacecraft of the Cluster mission are equipped with Active Spacecraft Potential Control (ASPOC) instruments that control the spacecraft potential. Although the ASPOC operation increases the accuracy of electric field and plasma measurements, it prevents a direct use of the spacecraft potential variations to derive plasma densities. In this work we develop a new reconstruction method of uncontrolled spacecraft potential from controlled spacecraft potential data and a derived photoelectron curve, using multispacecraft observations. We assume that the same curve governs the plasma environment for the spacecraft with ASPOC on and off. The current work focuses on reconstructions in the magnetotail region. The period that was more extensively studied was the one from August to October 2003, when the spacecraft were close to each other, while results from the periods of August-October 2001, 2002, and 2004, when the Cluster spacecraft had their apogee in the magnetotail region, are also presented. In this way, we investigate how the photoelectron curve varies at different time intervals and also how the reconstruction results are modified when the distance between the spacecraft is increasing. Finally, by using the reconstructed results, we proceed by estimating the plasma densities and we discuss the uncertainties of such estimations. While, on average, spacecraft potential measurements are successfully reconstructed, plasma and solar activity variations on short timescales seem to affect the reconstructions, requiring in some cases more detailed analysis in order to achieve results with higher accuracy. Moreover, there are some limitations while deriving results in very tenuous plasma regions due to increased uncertainties in some of the scientific measurements used there. The results and the methods developed for this work can be applied for any other current and future mission with instruments that control the spacecraft potential, such as the recently launched Magnetospheric Multiscale Mission.