Electrons gain kinetic energy by reflecting from the ends of the contracting 'magnetic islands' that form as reconnection proceeds. The repetitive interaction of electrons with many islands allows large numbers to be efficiently accelerated to high energy. 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 reconnects4. In solar flares, upwards of 50 per cent of the energy released can appear as energetic electrons5,6. 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.

http://www.physics.udel.edu/~shay/papers/DrakeJ.2006.Nat.443.553.Shay.pdf

Electron acceleration from contracting magnetic islands during reconnection

Kinetic simulations of magnetic reconnection typically employ periodic boundary conditions that limit the duration in which the results are physically meaningful. To address this issue, a new model is proposed that is open with respect to particles, magnetic flux, and electromagnetic radiation. The model is used to examine undriven reconnection in a neutral sheet initialized with a single x-point. While at early times the results are in excellent agreement with previous periodic studies, the evolution over longer intervals is entirely different. In particular, the length of the electron diffusion region is observed to increase with time resulting in the formation of an extended electron current sheet. As a consequence, the electron diffusion region forms a bottleneck and the reconnection rate is substantially reduced. Periodically, the electron layer becomes unstable and produces a secondary island, breaking the diffusion region into two shorter segments. After growing for some period, the island is ejected and the diffusion region again expands until a new island is formed. Fast reconnection may still be possible provided that the generation of secondary islands remains sufficiently robust. These results indicate that reconnection in a neutral sheet may be inherently unsteady and raise serious questions regarding the standard model of Hall mediated reconnection.

Fully kinetic simulations of undriven magnetic reconnection with open boundary conditions

We review the physical processes of particle acceleration, injection, propagation, trapping, and energy loss in solar flare conditions. An understanding of these basic physical processes is inexorable to interpret the detailed timing and spectral evolution of the radiative signatures caused by nonthermal particles in hard X-rays, gamma-rays, and radio wavelengths. In contrast to other more theoretically oriented reviews on particle acceleration processes, we aim here to capitalize on the numerous observations from recent spacecraft missions, such as from the Compton Gamma Ray Observatory (CGRO), the Yohkoh Hard X-Ray Telescope (HXT) and Soft X-Ray Telescope (SXT), and the Transition Region and Coronal Explorer (TRACE). High-precision energy-dependent time delay measurements from CGRO and spatial imaging with Yohkoh and TRACE provide invaluable observational constraints on the topology of the acceleration region, the reconstruction of magnetic reconnection processes, the resulting electromagnetic fields, and the kinematics of energized (nonthermal) particles.

/pdf/particle-acceleration-and-kinematics-in-solar-flares-a-4iyjh5x0g8.pdf

Particle acceleration and kinematics in solar flares – A Synthesis of Recent Observations and Theoretical Concepts (Invited Review)

We review both observational and theoretical aspects of the generation of auroral radio emissions at the outer planets, trying to organize the former in a coherent frame set by the latter. Important results have been obtained in the past few years on these radio emissions at the five magnetized planets, from the observations of Ulysses at Jupiter and of Wind and other Global Geospace Science spacecraft in Earth orbit, from the reanalysis of Voyager data about Saturn, Uranus, and Neptune, from ground-based high frequency-time resolution and full polarization measurements, and from pioneering multispectral observations of the Jovian and Saturnian aurorae (radio/UV/IR). In parallel, considerable progress has been made in their generation theory (Cyclotron-Maser operating in small-scale, laminar, hot-plasma-dominated radio source structures), mostly on the basis of in situ observations of terrestrial radio sources. Particle acceleration and precipitation is also better documented, thanks to in situ measurements in the Earth auroral zones and to multispectral studies of Jupiter and Saturn. Finally, the modeling of the planetary magnetic field and magnetospheric plasma at these two planets has also been considerably improved. To organize the wealth of observational results within a coherent theoretical frame, we emphasize unresolved questions (e.g., planetary radio bursts generation) and contradictions and propose ways to answer them. Our ability, already significant, to perform remote sensing of magnetoplasmas at the giant planets and, hopefully, at other distant radio sources (solar, stellar) in the near future, depends on the good understanding of the physical processes underlying the generation of auroral electromagnetic emissions. The question of the existence of exoplanetary radio emissions and the possibility to detect and study them is briefly discussed.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JE01323

Auroral radio emissions at the outer planets: Observations and theories

The Geospace Environment Modeling (GEM) Challenge Harris current sheet problem is simulated in 2 1/2 dimensions using full particle, hybrid, and Hall MHD simulations The same gross reconnection rate is found in all of the simulations independent of the type of code used, as long as the Hall term is included In addition, the reconnection rate is independent of the mechanism which breaks the frozen-in flux condition, whether it is electron inertia or grid scale diffusion The insensitivity to the mechanism which breaks the frozen-in condition is a consequence of whistler waves, which control the plasma dynamics at the small scales where the ions become unmagnetized The dispersive character of whistlers, in which the phase velocity increases with decreasing scale size, allows the flux of electrons flowing away from the dissipation region to remain finite even as the strength of the dissipation approaches zero As a consequence, the throttling of the reconnection process as a result of the small scale size of the dissipation region, which occurs in the magnetohydrodynamic model, iio longer takes place The important consequence is that the minimum physical model necessary to produce physically correct reconnection rates is a Hall MHD description which includes the Hall term in Ohm's law A density depletion layer, which lies just downstream from the magnetic separatrix, is identified and linked to the strong in-plane Hall currents which characterize kinetic models of magnetic reconnection

