From a survey of the first nightside season of NASA's Van Allen Probes mission (December 2012 to September 2013), 47 energetic (tens to hundreds of keV) electron injection events were found at L shells ≤ 4, all of which are deeper than any previously reported substorm‐related injections. Preliminary details from these events are presented, including how all occurred shortly after dipolarization signatures and injections were observed at higher L shells, how the deepest observed injection was at L ~ 2.5, and, surprisingly, how L ≤ 4 injections are limited in energy to ≤250 keV. We present a detailed case study of one example event revealing that the injection of electrons down to L ~ 3.5 was different from injections observed at higher L and likely resulted from electrons interacting with a fast magnetosonic wave in the Pi2 frequency range inside the plasmasphere. These observations demonstrate that injections occur at very low L shells and may play an important role for inner zone electrons.

[1] The theory of plasma transport in Earth's plasma sheet depends critically on the entropy parameter PV 5/3 , where P is particle pressure and V is the volume of a closed flux tube containing one unit of magnetic flux. Theory suggests that earthward moving flow bursts that inject plasma into the inner magnetosphere consist of flux tubes that have PV 5/3 values that are lower than those of neighboring slow-moving flux tubes. However, there is no way to measure flux tube volume from one spacecraft or a small number of spacecraft. We propose a formula for estimating local PV 5/3 from a single spacecraft in the plasma sheet based on a simple two-dimensional analytic model of plasma in force equilibrium, with some parameters set from local measurements at a spacecraft and other parameters set to fit a series of equilibrated Tsyganenko models. To gain an idea of the expected error, the resulting formula is then tested against various relaxed Tsyganenko models, an equilibrium magnetic field/plasma model with a depleted channel and also a thin-filament MHD calculation. The formula is used to estimate the entropy parameter of flux tubes injected in two substorms, using spacecraft measurements near X = À10 R E in the central plasma sheet.

[1] We simulate plasma transport from the plasma sheet to the ring current, for the first time including the feedback effect of the drifting particles on both the electric and magnetic fields. Results suggest that strong, steady adiabatic convection throughout the middle plasma sheet leads to a highly stretched inner plasma sheet, but no ring current particle flux increases. We subsequently impose a substantial reduction of the specific entropy PV 5/3 near midnight outside 10 R E , where P is particle pressure and V = R ds/B is flux tube volume. This produces a strong enhancement of the asymmetric ring current, which becomes symmetric when the pressure depletion and strong convection are quelled. We suggest that a reduction of the specific entropy in a region of the inner plasma sheet, apparently by some process that violates the assumption of adiabatic drift, plays a major role in the injection of a storm-time ring current.

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[1] We describe a method to compute three-dimensional force equilibria in the Earth's magnetosphere. The method is embodied in a code called the MagnetoFriction code which solves a set of ideal magnetohydrodynamic (MHD) equations that are modified to include a frictional dissipation term in the momentum equation. The friction takes the form of a force which is directed against the fluid motion and is therefore an energy sink. This allows the system to settle into a minimum energy equilibrium. A nonuniform cartesian grid is used along with initial conditions supplied by empirical magnetic field and pressure models. These initial conditions do not, in general, satisfy the force balance conditioñ J ÂB ¼ r p , and the code must iterate until approximate force balance is achieved. Pressure and magnetic field solutions are presented for several different configurations of the magnetosphere.