Turbulence, Magnetic Reconnection in Turbulent Fluids and Energetic Particle Acceleration

Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show how fast and slow modes accelerate energetic particles through the second order Fermi acceleration, while density fluctuations generate magnetic fields in pre-shock regions enabling the first order Fermi acceleration of high energy cosmic rays. Very importantly, however, the first order Fermi cosmic ray acceleration is also possible in sites of magnetic reconnection. In the presence of turbulence this reconnection gets fast and we present numerical evidence supporting the predictions of the Lazarian and Vishniac (Astrophys. J. 517:700–718, 1999) model of fast reconnection. The efficiency of this process suggests that magnetic reconnection can release substantial amounts of energy in short periods of time. As the particle tracing numerical simulations show that the particles can be efficiently accelerated during the reconnection, we argue that the process of magnetic reconnection may be much more important for particle acceleration than it is currently accepted. In particular, we discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers as well as the origin cosmic ray excess in the direction of Heliotail.     

Microphysics of Magnetic Reconnection

Magnetic reconnection is a universal phenomenon where energy is efficiently converted from the magnetic field to charged particles as a result of global magnetic topology changes during which earlier separated plasma regions become magnetically connected. While the reconnection affects large volumes in space most of the topology changes and of the energization occur within small localized regions. Regions of special importance are the X-region and the separatrix region. The understanding of the microphysics of these regions is crucial for the overall understanding of the reconnection. The Earth magnetosphere is the best environment where the details of these regions can be studied in situ. We summarize their main properties and discuss recent spacecraft observations.     

Critical Issues on Magnetic Reconnection in Space Plasmas

The idea of expedient energy transformation by magnetic reconnection (MR) has generated much enthusiasm in the space plasma community. The early concept of MR, which was envisioned for the solar flare phenomenon in a simple two-dimensional (2D) steady-state situation, is in dire need for extension to encompass three-dimensional (3D) non-steady-state phenomena prevalent in space plasmas in nature like in the magnetosphere. A workshop was organized to address this and related critical issues on MR. The essential outcome of this workshop is summarized in this review. After a brief evaluation on the pros and cons of existing definitions of MR, we propose essentially a working definition that can be used to identify MR in transient and spatially localized phenomena. The word “essentially” reflects a slight diversity in the opinion on how transient and localized 3D MR process might be defined. MR is defined here as a process with the following characteristics: (1) there is a plasma bulk flow across a boundary separating regions with topologically different magnetic field lines if projected on the plane of MR, thereby converting magnetic energy into kinetic particle energy, (2) there can be an out-of-the-plane magnetic field component (the so-called guide field) present such that the reconnected magnetic flux tubes are twisted to form flux ropes, and (3) the region exhibiting non-ideal MHD conditions should be localized to a scale comparable to the ion inertial length in the direction of the plasma inflow velocity. This definition captures the most important 3D aspects and preserves many essential characteristics of the 2D case. It may be considered as the first step in the generalization of the traditional 2D concept. As a demonstration on the utility of this definition, we apply it to identify MR associated with plasma phenomena in the dayside magnetopause and nightside magnetotail of the Earth’s magnetosphere. How MR may be distinguished from other competing mechanisms for these magnetospheric phenomena are then discussed.This revised version was published online in July 2005 with a corrected cover date.     

