Electron acceleration from contracting magnetic islands during reconnection

Key aspects of coronal heating

We highlight 10 key aspects of coronal heating that must be understood before we can consider the problem to be solved. (1) All coronal heating is impulsive. (2) The details of coronal heating matter. (3) The corona is filled with elemental magnetic stands. (4) The corona is densely populated with current sheets. (5) The strands must reconnect to prevent an infinite build-up of stress. (6) Nanoflares repeat with different frequencies. (7) What is the characteristic magnitude of energy release? (8) What causes the collective behaviour responsible for loops? (9) What are the onset conditions for energy release? (10) Chromospheric nanoflares are not a primary source of coronal plasma. Significant progress in solving the coronal heating problem will require coordination of approaches: observational studies, field-aligned hydrodynamic simulations, large-scale and localized three-dimensional magnetohydrodynamic simulations, and possibly also kinetic simulations. There is a unique value to each of these approaches, and the community must strive to coordinate better.

A dynamical model of plasma turbulence in the solar wind

A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.

Turbulent reconnection and its implications

Magnetic reconnection is a process of magnetic field topology change, which is one of the most fundamental processes happening in magnetized plasmas. In most astrophysical environments, the Reynolds numbers corresponding to plasma flows are large and therefore the transition to turbulence is inevitable. This turbulence, which can be pre-existing or driven by magnetic reconnection itself, must be taken into account for any theory of magnetic reconnection that attempts to describe the process in the aforementioned environments. This necessity is obvious as three-dimensional high-resolution numerical simulations show the transition to the turbulence state of initially laminar reconnecting magnetic fields. We discuss ideas of how turbulence can modify reconnection with the focus on the Lazarian & Vishniac (Lazarian & Vishniac 1999 Astrophys. J. 517, 700-718 (doi:10.1086/307233)) reconnection model. We present numerical evidence supporting the model and demonstrate that it is closely connected to the experimentally proven concept of Richardson dispersion/diffusion as well as to more recent advances in understanding of the Lagrangian dynamics of magnetized fluids. We point out that the generalized Ohm's law that accounts for turbulent motion predicts the subdominance of the microphysical plasma effects for reconnection for realistically turbulent media. We show that one of the most dramatic consequences of turbulence is the violation of the generally accepted notion of magnetic flux freezing. This notion is a cornerstone of most theories dealing with magnetized plasmas, and therefore its change induces fundamental shifts in accepted paradigms, for instance, turbulent reconnection entails reconnection diffusion process that is essential for understanding star formation. We argue that at sufficiently high Reynolds numbers the process of tearing reconnection should transfer to turbulent reconnection. We discuss flares that are predicted by turbulent reconnection and relate this process to solar flares and γ-ray bursts. With reference to experiments, we analyse solar observations in situ as measurements in the solar wind or heliospheric current sheet and show the correspondence of data with turbulent reconnection predictions. Finally, we discuss first-order Fermi acceleration of particles that is a natural consequence of the turbulent reconnection.

Formation of hard power laws in the energetic particle spectra resulting from relativistic magnetic reconnection

Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density σ ≡ B(2)/(4πnm(e)c(2))>1 and when the system size is sufficiently large. In the limit σ ≫ 1, the spectral index approaches p = 1 and most of the available energy is converted into nonthermal particles. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection.

Stochastic acceleration by multi-island contraction during turbulent magnetic reconnection

The acceleration of charged particles in magnetized plasmas is considered during turbulent multi-island magnetic reconnection. The particle acceleration model is constructed for an ensemble of islands which produce adiabatic compression of the particles. The model takes into account the statistical fluctuations in the compression rate experienced by the particles during their transport in the acceleration region. The evolution of the particle distribution function is described as a simultaneous first- and second-order Fermi acceleration process. While the efficiency of the first-order process is controlled by the average rate of compression, the second-order process involves the variance in the compression rate. Moreover, the acceleration efficiency associated with the second-order process involves both the Eulerian properties of the compression field and the Lagrangian properties of the particles. The stochastic contribution to the acceleration is nonresonant and can dominate the systematic part in the case of a large variance in the compression rate. The model addresses the role of the second-order process, how the latter can be related to the large-scale turbulent transport of particles, and explains some features of the numerical simulations of particle acceleration by multi-island contraction during magnetic reconnection.

