Derivation of Ambient Electron Density Using Spacecraft Potential Measurements From the MMS and Van Allen Satellites: Application to the Plasmasphere

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Abstract
We investigate the empirical relationship between the spacecraft potential ( V s ) measured by the Electric Field Double Probes, and the electron density ( N e ) measured by the Fast Plasma Instrument on the MMS spacecraft. We derive their relationship during fast‐mode intervals when the Active Spacecraft Potential Control Devices are off. Then we apply this relationship to slow‐mode intervals during the perigee passes where V s can be less than +2 V and N e can exceed 1,000 cm −3 . Because such a parameter range is never observed by MMS during fast‐mode intervals, we define this part of the relationship using simultaneous observations from the Van Allen mission where N e is measured up to 3,000 cm −3 while V s is less than +2 V. We compare the empirical relationship to the predictions by an orbital motion limited theory. This suggests how to model the photoelectron current above +5 V and the collection of ambient electrons for moderate Debye lengths. We apply the empirical relationship (i.e., theoretical curves are not used here) to several consecutive plasmapause crossings by MMS during two magnetic storms. The erosion rates of the plasmasphere were ∼60 cm −3 /day at 7 MLT and ∼30 cm −3 /day at 14 MLT. In the duskside, the erosion rate decreases with L due to increasing flux tube volumes, being about 10–20 cm −3 /day at L ∼ 7. The refilling rates are similar to the erosion rates, but in the dawnside, the refilling is delayed due to a slow expansion of the plasmapause to higher L .

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