Stability Analysis of Interchange-Stable Plasma Sheet to ExB Shear Flow
at Substorm Onset
Abstract
The shear flow-interchange instability is proposed as the initiating
mechanism behind substorm onset. ULF waves occurring within minutes of
substorm onset are observed in the magnetotail at frequencies similar to
those of the auroral beads, which are a result of a near-earth
magnetospheric instability initiating current disruption in the plasma
sheet. Growth rates were statistically determined as a function of
wavenumber by Kalmoni et al. (2015) using ASI data from a set of
substorm events. The RCM-E provides growth phase-evolved runs of
background fields for stability analysis of a magnetospheric wave
equation for shear flow-interchange modes derived in Derr et al. (2019),
from which growth rates and dispersion relations can be calculated for
comparison with the statistically-determined growth rates and
frequencies of the beads. In the plasma sheet, interchange and shear
flow represent a competition between Kelvin-Helmholtz instability and
overall interchange stability. On average, flux-entropy increases with
radial distance. As the growth phase proceeds, the middle plasma sheet
becomes nearly interchange stable, but flux-entropy decreases sharply at
the inner edge. Destabilizing shear is weak in the middle of the sheet
but quite strong in the SAPS region, earthward of the inner edge. We
examine the conditions under which shear can overwhelm interchange
stability to trigger instability. Instability phenomenology will be
discussed in detail, including discussion of Doppler-resonance structure
and a dimensionless parameter W* for characterizing stability domains.
Mapping spatial properties to the ionosphere along field lines allows
for comparison of instability wavelengths with those of the auroral
beads. All substorms terminate in relaxation, either because higher
order nonlinearities ultimately suppress growth or due to external
conditions which alter the background fields to suppress nonlinear
growth. If higher order amplitude expansion terms contribute negatively
at some order, then nonlinear relaxation occurs, and a method for
determining field saturation values is established.