Magnetic Reconnection in Extreme Astrophysical Environments

Magnetic reconnection is a fundamental plasma physics process in which ideal-MHD??s frozen-in constraints are broken and the magnetic field topology is dramatically re-arranged, which often leads to a violent release of the free magnetic energy. Most of the magnetic reconnection research done to date has been motivated by the applications to systems such as the solar corona, Earth??s magnetosphere, and magnetic confinement devices for thermonuclear fusion. These environments have relatively low energy densities and the plasma is adequately described as a mixture of equal numbers of electrons and ions and where the dissipated magnetic energy always stays with the plasma. In contrast, in this paper I would like to introduce a different, new direction of research??reconnection in high energy density radiative plasmas, in which photons play as important a role as electrons and ions; in particular, in which radiation pressure and radiative cooling become dominant factors in the pressure and energy balance. This research is motivated in part by rapid theoretical and experimental advances in High Energy Density Physics, and in part by several important problems in modern high-energy astrophysics. I first discuss some astrophysical examples of high-energy-density reconnection and then identify the key physical processes that distinguish them from traditional reconnection. Among the most important of these processes are: special-relativistic effects; radiative effects (radiative cooling, radiation pressure, and radiative resistivity); and, at the most extreme end??QED effects, including pair creation. The most notable among the astrophysical applications are situations involving magnetar-strength fields (10¹⁴?C10¹⁵ G, exceeding the quantum critical field B _??4×10¹³ G). The most important examples are giant flares in soft gamma repeaters (SGRs) and magnetic models of the central engines and relativistic jets of Gamma Ray Bursts (GRBs). The magnetic energy density in these environments is so high that, when it is suddenly released, the plasma is heated to ultra-relativistic temperatures. As a result, electron-positron pairs are created in copious quantities, dressing the reconnection layer in an optically thick pair coat, thereby trapping the photons. The plasma pressure inside the layer is then dominated by the combined radiation and pair pressure. At the same time, the timescale for radiation diffusion across the layer may, under some conditions, still be shorter than the global (along the layer) Alfvén transit time, and hence radiative cooling starts to dominate the thermodynamics of the problem. The reconnection problem then becomes essentially a radiative transfer problem. In addition, the high pair density makes the reconnection layer highly collisional, independent of the upstream plasma density, and hence radiative resistive MHD applies. The presence of all these processes calls for a substantial revision of our traditional physical picture of reconnection when applied to these environments and thus opens a new frontier in reconnection research.     

Magnetic Reconnection in the Solar Wind

It is only within the last 5 years that we have learned how to recognize the unambiguous signature of magnetic reconnection in the solar wind in the form of roughly Alfvénic accelerated plasma flows embedded within bifurcated magnetic field reversal regions (current sheets). This paper provides a brief overview of what has since been learned about reconnection in the solar wind from both single and multi-spacecraft observations of these so-called reconnection exhausts.     

Location of Magnetic Reconnection in the Magnetotail

It is a crucial issue to know where magnetic reconnection takes place in the near-Earth magnetotail for substorm onsets. It is found on the basis of Geotail observations that the factor that controls the magnetic reconnection site in the magnetotail is the solar wind energy input. Magnetic reconnection forms close to (far from) the Earth in the magnetotail for high (low) solar wind energy input conditions.With the early Vela spacecraft observations, it was believed that magnetic reconnection started inside the Vela position, likely at 15 R_E. The later ISEE/IRM observations put magnetic reconnection beyond 20 R_E. The Vela event studies were made for highly active conditions, while the ISEE/IRM survey studies were made for moderate or quiet conditions. The finding of the factor that controls the site of magnetic reconnection in the magnetotail resolves the apparent discrepancy among various spacecraft results, and suggests solar cycle variation of the magnetotail reconnection site.     

Magnetic Reconnection Phenomena In Interplanetary Space

Interplanetary magnetic reconnection(IMR) phenomena are explored based on the observational data with various time resolutions from Helios, IMP-8, ISEE3, Wind, etc. We discover that the observational evidence of the magnetic reconnection may be found in the various solar wind structures, such as at the boundary of magnetic cloud, near the current sheet, and small-scale turbulence structures, etc. We have developed a third order accuracy upwind compact difference scheme to numerically study the magnetic reconnection phenomena with high-magnetic Reynolds number (R _M=2000–10000) in interplanetary space. The simulated results show that the magnetic reconnection process could occur under the typical interplanetary conditions. These obtained magnetic reconnection processes own basic characteristics of the high R _M reconnection in interplanetary space, including multiple X-line reconnection, vortex velocity structures, filament current systems, splitting, collapse of plasma bulk, merging and evolving of magnetic islands, and lifetime in the range from minutes to hours, etc. These results could be helpful for further understanding the interplanetary basic physical processes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electron Physics of Asymmetric Magnetic Field Reconnection

There have been many significant advances in understanding magnetic field reconnection as a result of improved space measurements and two-dimensional computer simulations. While reviews of recent work have tended to focus on symmetric reconnection on ion and larger spatial scales, the present review will focus on asymmetric reconnection and on electron scale physics involving the reconnection site, parallel electric fields, and electron acceleration.     