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JA001007

Alfvénic collisionless magnetic reconnection and the Hall term

[1] Previous investigations of collisionless magnetic reconnection in a standard Harris neutral sheet configuration have demonstrated the importance of the Hall term for producing near-Alfvenic rates of reconnection and the existence of a very thin (∼c/ωpe) electron current layer and sharp density/pressure gradients on c/ωpi scales. The present work uses three-dimensional (3-D) particle-in-cell simulations with an open geometry to investigate the changes in the reconnection physics produced by a “guide field” component B0y of the magnetic field. With B0y ≲ B0, the nonlinear reconnection rate is not substantially modified from that for the Harris case. The properties of the reconnection fields and particle dynamics, however, are strongly altered. The familiar quadrupole By pattern is replaced by an enhancement of ∣By∣ between the separatrices. The enhanced parallel electric field and parallel electron velocity are confined to one pair of separatrix arms (which are positively charged), while the electron current peaks on the other pair (which are negatively charged). The ion outflow along the current sheet polarizes the separatrices, thereby creating large components of the in-plane electric field. The electrons are accelerated to form a beam structure with parallel speed limited by the electron Alfven speed. The beam-dominated electron distribution produces some y-dependent structures in E∥. For B0y ≫ B0, the reconnection rate is reduced by a factor of 2–3, and the parallel fields and velocities are somewhat smaller; the Hall current produced perturbations in By are considerably reduced.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2003JA009999

Three‐dimensional collisionless magnetic reconnection in the presence of a guide field

[1] Three-dimensional electromagnetic particle-in-cell simulations are used to investigate the stability properties of a plasma sheet equilibrium with a minimum in the magnetic normal (Bz) component. Such a configuration is found to be unstable to a ballooning/interchange type mode that is localized tailward of the Bz minimum. The mode has a relatively short dawn-dusk wavelength of the order of the ion Larmor radius in the Bz field (∼2000 km) and a phase velocity in the direction of the ion diamagnetic drift with a magnitude about one-fifth of the drift speed. The real frequency is about 60% of the midplane ion cyclotron frequency. The dominant mode polarization is δϕ and δB∥. A linear kinetic analysis including bounce and drift resonance interactions for the electrons and an orbit average over the flux tube volume for the Boltzmann term in the ion density perturbation produces agreement with the simulation mode properties and permits identification of the mode as the low-frequency extension of the lower hybrid drift instability in straight magnetic geometry. In its nonlinear evolution, the mode develops Rayleigh-Taylor fingers that extend across the Bz minimum and into the near-Earth dipole region. These fingers transport magnetic flux earthward, and the flux is redistributed by electron Hall currents that flow around the fingers. This mode is likely to contribute to the nearly continuous presence of turbulence in the center of the plasma sheet.

A kinetic ballooning/interchange instability in the magnetotail

In a thin current sheet (ρi0/L ≲ 1, where ρi0 is the ion gyroradius in the lobe field and L is the current sheet half thickness) of the generalized Harris type, the relative ion-electron cross-field drift is comparable to the ion thermal velocity. The three-dimensional stability properties of such a thin current sheet are investigated by means of nonlocal two-fluid theory and two-dimensional and three-dimensional full particle simulations. As was suggested originally by Zhu et al. [1992], the drift kink mode is found to be of critical importance. For the simple case of no initial Bz field, the fluid theory demonstrates that the drift kink mode is a non-MHD mode with a polarization structure such that E1y is an antisymmetric function of z while E1z is a symmetric function with E1z(0) ≠ 0. Two-dimensional (y,z) particle simulations indicate that the nonlinear behavior of this mode is dominated by long-wavelength modes with kyL ∼ 1 and frequency ωr ∼ Ωi0, where Ωi0 is the ion gyrofrequency in the lobe field. Three-dimensional particle simulations performed on a massively parallel computer show that while the growth rates for the drift kink mode are reduced by the finite Bz, they can still be appreciable (γ/Ωi0 ≲ 0.05–0.10). The kyL ∼ 1 drift kink modes are always the first to grow in the simulations; subsequently, tearing-like modes with a dominant kx wave vector also become unstable. Implications of these results for the triggering of substorms are discussed.

Three-dimensional stability of thin quasi-neutral current sheets

A two-dimensional particle simulation model based on the Darwin approximation to Maxwell's equations for studying collisionless reconnection in the magnetotail has been developed. Simulations of the pure ion tearing mode in a thin current sheet with normal B(z) field component demonstrate that in this limit this mode grows more slowly than expected based on previous analytic estimates. The saturation level of the tearing instability greatly surpasses estimates based on a simple trapping argument. The effect of the normal field component on the evolution of the tearing instability is considered. It is found that a normal field of even a few percent on axis strongly inhibits the growth of the instability.

Collisionless reconnection in two-dimensional magnetotail equilibria

[1] The production of relativistic electrons during guide field magnetic reconnection is investigated with two-dimensional particle-in-cell simulations. The acceleration mechanism is found to consist of two important elements. The parallel electric field that exists in the low-density cavities along two of the separatrices leads to the production of a cold electron beam. This beam is funneled into the near vicinity (of the order of a few ion inertia lengths) of the X line where the electrons are further accelerated by the parallel electric field to form the relativistic portion of the electron spectrum. This combined process is more efficient than for undriven magnetic reconnection without a guide field and produces a harder spectrum. Secondary islands which can appear as transient structures during the guide field reconnection process do not appear to play an important role in the production of the relativistic electrons.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006JA011793

P. L. Pritchett

Papers

Three‐dimensional collisionless magnetic reconnection in the presence of a guide field

A kinetic ballooning/interchange instability in the magnetotail

Three-dimensional stability of thin quasi-neutral current sheets

Collisionless reconnection in two-dimensional magnetotail equilibria

Relativistic electron production during guide field magnetic reconnection