Multisatellite MMS Analysis of Electron Holes in the Earth's Magnetotail: Origin, Properties, Velocity Gap, and Transverse Instability

We present a statistical analysis of more than 2400 bipolar electrostatic solitary waves measured aboard at least three MMS spacecraft in the Earth's magnetotail. These bipolar solitary waves are interpreted in terms of electron holes, because of positive electrostatic potentials. The multi- spacecraft interferometry is used to estimate the velocity of propagation of the electron holes and address their origin and properties. The electron hole velocities in the plasma rest frame are in the range from just a few km/s, that is much smaller than ion thermal velocity VTi, up to 20,000 km/s, which is comparable to electron thermal velocity VTe. We argue that fast electron holes with velocities larger than about 0.1 VTe are produced by bump-on-tail instabilities, while the most of slow electron holes with velocities below about 0.05 VTe is predominantly produced by warm bi- stream instabilities. We have identified a gap in the distribution of electron hole velocities between about VTi and 2VTi, which is considered to be an evidence for recently simulated self-acceleration process [Zhou and Hutchinson, 2018] or / and ion Landau damping of electron holes. In accordance with previous measurements, the amplitudes and parallel spatial scales of the electron holes are typically D d| | 10 D and 10-3 Te e0 0.1 Te. We show that electron hole amplitudes are below a threshold of the transverse electron hole instability and highly likely restricted by the nonlinear saturation criterion of electron streaming instabilities seeding electron hole formation. The transverse instability and nonlinear saturation criterion are suggested to restrict electron hole amplitudes as e0 me 2d2| |, where = min(, 1.5 ce), where is the increment of instabilities seeding electron hole formation, while ce is electron cyclotron frequency.