Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media

Astrophysical fluids have very large Reynolds numbers and therefore turbulence is their natural state. Magnetic reconnection is an important process in many astrophysical plasmas, which allows restructuring of magnetic fields and conversion of stored magnetic energy into heat and kinetic energy. Turbulence is known to dramatically change different transport processes and therefore it is not unexpected that turbulence can alter the dynamics of magnetic field lines within the reconnection process. We shall review the interaction between turbulence and reconnection at different scales, showing how a state of turbulent reconnection is natural in astrophysical plasmas, with implications for a range of phenomena across astrophysics. We consider the process of magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit and discuss how turbulence—both externally driven and generated in the reconnecting system—can make reconnection independent on the microphysical properties of plasmas. We will also show how relaxation theory can be used to calculate the energy dissipated in turbulent reconnecting fields. As well as heating the plasma, the energy dissipated by turbulent reconnection may cause acceleration of non-thermal particles, which is briefly discussed here.     

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.     

Order out of Randomness: Self-Organization Processes in Astrophysics

Self-organization is a property of dissipative nonlinear processes that are governed by a global driving force and a local positive feedback mechanism, which creates regular geometric and/or temporal patterns, and decreases the entropy locally, in contrast to random processes. Here we investigate for the first time a comprehensive number of (17) self-organization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Self-organizing systems create spontaneous “order out of randomness”, during the evolution from an initially disordered system to an ordered quasi-stationary system, mostly by quasi-periodic limit-cycle dynamics, but also by harmonic (mechanical or gyromagnetic) resonances. The global driving force can be due to gravity, electromagnetic forces, mechanical forces (e.g., rotation or differential rotation), thermal pressure, or acceleration of nonthermal particles, while the positive feedback mechanism is often an instability, such as the magneto-rotational (Balbus-Hawley) instability, the convective (Rayleigh-Bénard) instability, turbulence, vortex attraction, magnetic reconnection, plasma condensation, or a loss-cone instability. Physical models of astrophysical self-organization processes require hydrodynamic, magneto-hydrodynamic (MHD), plasma, or N-body simulations. Analytical formulations of self-organizing systems generally involve coupled differential equations with limit-cycle solutions of the Lotka-Volterra or Hopf-bifurcation type.     

Reconnection in the magnetotail

The ion tearing mode is considered as the only mechanism capable of initiating reconnection processes in the equilibrium plasma sheet whose scale considerably exceeds the ion Larmor radius. The paper gives a brief review of linear theory of the tearing mode instability that allows the onset of its development to be determined. It is shown that the explosive growth of the tearing mode in a nonlinear stage is consistent with the dynamics of charged particle acceleration and the behaviour of the magnetic field variations and plasma flow in the magnetotail. The tail structure formed, as a result of the development of the tearing mode, is also discussed.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

Radio Diagnostics of the Solar Flare Reconnection

First, high-frequency (HF) slowly drifting pulsating structures are interpreted as radio emissions of electron beams accelerated in the magnetic reconnection volume and injected into magnetic islands (plasmoids). Then, the time evolution of plasma parameters (density, magnetic field, etc.) in a 2-D MHD model of solar flare reconnection is computed numerically. Assuming plasma radio emission from locations where the “double-resonance’’ instability generates upper-hybrid (UH) waves due to unstable distribution function of suprathermal electrons, the radio spectra and spatial source structures in the reconnection region are modeled. By comparison of the modeled and observed spectra a remarkable similarity has been found between the computed narrow-band emission and the observed lace bursts. Finally, a new diagnostics of the reconnection process is proposed.     

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.     

Topics in Microphysics of Relativistic Plasmas

Astrophysical plasmas can have parameters vastly different from the more studied laboratory and space plasmas. In particular, the magnetic fields can be the dominant component of the plasma, with energy-density exceeding the particle rest-mass energy density. Magnetic fields then determine the plasma dynamical evolution, energy dissipation and acceleration of non-thermal particles. Recent data coming from astrophysical high energy missions, like magnetar bursts and Crab nebula flares, point to the importance of magnetic reconnection in these objects. In this review we outline a broad spectrum of problems related to the astrophysical relevant processes in magnetically dominated relativistic plasmas. We discuss the problems of large scale dynamics of relativistic plasmas, relativistic reconnection and particle acceleration at reconnecting layers, turbulent cascade in force-fee plasmas. A number of astrophysical applications are also discussed.     

