A long-standing problem in the study of space and astrophysical plasmas is to explain the production of energetic electrons as magnetic fields 'reconnect' and release energy. In the Earth's ...magnetosphere, electron energies reach hundreds of thousands of electron volts (refs 1-3), whereas the typical electron energies associated with large-scale reconnection-driven flows are just a few electron volts. Recent observations further suggest that these energetic particles are produced in the region where the magnetic field reconnects. In solar flares, upwards of 50 per cent of the energy released can appear as energetic electrons. Here we show that electrons gain kinetic energy by reflecting from the ends of the contracting 'magnetic islands' that form as reconnection proceeds. The mechanism is analogous to the increase of energy of a ball reflecting between two converging walls-the ball gains energy with each bounce. The repetitive interaction of electrons with many islands allows large numbers to be efficiently accelerated to high energy. The back pressure of the energetic electrons throttles reconnection so that the electron energy gain is a large fraction of the released magnetic energy. The resultant energy spectra of electrons take the form of power laws with spectral indices that match the magnetospheric observations.
Power-law distributions are a near-universal feature of energetic particle spectra in the heliosphere. Anomalous cosmic rays (ACRs), super-Alfvenic ions in the solar wind, and the hardest energetic ...electron spectra in flares all have energy fluxes with power laws that depend on energy E approximately as E super(?1.5). We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocity-space anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of pressure anisotropy on the merging dynamics. By including pitch-angle scattering we obtain an equation for the omnidirectional particle distribution f (v, t) that is solved in closed form to reveal v super(-5) (corresponding to an energy flux varying as E super(?1.5)) as a near-universal solution as long as the characteristic acceleration time is short compared with the characteristic loss time. In such a state, the total energy in the energetic particles reaches parity with the remaining magnetic free energy. More generally, the resulting transport equation can serve as the basis for calculating the distribution of energetic particles resulting from reconnection in large-scale inhomogeneous systems.
Kinetic particle‐in‐cell simulations are used to identify signatures of the electron diffusion region (EDR) and its surroundings during asymmetric magnetic reconnection. A “shoulder” in the sunward ...pointing normal electric field (EN > 0) at the reconnection magnetic field reversal is a good indicator of the EDR and is caused by magnetosheath electron meandering orbits in the vicinity of the X line. Earthward of the X line, electrons accelerated by EN form strong currents and crescent‐shaped distribution functions in the plane perpendicular to B. Just downstream of the X line, parallel electric fields create field‐aligned crescent electron distribution functions. In the immediate upstream magnetosheath, magnetic field strength, plasma density, and perpendicular electron temperatures are lower than the asymptotic state. In the magnetosphere inflow region, magnetosheath ions intrude resulting in an Earthward pointing electric field and parallel heating of magnetospheric particles. Many of the above properties persist with a guide field of at least unity.
Key Points
Where the sunward normal electric field overlaps the magnetic field reversal (the “shoulder”) is a signature of electron diffusion region
Signatures in the regions upstream of the X line establish context to find the diffusion region
Cusp‐like motion of magnetosheath electrons associated with electron acceleration produce crescent‐shaped particle distributions
Two‐ and three‐dimensional particle‐in‐cell simulations of a recent encounter of the Magnetospheric Multiscale Mission (MMS) with an electron diffusion region at the magnetopause are presented. While ...the two‐dimensional simulation is laminar, turbulence develops at both the X line and along the magnetic separatrices in the three‐dimensional simulation. The turbulence is strong enough to make the magnetic field around the reconnection island chaotic and produces both anomalous resistivity and anomalous viscosity. Each contribute significantly to breaking the frozen‐in condition in the electron diffusion region. A surprise is that the crescent‐shaped features in velocity space seen both in MMS observations and in two‐dimensional simulations survive, even in the turbulent environment of the three‐dimensional system. This suggests that MMS's measurements of crescent distributions do not exclude the possibility that turbulence plays an important role in magnetopause reconnection.
Key Points
Three‐dimensional simulations of an MMS observation demonstrate that turbulence should exist at the X line and separatrices
This turbulence plays a significant role in balancing Ohm's law at the X line
As turbulence does not disrupt crescents in distribution functions, crescent observations cannot be used to diagnose the role of turbulence
Dipolarization fronts (DFs), characterized by a strong and steep increase of the tail magnetic field component Bz normal to the neutral plane and preceded by a much less negative dip of Bz, are ...reported in many observations of bursty bulk flows and substorm activations throughout the whole Earth's magnetotail. It is shown that similar structures appear in full‐particle simulations with open boundaries in a transient regime before the steady reconnection in the original Harris current sheet driven out of the equilibrium by the initial X‐line perturbation is established. Being secondary reconnection structures propagating with the Alfvén speed, DFs are different from the magnetic field pileup regions reported in earlier simulations with closed boundaries. They also differ from the secondary plasmoids with bipolar Bz changes reported in earlier fluid simulations and particle simulations with open boundaries. In spite of their transient nature, DFs are found to form when the force balance is already restored in the system, which justifies their interpretation as a nonlinear stage of the tearing instability developing in two magnetotail‐like structures on the left and on the right of the initial central X‐line. Both electrons and ions are magnetized at the front of the dipolarization wave. In contrast, in its trail, ions are unmagnetized and move slower compared to the E × B drift, whereas electrons either follow that drift being completely magnetized or move faster, forming super‐Alfvénic jets. In spite of the different motions of electrons and ions, the growth of the front is not accompanied by the corresponding growth of the electrostatic field and the energy dissipation in fronts is dominated by ions.
The onset of reconnection in 2‐D current sheet equilibria that include an X line separating tail‐like regions with magnetized electrons is simulated with a full‐particle code. The onset is driven by ...a finite convection electric field applied outside the current sheet. In the case of tearing stable tails with no accumulated magnetic flux, the convection electric field penetrates the sheet near the X line. In contrast, in multiscale equilibria where the X line is framed by local areas of enhanced flux, the electric field avoids the X line, directly penetrates the areas of increased flux, and ejects them downstream. The ejecta form dipolarization fronts (DFs), sharp magnetic pileups with a thickness on the order of the ion inertial length, much smaller than the mesoscales of the initial flux increase regions. The DFs move with the reconnection outflows in the direction opposite the magnetic field stretching, while behind them new X lines, distinct from the original, form. Simulations with a reduced driving field suggest that DF formation shares properties with the ion tearing instability, which is consistent with its potential destabilization in multiscale equilibria. Weak driving of equilibria with tearing stable tails first forms flux accumulation regions, which then rapidly transform into DFs, making 2‐D equilibria inherently metastable. The results are compared with observations of DFs, the statistical visualization of Earth's magnetotail during substorm onset, and the bubble‐blob pair formation model.
Key Points
Formation of dipolarization fronts is a key feature of reconnection onset
Reconnection onset in 2‐D equilbria is consistent with tearing stability theory
The 2‐D reconnecting current sheet behaves as a metastable system
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