Shear flow instabilities in the Earth's magnetotail
Abstract
Shear flow instability is studied in the Earth's magnetotail by treating plasma as compressible. A dispersion relation is derived from the linearized MHD equations using the oscillating boundary conditions at the inner central plasma sheet/outer central plasma sheet (OCPS) interface and OCPS/plasma-sheet boundary layer (PSBL) interface, whereas the surface-mode boundary condition is used at the PSBL/lobe interface. The growth rates and the real frequencies are obtained numerically for near-Earth (∣<i>X</i>∣~10–15 <i>R<sub>E</sub></i>) and far-Earth (∣<i>X</i>∣~100 <i>R<sub>E</sub></i>) magnetotail parameters. The periods and wavelengths of excited modes depend sensitively on the value of plasma-sheet half thickness, <i>L</i>, which is taken as <i>L</i>=5 <i>R<sub>E</sub></i> for quiet time and <i>L</i>=1 <i>R<sub>E</sub></i> for disturbed time. The plasma-sheet region is found to be stable for constant plasma flows unless <i>M<sub>A3</sub></i>>1.25, where <i>M<sub>A3</sub></i> is the Alfvén Mach number in PSBL. For near-Earth magnetotail, the excited oscillations have periods of 2–20 min (quiet time) and 0.5–4 min (disturbed time) with typical transverse wavelengths of 2–30 <i>R<sub>E</sub></i> and 0.5–6.5 <i>R<sub>E</sub></i>, respectively; whereas for distant magnetotail, the analysis predicts the oscillation periods of ~8–80 min for quiet periods and 2–16 min for disturbed periods.
