Statistical characterization of the growth and spatial scales of the substorm onset arc

We present the first multievent study of the spatial and temporal structuring of the aurora to provide statistical evidence of the near-Earth plasma instability which causes the substorm onset arc. Using data from ground-based auroral imagers, we study repeatable signatures of along-arc auroral beads, which are thought to represent the ionospheric projection of magnetospheric instability in the near-Earth plasma sheet. We show that the growth and spatial scales of these wave-like fluctuations are similar across multiple events, indicating that each sudden auroral brightening has a common explanation. We find statistically that growth rates for auroral beads peak at low wave number with the most unstable spatial scales mapping to an azimuthal wavelength λ≈ 1700-2500 km in the equatorial magnetosphere at around 9-12 R_E . We compare growth rates and spatial scales with a range of theoretical predictions of magnetotail instabilities, including the Cross-Field Current Instability and the Shear Flow Ballooning Instability. We conclude that, although the Cross-Field Current instability can generate similar magnitude of growth rates, the range of unstable wave numbers indicates that the Shear Flow Ballooning Instability is the most likely explanation for our observations.