Understanding the Dynamics of Magnetic Reconnection Layer

We review progress in understanding the dynamics of a typical magnetic reconnection layer by describing the historical development of theory and the recent findings and discoveries in space and laboratory plasmas. The emphasis is on the dynamics of electrons moving with respect to ions in the collision-free neutral sheet. We make a detailed comparison of experimental results from the Magnetic Reconnection Experiment (MRX) with those from theory and numerical simulations. The collaboration between space and laboratory scientists on reconnection research has recently reached a point where we can compare measurements of the reconnection layer profile in detail with support from numerical simulations. In spite of the large difference in physical scales by 10⁶?C10⁷, we find remarkable commonalities in the features of the magnetic reconnection region in laboratory and magnetospheric plasmas. A newly planned laboratory experiment, in which a current sheet is swept in the way a magnetosphere current sheet crosses space satellites, is also described.     

The Role of Magnetic Reconnection in CME Acceleration

Observations carried out from the coronagraphs on board space missions (LASCO/SOHO, Solar Maximum and Skylab) and ground-based facilities (HAO/Mauna Loa Observatory) show that coronal mass ejections (CMEs) can be classified into two classes based on their kinematics evolution. These two classes of CMEs are so-called fast and slow CMEs. The fast CME starts with a high initial speed that remains more or less constant; it is also called the constant-speed CME. On the other hand, the slow CME starts with a low initial speed, but shows a gradual acceleration; it is also called the accelerated and slow CME. Low and Zhang [Astrophys. J. 564, L53–L56, 2002] suggested that these two classes of CMEs could be a result of a difference in the initial topology of the magnetic fields associated with the underlying quiescent prominences. A normal prominence magnetic field topology will lead to a fast CME, while an inverse quiescent prominence results in a slow CME, because of the nature of the magnetic reconnection processes. In a recent study given by Wu et al. [Solar Phys. 225, 157–175, 2004], it was shown that an inverse quiescent prominence magnetic topology also could produce a fast CME. In this study, we perform a numerical MHD simulation for CMEs occurring in both normal and inverse quiescent prominence magnetic topology. This study demonstrates three major physical processes responsible for destabilization of these two types of prominence magnetic field topologies that can launch CMEs. These three initiation processes are identical to those used by Wu et al. [Solar Phys. 225, 157–175, 2004]. The simulations show that both fast and slow CMEs can be initiated from these two different types of magnetic topologies. However, the normal quiescent prominence magnetic topology does show the possibility for launching a reconnection island (or secondary O-line) that might be thought of as a “CME’’.     

Reconnection Diffusion in Turbulent Fluids and Its Implications for Star Formation

Astrophysical fluids are turbulent a fact which changes the dynamics of many key processes, including magnetic reconnection. Fast reconnection of magnetic field in turbulent fluids allows the field to change its topology and connections. As a result, the traditional concept of magnetic fields being frozen into the plasma is no longer applicable. Plasma associated with a given magnetic field line at one instant is distributed along a different set of magnetic field lines at the next instant. This diffusion of plasmas and magnetic field is enabled by reconnection and therefore is termed “reconnection diffusion”. The astrophysical implications of this concept include heat transfer in plasmas, advection of heavy elements in interstellar medium, magnetic field generation etc. However, the most dramatic implications of the concept are related to the star formation process. The reason is that magnetic fields are dynamically important for most of the stages of star formation. The existing theory of star formation has been developed ignoring the possibility of reconnection diffusion. Instead, it appeals to the decoupling of mass and magnetic field arising from neutrals drifting in respect to ions entrained on magnetic field lines, i.e. through the process that is termed “ambipolar diffusion”. The predictions of ambipolar diffusion and reconnection diffusion are very different. For instance, if the ionization of media is high, ambipolar diffusion predicts that the coupling of mass and magnetic field is nearly perfect. At the same time, reconnection diffusion is independent of the ionization but depends on the scale of the turbulent eddies and on the turbulent velocities. In the paper we explain the physics of reconnection diffusion both from macroscopic and microscopic points of view, i.e. appealing to the reconnection of flux tubes and to the diffusion of magnetic field lines. We make use of the Lazarian and Vishniac (Astrophys. J. 517:700, 1999) theory of magnetic reconnection and show that this theory is applicable to the partially ionized gas. We quantify the reconnection diffusion rate both for weak and strong MHD turbulence and address the problem of reconnection diffusion acting together with ambipolar diffusion. In addition, we provide a criterion for correctly representing the magnetic diffusivity in simulations of star formation. We discuss the intimate relation between the processes of reconnection diffusion, field wandering and turbulent mixing of a magnetized media and show that the role of the plasma effects is limited to “breaking up lines” on small scales and does not affect the rate of reconnection diffusion. We address the existing observational results and demonstrate how reconnection diffusion can explain the puzzles presented by observations, in particular, the observed higher magnetization of cloud cores in comparison with the magnetization of envelopes. We also outline a possible set of observational tests of the reconnection diffusion concept and discuss how the application of the new concept changes our understanding of star formation and its numerical modeling. Finally, we outline the differences of the process of reconnection diffusion and the process of accumulation of matter along magnetic field lines that is frequently invoked to explain the results of numerical simulations.     

