Study of the characteristics of electron firehose unstable conditions in the terrestrial magnetotail plasma sheet

Electron firehose instabilities can be excited at dipolarization fronts and in the magnetic reconnection outflow in the terrestrial magnetotail, but their occurrence rate in the plasma sheet is unclear. Here, we investigate the characteristics of electron firehose unstable conditions in the magnetotail plasma sheet based on observations of the Magnetospheric Multiscale mission. We find an Alfvénic magnetic field fluctuation accompanied by a strong field-aligned current during a flapping motion. This fluctuation occurs where the local plasma is electron firehose unstable, indicating that the electron firehose instability in the plasma sheet can occur in the region besides dipolarization fronts and magnetic reconnection outflow. We statistically find that the local plasma near the neutral sheet has a small probability with the maximum value <1.4% to be electron firehose unstable, which mainly occurs in the central plasma sheet with B XY /B L < 0.3. The maximum probability of T ef > 0 (electron firehose unstable condition) is ∼1.36% (1.32%) at B XY /B L ≈ 0.05 (0.15) during fast (non-fast) flows. During fast flows, the plasma near the neutral sheet tends to have a higher probability of T ef > 0 when the local V T is larger. During non-fast flows, the plasma near the neutral sheet tends to have a higher probability of T ef > 0 when T e is larger. The probability of T ef > 0 shows a dawn-dusk asymmetry during fast flows and non-fast flows. In addition, the probability of T ef > 0 during fast flows tends to be larger when the ambient B Z is weak, which shows opposite characteristics during non-fast flows. These findings help to assess the importance of the role of electron firehose instabilities in the magnetotail plasma sheet.