Extensive electron transport and energization via multiple, localized dipolarizing flux bundles

Using an analytical model of multiple dipolarizing flux bundles (DFBs) embedded in earthward traveling bursty bulk flows, we demonstrate how equatorially mirroring electrons can travel long distances and gain hundreds of keV from betatron acceleration. The model parameters are constrained by four Time History of Events and Macroscale Interactions during Substorms satellite observations, putting limits on the DFBs' speed, location, and magnetic and electric field magnitudes. We find that the sharp, localized peaks in magnetic field have such strong spatial gradients that energetic electrons ∇ B drift in closed paths around the peaks as those peaks travel earthward. This is understood in terms of the third adiabatic invariant, which remains constant when the field changes on timescales longer than the electron's drift timescale: An energetic electron encircles a sharp peak in magnetic field in a closed path subtending an area of approximately constant flux. As the flux bundle magnetic field increases the electron's drift path area shrinks and the electron is prevented from escaping to the ambient plasma sheet, while it continues to gain energy via betatron acceleration. When the flux bundles arrive at and merge with the inner magnetosphere, where the background field is strong, the electrons suddenly gain access to previously closed drift paths around the Earth. DFBs are therefore instrumental in transporting and energizing energetic electrons over long distances along the magnetotail, bringing them to the inner magnetosphere and energizing them by hundreds of keV.