Magnetic Reconnection for Coronal Conditions: Reconnection Rates, Secondary Islands and Onset

Magnetic reconnection may play an important role in heating the corona through a release of magnetic energy. An understanding of how reconnection proceeds can contribute to explaining the observed behavior. Here, recent theoretical work on magnetic reconnection for coronal conditions is reviewed. Topics include the rate that collisionless (Hall) reconnection proceeds, the conditions under which Hall reconnection begins, and the effect of secondary islands (plasmoids) both on the scaling and properties of collisional (Sweet-Parker) reconnection and on the onset of Hall reconnection. Applications to magnetic energy storage and release in the corona are discussed.     

Properties of Near-Earth Magnetic Reconnection from In-Situ Observations

Many properties of magnetic reconnection have been determined from in-situ spacecraft observations in the Earth??s magnetosphere. Recent studies have focused on ion scale lengths and have largely confirmed theoretical predictions. In addition, some interesting features of reconnection regions on electron scale lengths have been identified. These recent studies have demonstrated the need for combined plasma and field measurements on electron scale lengths in the reconnection diffusion regions at the magnetopause and in the magnetotail. They have also indicated that measurements, such as those that will be made by the Magnetospheric Multiscale mission in the near future, will have a significant impact on understanding magnetic reconnection as a fundamental plasma process.     

Some Observational Evidence of Alfven Surface Waves Induced Magnetic Reconnection

The surface wave induced magnetic reconnection (SWIMR) model based on Alfven Resonance theory will be discussed briefly both for collisional and collisionless plasmas. It is shown that the spatial scales and time delays associated with Flux Transfer Events and Pulsed Ionospheric Flows, as observed by satellites and SuperDARN radars and the magnetic bubbles, observed at the high latitude boundary of the magnetopause, can be explained by the SWIMR model. This revised version was published online in August 2006 with corrections to the Cover Date.     

Three-Dimensional Simulations of Magnetic Reconnection with or Without Velocity Shears

The properties of spontaneous reconnection of a current sheet analyzed via direct three-dimensional simulations are presented. In particular the non-linear dynamics of resistive instabilities has been studied in absence or in presence of velocity shears. It is shown that full three-dimensional simulations allow the inclusion of a rich variety of (ideal) secondary instabilities which, depending on the initial equilibrium magnetic field configuration, determine the final fate of the system in the fully non linear regime. In particular in presence of a guide-field the dynamic is similar to what observed in two-dimensional simulations with energy driven toward both smaller and larger scales and energy spectra anisotropy. For different magnetic field configurations, the final state is characterized by the disruption of the coalesced structure created during the resistive phase and the system is characterized by a more chaotic state. A?discussion on the importance of high-order numerical techniques in numerical simulations of magnetic reconnection is also present.     

A new paradigm for 3D Collisionless Magnetic Reconnection

A new paradigm is suggested for 3D magnetic reconnection where the interaction of reconnection processes with current aligned instabilities plays an important role. According to the new paradigm, the initial equilibrium is rendered unstable by current aligned instabilities (lower-hybrid drift instability first, drift-kink instability later) and the non-uniform development of kinking modes leads to a compression of magnetic field lines in certain locations and a rarefaction in others. The areas where the flow is compressional are subjected to a driven reconnection process. In the present paper we illustrate this series of events with a selection of simulation results. This revised version was published online in August 2006 with corrections to the Cover Date.     