Quasi-Periodic Pulsations in Solar Flares

Quasi-periodic pulsations (QPP) are a common feature of flaring energy releases in the solar atmosphere, observed in all bands, from radio to hard X-ray. In this review we concentrate on QPP with the periods longer than one second. Physical mechanisms responsible for the generation of long QPP split into two groups: “load/unload” mechanisms and MHD oscillations. Load/unload mechanisms are repetitive regimes of flaring energy releases by magnetic reconnection or by other means. MHD oscillations can affect all elements of the flaring emission generation: triggering of reconnection and modulation of its rate, acceleration and dynamics of non-thermal electrons, and physical conditions in the emitting plasmas. In the case of MHD oscillations, the periodicity of QPP is determined either by the presence of some resonances, e.g. standing modes of plasma structures, or by wave dispersion. Periods and other parameters of QPP are linked with properties of flaring plasmas and their morphology. Observational investigation of the QPP generation mechanisms based upon the use of spatial information, broadband spectral coverage and multi-periodicity is discussed.     

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.     

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.     

Theory and Simulation of Reconnection

Reconnection is a major commonality of solar and magnetospheric physics. It was conjectured by Giovanelli in 1946 to explain particle acceleration in solar flares near magnetic neutral points. Since than it has been broadly applied in space physics including magnetospheric physics. In a special way this is due to Harry Petschek, who in 1994 published his ground breaking solution for a 2D magnetized plasma flow in regions containing singularities of vanishing magnetic field. Petschek’s reconnection theory was questioned in endless disputes and arguments, but his work stimulated the further investigation of this phenomenon like no other. However, there are questions left open. We consider two of them – “anomalous” resistivity in collisionless space plasma and the nature of reconnection in three dimensions. The CLUSTER and SOHO missions address these two aspects of reconnection in a complementary way -- the resistivity problem in situ in the magnetosphere and the 3D aspect by remote sensing of the Sun. We demonstrate that the search for answers to both questions leads beyond the applicability of analytical theories and that appropriate numerical approaches are necessary to investigate the essentially nonlinear and nonlocal processes involved. Necessary are both micro-physical, kinetic Vlasov-equation based methods of investigation as well as large scale (MHD) simulations to obtain the geometry and topology of the acting fields and flows.     

Stability and waves of transonic laboratory and space plasmas

The properties of magnetohydrodynamic waves and instabilities of laboratory and space plasmas are determined by the overall magnetic confinement geometry and by the detailed distributions of the density, pressure, magnetic field, and background velocity of the plasma. Consequently, measurement of the spectrum of MHD waves (MHD spectroscopy) gives direct information on the internal state of the plasma, provided a theoretical model is available to solve the forward as well as the inverse spectral problems. This terminology entails a program, viz. to improve the accuracy of our knowledge of plasmas, both in the laboratory and in space. Here, helioseismology (which could be considered as one of the forms of MHD spectroscopy) may serve as a luminous example. The required study of magnetohydrodynamic waves and instabilities of both laboratory and space plasmas has been conducted for many years starting from the assumption of static equilibrium. Recently, there is a outburst of interest for plasma states where this assumption is violated. In fusion research, this interest is due to the importance of neutral beam heating and pumped divertor action for the extraction of heat and exhaust needed in future tokamak reactors. Both result in rotation of the plasma with speeds that do not permit the assumption of static equilibrium anymore. In astrophysics, observations in the full range of electromagnetic radiation has revealed the primary importance of plasma flows in such diverse situations as coronal flux tubes, stellar winds, rotating accretion disks, and jets emitted from radio galaxies. These flows have speeds which substantially influence the background stationary equilibrium state, if such a state exists at all. Consequently, it is important to study both the stationary states of magnetized plasmas with flow and the waves and instabilities they exhibit. We will present new results along these lines, extending from the discovery of gaps in the continuous spectrum and low-frequency Alfvén waves driven by rotation to the nonlinear flow patterns that occur when the background speed traverses the full range from sub-slow to super-fast. This revised version was published online in August 2006 with corrections to the 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.     

Transonic Flows in Two-Fluid Plasmas

Transonically rotating toroidal plasmas occur at all scales in the plasma universe and, recently, also in laboratory tokamak plasmas. This offers great opportunities for new insights of the effects of transonic transitions on the background equilibrium flows, and on the waves and instabilities excited. Transfer of knowledge and computational methods on MHD and two-fluid waves and instabilities in magnetically confined laboratory fusion plasmas to space and astrophysical plasmas is seriously hampered though by two related difficulties:

1. in contrast to laboratory plasmas, astrophysical plasmas always have sizeable plasma flows so that they can never be described as a static equilibrium;
2. these flows are usually ‘transonic’, i.e., surpass one of the critical speeds related to the different flow regimes with quite different physical characteristics.

