Multi-satellite MMS analysis of electron holes in the Earth's magnetotail: origin, properties, velocity gap and transverse instability

Abstract:

We present a statistical analysis of more than 2400 electrostatic solitary waves interpreted as electron holes (EH) measured aboard at least three MMS spacecraft in the Earth's magnetotail. The velocities of EHs are estimated using the multi-spacecraft interferometry. The EH velocities in the plasma rest frame are in the range from just a few km/s, that is much smaller than ion thermal velocity $V_{Ti}$, up to 20,000 km/s, which is comparable to electron thermal velocity $V_{Te}$. We argue that fast EHs with velocities larger than about 0.1$\;V_{Te}$ are produced by bump-on-tail instabilities, while slow EHs with velocities below about 0.05$\;V_{Te}$ can be produced by warm bi-stream and, probably, Buneman type instabilities. We show that typically fast and slow EHs do not co-exist, indicating that the instabilities producing EHs of different types operate independently. We have identified a gap in the distribution of EH velocities between $V_{Ti}$ and $2V_{Ti}$, which is considered to be the evidence for self-acceleration [Zhou and Hutchinson, 2018] or ion Landau damping of EHs. Parallel spatial scales and amplitudes of EHs are typically between $\lambda_{D}$ and 10 $\lambda_{D}$ and between $10^{-3}\;T_{e}$ and $0.1\;T_{e}$, respectively. We show that electrostatic potential amplitudes of EHs are below the threshold of the transverse instability and highly likely restricted by the nonlinear saturation criterion of electron streaming instabilities seeding electron hole formation: $e\Phi_0\lesssim m_{e}\varpi^2d_{||}^2$, where $\varpi={\rm min} (\gamma,1.5\;\omega_{ce})$, where $\gamma$ is the increment of instabilities seeding EH formation, while $\omega_{ce}$ is electron cyclotron frequency. The implications of the presented results are discussed.