Fermi acceleration in plasmoids interacting with fast shocks of reconnection via fractal reconnection

We propose the particle acceleration model coupled with multiple plasmoid ejections in a solar flare. Unsteady reconnection produces plasmoids in a current sheet and ejects them out to the fast shocks, where particles in a plasmoid are reflected upstream the shock front by magnetic mirror effect. As the plasmoid passes through the shock front, the reflection distance becomes shorter and shorter driving Fermi acceleration, until it becomes proton Larmor radius. The fractal distribution of plasmoids may also have a role in naturally explaining the power-law spectrum in nonthermal emissions.

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

A two-dimensional (2D) linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of reduced magnetohydrodynamics. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al., Phys. Plasmas 14, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids (k(max)L(CS)~S(3/8), where k(max) is the wave number of fastest growing mode, S=L(CS)V(A)/η is the Lundquist number, L(CS) is the length of the sheet, V(A) is the Alfvén speed, and η is the plasma resistivity), which grows super Alfvénically fast (γ(max)τ(A)~S(1/4), where γ(max) is the maximum growth rate, and τ(A)=L(CS)/V(A)). For typical background profiles, the growth rate and the wave number are found to increase in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfvén speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability γ(max)τ(A)~k(max)L(CS)~S(1/2). The effect of viscosity (ν) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers Pm=ν/η, it is found that γ(max)~S(1/4)Pm(-5/8) and k(max)L(CS)~S(3/8)Pm(-3/16), leading to the prediction that the critical Lundquist number for plasmoid instability in the Pm>>1 regime is S(crit)~10(4)Pm(1/2). These results are verified via direct numerical simulation of the linearized equations, using an analytical 2D SP equilibrium solution.

Distribution of plasmoids in high-Lundquist-number magnetic reconnection

The distribution function f(ψ) of magnetic flux ψ in plasmoids formed in high-Lundquist-number current sheets is studied by means of an analytic phenomenological model and direct numerical simulations. The distribution function is shown to follow a power law f(ψ)∼ψ(-1), which differs from other recent theoretical predictions. Physical explanations are given for the discrepant predictions of other theoretical models.

Secondary magnetic islands generated by the Kelvin-Helmholtz instability in a reconnecting current sheet

Magnetic islands or flux ropes produced by magnetic reconnection have been observed on the magnetopause, in the magnetotail, and in coronal current sheets. Particle-in-cell simulations of magnetic reconnection with a guide field produce elongated electron current layers that spontaneously produce secondary islands. Here, we explore the seed mechanism that gives birth to these islands. The most commonly suggested theory for island formation is the tearing instability. We demonstrate that in our simulations these structures typically start out, not as magnetic islands, but as electron flow vortices within the electron current sheet. When some of these vortices first form, they do not coincide with closed magnetic field lines, as would be the case if they were islands. Only after they have grown larger than the electron skin depth do they couple to the magnetic field and seed the growth of finite-sized islands. The streaming of electrons along the magnetic separatrix produces the flow shear necessary to drive an electron Kelvin-Helmholtz instability and produce the initial vortices. The conditions under which this instability is the dominant mechanism for seeding magnetic islands are explored.

Plasmoid ejection and secondary current sheet generation from magnetic reconnection in laser-plasma interaction

Reconnection of the self-generated magnetic fields in laser-plasma interaction was first investigated experimentally by Nilson et al. [Phys. Rev. Lett. 97, 255001 (2006)] by shining two laser pulses a distance apart on a solid target layer. An elongated current sheet (CS) was observed in the plasma between the two laser spots. In order to more closely model magnetotail reconnection, here two side-by-side thin target layers, instead of a single one, are used. It is found that at one end of the elongated CS a fanlike electron outflow region including three well-collimated electron jets appears. The (>1 MeV) tail of the jet energy distribution exhibits a power-law scaling. The enhanced electron acceleration is attributed to the intense inductive electric field in the narrow electron dominated reconnection region, as well as additional acceleration as they are trapped inside the rapidly moving plasmoid formed in and ejected from the CS. The ejection also induces a secondary CS.

