Electron motion and acceleration in magnetic flux ropes produced by magnetic reconnection in quasi-parallel shocks

In the Earth's bow shock, magnetic reconnection can occur in the shock transition and downstream regions, and many magnetic flux ropes are produced. We discuss electron motion and acceleration in these flux ropes, based on results obtained by theory and 2D particle-in-cell (PIC) simulations. In 2D PIC simulations where the parameters are consistent with a quasi-parallel Earth's bow shock, electron temperature becomes significantly large inside the flux ropes, and the electron energy distribution shows a power-law with an index of 6. 

We analyze the motion of an electron trapped in a flux rope that is moving in a certain direction. We derive a drift motion due to the magnetic field gradient in the flux rope, showing that the drift speed is much larger than the grad-B drift. However, we show that the combination of this drift motion and the gyromotion does not contribute to energize the electron at all. We also show that the work done by the ExB drift and the motional electric field can be canceled out with the work done by the non-ideal electric field. As a result, the work done by the Hall electric field and the in-plan velocity can become the most dominant source of the energization, when the island is moving. 

The simulation shows that almost half of the most energetic group of electrons can be explained by the Hall field acceleration. We also discuss the production of power law spectrum with this mechanism.