Emerging Parameter Space Map of Magnetic Reconnection in Collisional and Kinetic Regimes

In large-scale systems of interest to solar physics, there is growing evidence that magnetic reconnection involves the formation of extended current sheets which are unstable to plasmoids (secondary magnetic islands). Recent results suggest that plasmoids may play a critical role in the evolution of reconnection, and have raised fundamental questions regarding the applicability of resistive MHD to various regimes. In collisional plasmas, where the thickness of all resistive layers remain larger than the ion gyroradius, simulations results indicate that plasmoids permit reconnection to proceed much faster than the slow Sweet-Parker scaling. However, it appears these rates are still a factor of ～10× slower than observed in kinetic regimes, where the diffusion region current sheet falls below the ion gyroradius and additional physics beyond MHD becomes crucially important. Over a broad range of interesting parameters, the formation of plasmoids may naturally induce a transition into these kinetic regimes. New insights into this scenario have emerged in recent years based on a combination of linear theory, fluid simulations and fully kinetic simulations which retain a Fokker-Planck collision operator to allow a rigorous treatment of Coulomb collisions as the reconnection electric field exceeds the runaway limit. Here, we present some new results from this approach for guide field reconnection. Based upon these results, a parameter space map is constructed that summarizes the present understanding of how reconnection proceeds in various regimes.     

Recent Evolution in the Theory of Magnetic Reconnection and Its Connection with Turbulence

The concept of reconnection is found in many fields of physics with the closest analogue to magnetic reconnection being the reconnection of vortex tubes in hydrodynamics. In plasmas, magnetic reconnection plays an important role in release of energy associated with the magnetic shear into particle energy. Although most studies to date have focused on 2D reconnection, the availability of 3D petascale kinetic simulations have brought the complexity of 3D reconnection to the forefront in collisionless reconnection studies. Here we briefly review the latest advances in 2D and compare and contrast the results with recent 3D studies that address role of anomalous transport in reconnection, effects of turbulence on the rate and structure, among others. Another outcome of recent research is the realization of a deeper link between turbulence and reconnection where the common denominator is the generic formation of electron scale sheets which dissipate the energy through reconnection. Finally, we close the review by listing some of the major outstanding problems in reconnection physics.     

Ion Heating and Acceleration During Magnetic Reconnection Relevant to the Corona

The heating and acceleration of ions during magnetic reconnection relevant to coronal heating and flares is explored via particle-in-cell (PIC) simulations and analytic modeling. We show that the dominant heating mechanism of sub-Alvénic ions during reconnection with a guide field, the case of greatest relevance to the corona, results from pickup behavior during the entry into reconnection exhausts, which produces effective thermal speeds of the order of the Alfvén velocity based on the reconnecting magnetic field. There is a mass-to-charge (M/Q) threshold for pickup behavior that favors the heating of high-M/Q ions. Ions below the threshold gain little energy beyond that associated with convective flow. PIC simulations with protons and alphas confirm the pickup threshold. The enhanced heating of high M/Q ions is consistent with observations of abundance enhancements of such ions in impulsive flares. In contrast to anti-parallel reconnection, the temperature increment during ion pickup is dominantly transverse, rather than parallel, to the local magnetic field. The simulations reveal the dominance of perpendicular heating, which is also consistent with observations. We suggest that the acceleration of ions to energies well above that associated with the Alfvén speed takes place during the interaction with many magnetic islands, which spontaneously develop during 3-D guide-field reconnection. The exploration of particle acceleration in a full 3-D multi-island system remains computationally intractable. Instead we explore ion acceleration in a multi-current layer system with low initial β. Ion energy gain takes place due to Fermi reflection in contracting and merging magnetic islands. Particle acceleration continues until the available magnetic free-energy is significantly depleted so that the pressure of energetic ions approaches that of the reconnecting field. Depending on the strength of the ambient guide field and in spite of the low initial plasma β, the dominance of parallel heating can cause significant regions of the plasma to exceed the marginal firehose condition.     

Magnetohydrodynamics of sunspots

Current theories are reviewed concerning the pressure equilibrium and thermal balance of sunspots, their hydromagnetic stability, energy transport mechanisms, and propagation of waves.Invited review presented at the Joint Meeting of IAU Commissions 10, 12, and 44, The MHD of Sunspots in Montreal, 20 August 1979.The National Center for Atmospheric Research is sponsored by the National Science Foundation.