Electron Phase-Space Holes in Three Dimensions: Multispacecraft Observations by Magnetospheric Multiscale

Electron phase-space holes are kinetic plasma structures commonly observed in space plasmas on Debye length scales. Near the Earth's duskside flank at 10 Earth radii, a series of 32 electron holes (EHs) are detected within a 1-s window on all four Magnetospheric Multiscale spacecraft. The spacecraft separation of <7 km is similar to the expected EH size in this region. Length, width, amplitude, and relative positions are determined for individual EHs using a cylindrically symmetric model fit to Magnetospheric Multiscale E field measurements. The model shows good agreement with observed E fields far from the EH center. Deviations in E-perpendicular to from the model are present near the center, indicating observed EHs have complex, sometimes irregular, internal structure. Perturbation magnetic fields delta B modeled assuming an E x B-0 electron current reproduce the measured parallel perturbation in most cases, although there is a systematic variation due to geometric and finite gyroradius effects. Many EHs in this event have large amplitude for their size, reaching the theoretical lower limit in length parallel to the background magnetic field, which requires the electron phase-space density to approach 0 in the center. It is possible that EHs of this type have recently formed, eventually weakening or becoming longer over time. This study provides the most detailed measurements of EHs to date. Their derived properties are largely in agreement with expectations from previous research. It remains unclear whether the few notable differences are due to rapid time evolution or are specific to the local environment.