Deriving the Ionospheric Electric Field From the Bulk Motion of Radar Aurora in the E-Region

In the auroral E-region strong electric fields can create an environment characterized by fast plasma drifts. These fields lead to strong Hall currents which trigger small-scale plasma instabilities that evolve into turbulence. Radio waves transmitted by radars are scattered off of this turbulence, giving rise to the ‘radar aurora’. However, the Doppler shift from the scattered signal does not describe the F-region plasma flow, the $E\times B$ drift imposed by the magnetosphere. Instead, the radar aurora Doppler shift is typically limited by nonlinear processes to not exceed the local ion-acoustic speed of the E-region. This being stated, recent advances in radar interferometry enable the tracking of the bulk motion of the radar aurora, which can be quite different and is typically larger than the motion inferred from the Doppler shift retrieved from turbulence scatter. We argue that the bulk motion inferred from the radar aurora tracks the motion of turbulent source regions (provided by auroras). This allows us to retrieve the electric field responsible for the motion of field tubes involved in auroral particle precipitation, since the precipitating electrons must $E\times B$ drift. Through a number of case studies, as well as a statistical analysis, we demonstrate that, as a result, the radar aurora bulk motion is closely associated with the high-latitude convection electric field. We conclude that, while still in need of further refinement, the method of tracking structures in the radar aurora has the potential to provide reliable estimates of the ionospheric electric field that are consistent with nature.