Based on previously obtained MHD results on the stationary states and instabilities of transonically rotating accretion disks about compact objects, the extension to two-fluid plasmas is initiated: A variational principle for the computation of two-fluid stationary states is constructed which involves seven fields determining the different physical variables, and six arbitrary stream functions that should be determined by spatially resolved astrophysical observations. It exhibits all the intricacies due to the electron and ion flow excursions from the magnetic flux surfaces. New hyperbolic flow regimes are found with quite different properties than the MHD ones.     

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.     

Dayside Proton Aurora: Comparisons between Global MHD Simulations and IMAGE Observations

The IMAGE mission provides a unique opportunity to evaluate the accuracy of current global models of the solar wind interaction with the Earth's magnetosphere. In particular, images of proton auroras from the Far Ultraviolet Instrument (FUV) onboard the IMAGE spacecraft are well suited to support investigations of the response of the Earth's magnetosphere to interplanetary disturbances. Accordingly, we have modeled two events that occurred on June 8 and July 28, 2000, using plasma and magnetic field parameters measured upstream of the bow shock as input to three-dimensional magnetohydrodynamic (MHD) simulations. This paper begins with a discussion of images of proton auroras from the FUV SI-12 instrument in comparison with the simulation results. The comparison showed a very good agreement between intensifications in the auroral emissions measured by FUV SI-12 and the enhancement of plasma flows into the dayside ionosphere predicted by the global simulations. Subsequently, the IMAGE observations are analyzed in the context of the dayside magnetosphere's topological changes in magnetic field and plasma flows inferred from the simulation results. Finding include that the global dynamics of the auroral proton precipitation patterns observed by IMAGE are consistent with magnetic field reconnection occurring as a continuous process while the IMF changes in direction and the solar wind dynamic pressure varies. The global simulations also indicate that some of the transient patterns observed by IMAGE are consistent with sporadic reconnection processes. Global merging patterns found in the simulations agree with the antiparallel merging model, though locally component merging might broaden the merging region, especially in the region where shocked solar wind discontinuities first reach the magnetopause. Finally, the simulations predict the accretion of plasma near the bow shock in the regions threaded by newly open field lines on which plasma flows into the dayside ionosphere are enhanced. Overall the results of these initial comparisons between global MHD simulation results and IMAGE observations emphasize the interplay between reconnection and dynamic pressure processes at the dayside magnetopause, as well as the intricate connection between the bow shock and the auroral region.     

MHD ANALYSIS OF PETSCHEK-TYPE RECONNECTION IN NON-UNIFORM FIELD AND FLOW GEOMETRIES

Analytical studies of reconnection have, for the most part, been confined to steady and uniform current sheet geometries. In contrast to these implifications, natural phenomena associated with the presence of current sheets indicate highly non-uniform structure and time-varying behaviour. Examples include the violent outbursts of energy on the Sun known as solar flares, and magnetospheric phenomena such as flux transfer events, plasmoids, and auroral activity. Unlike the theoretical models, reconnection therefore occurs in a highly dynamic and structured plasma environment. In this article we review the mathematical tools and techniques which are available to formulate models capable of describing the effects of reconnection in such situations. We confine attention to variants of the reconnection model first discussed by Petschek in the 1960s, in view of its successful application in predicting and interpreting phenomena in the terrestrial magnetosphere. The analysis of Petschek-type reconnection is based on the equations of ideal magnetohydrodynamics (MHD), which describe the large-scale behaviour of the magnetic field and plasma flow outside the diffusion region, which we determine as a localised part of the current sheet in which reconnection is initiated. The approach we adopt here is to transform the MHD equations into a Lagrangian or so-called 'frozen-in' coordinate system. In this coordinate system, the equation of motion transforms into a set of coupled nonlinear equations, in which the presence of inhomogeneous magnetic fields and/or plasma flows gives rise to a term similar to that which appears in the study of the ordinary string equation in a non-homogeneous medium. As demonstrated here, this approach not only clarifies and highlights the effects of such non-uniformities, it also simplifies the solution of the original set of MHD equations. In particular, this is true for those types of problem in which the total pressure can be considered as a known quantity from the outset. To illustrate the method, we solve several 2D problems involving magnetic field and flow non-uniformities: reconnection in a stagnation-point flow geometry with antiparallel magnetic fields; reconnection in a Y-type magnetic field geometry with and without velocity shear across the current sheet; and reconnection in a force-free magnetic field geometry with field lines of the form xy = const. These case examples, chosen for their tractability, each incorporate some aspects of the field and flow geomtries encountered in solar-terrestrial applications, and they provide a starting point for further analytical as well as numerical studies of reconnection.