Stochastic particle acceleration in multiple magnetic islands during reconnection

A nonthermal particle acceleration mechanism involving the interaction of a charged particle with multiple magnetic islands is proposed. The original Fermi acceleration model, which assumes randomly distributed magnetic clouds moving at random velocity V(c) in the interstellar medium, is known to be of second-order acceleration of O(V(c)/c)(2) owing to the combination of head-on and head-tail collisions. In this Letter, we reconsider the original Fermi model by introducing multiple magnetic islands during reconnection instead of magnetic clouds. We discuss that the energetic particles have a tendency to be distributed outside the magnetic islands, and they mainly interact with reconnection outflow jets. As a result, the acceleration efficiency becomes first order of O(V(A)/c), where V(A) and c are the Alfvén velocity and the speed of light, respectively.

Direct evidence for a three-dimensional magnetic flux rope flanked by two active magnetic reconnection X lines at Earth's magnetopause

We report the direct detection by three THEMIS spacecraft of a magnetic flux rope flanked by two active X lines producing colliding plasma jets near the center of the flux rope. The observed density depletion and open magnetic field topology inside the flux rope reveal important three-dimensional effects. There was also evidence for nonthermal electron energization within the flux rope core where the fluxes of 1-4 keV superthermal electrons were higher than those in the converging reconnection jets. The observed ion and electron energizations differ from current theoretical predictions.

Anisotropic ion heating and tail generation during tearing mode magnetic reconnection in a high-temperature plasma

Complementary measurements of ion energy distributions in a magnetically confined high-temperature plasma show that magnetic reconnection results in both anisotropic ion heating and the generation of suprathermal ions. The anisotropy, observed in the C(+6) impurity ions, is such that the temperature perpendicular to the magnetic field is larger than the temperature parallel to the magnetic field. The suprathermal tail appears in the majority ion distribution and is well described by a power law to energies 10 times the thermal energy. These observations may offer insight into the energization process.

Energetic electrons associated with magnetic reconnection in the magnetic cloud boundary layer

Here is reported in situ observation of energetic electrons (∼100-500 keV) associated with magnetic reconnection in the solar wind by the ACE and Wind spacecraft. The properties of this magnetic cloud driving reconnection and the associated energetic electron acceleration problem are discussed. Further analyses indicate that the electric field acceleration and Fermi-type mechanism are two fundamental elements in the electron acceleration processes and the trapping effect of the specific magnetic field configuration maintains the acceleration status that increases the totally gained energy.

In situ observations of a secondary magnetic island in an ion diffusion region and associated energetic electrons

Numerical simulations have predicted that an extended current sheet may be unstable to secondary magnetic islands in the vicinity of the X line, and these islands can dramatically influence the reconnection rate. In this Letter, we present the first evidence of such a secondary island near the center of an ion diffusion region, which is consistent with the action of the secondary island instability occurring in the vicinity of the X line. The island is squashed in the z direction with a strong core magnetic field. Energetic electrons with anisotropic or field-aligned bidirectional fluxes are found in the ion diffusion region, and the enhancement of energetic electron fluxes is more obvious inside the secondary island.

The science of space weather

The basic physics underpinning space weather is reviewed, beginning with a brief overview of the main causes of variability in the near-Earth space environment. Although many plasma phenomena contribute to space weather, one of the most important is magnetic reconnection, and recent cutting edge research in this field is reviewed. We then place this research in context by discussing a number of specific types of space weather in more detail. As society inexorably increases its dependence on space, the necessity of predicting and mitigating space weather will become ever more acute. This requires a deep understanding of the complexities inherent in the plasmas that fill space and has prompted the development of a new generation of scientific space missions at the international level.

Velocity statistics distinguish quantum turbulence from classical turbulence

By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid 4He are strongly non-Gaussian with 1/v(3) power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.

Self-feeding turbulent magnetic reconnection on macroscopic scales

Within a MHD approach we find magnetic reconnection to progress in two entirely different ways. The first is well known: the laminar Sweet-Parker process. But a second, completely different and chaotic reconnection process is possible. This regime has properties of immediate practical relevance: (i) it is much faster, developing on scales of the order of the Alfvén time, and (ii) the areas of reconnection become distributed chaotically over a macroscopic region. The onset of the faster process is the formation of closed-circulation patterns where the jets going out of the reconnection regions turn around and force their way back in, carrying along copious amounts of magnetic flux.