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.本研究针对地球磁尾中至少3艘磁层多尺度（Magnetospheric Multiscale, MMS）航天器探测到的2400余例双极性静电孤立波开展统计分析。鉴于此类双极性静电孤立波呈现正静电势，故将其归因为电子空穴（electron holes）。本研究采用多航天器干涉测量法估算电子空穴的传播速度，并探究其起源与物理特性。等离子体静止坐标系下的电子空穴传播速度范围为数km/s至20000 km/s：其中低速端仅为数km/s，远低于离子热速度（VTi）；高速端可达20000 km/s，与电子热速度（VTe）相当。本研究认为，传播速度大于约0.1 VTe的高速电子空穴由尾峰不稳定性（bump-on-tail instabilities）激发产生；而绝大多数传播速度低于约0.05 VTe的低速电子空穴，则主要由暖双束流不稳定性（warm bi-stream instabilities）驱动形成。本研究在电子空穴速度分布中发现，在约VTi至2VTi区间存在一处速度间隙，该现象被认为是近期模拟得到的自加速过程[Zhou与Hutchinson, 2018]或电子空穴的离子朗道阻尼（ion Landau damping）的佐证。结合既往探测结果，电子空穴的振幅与平行空间尺度通常满足Δd∥ ≈ 10D 及10^-3 ε0 Δφ ≈ 0.1 T_e。本研究表明，电子空穴的振幅低于横向电子空穴不稳定性（transverse electron hole instability）的阈值，且极有可能受激发电子空穴形成的电子束流不稳定性（electron streaming instabilities）的非线性饱和准则约束。本研究提出，横向不稳定性与非线性饱和准则对电子空穴振幅的约束关系可表示为ε0 m_e (2Δd∥)^2，其中γ = min(γ, 1.5ω_ce)，γ为激发电子空穴形成的不稳定性增长率，ω_ce为电子回旋频率（electron cyclotron frequency）。