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.     

Non-adiabatic Ion Acceleration in the Earth Magnetotail and Its Various Manifestations in the Plasma Sheet Boundary Layer

Many physical phenomena in space involve energy dissipation which generally leads to charged particle acceleration, often up to very high energies. In the Earth magnetosphere energy accumulation and release occur in the magnetotail, namely in its Current Sheet (CS). The kinetic analysis of non-adiabatic ion trajectories in the CS region with finite but positive normal component of the magnetic field demonstrated that this region is essentially non-uniform in terms of scattering characteristics of ion orbits and contains spatially localized, well-separated sites of enhanced and reduced chaotization. The latter represent sources from which accelerated and energy-collimated ions are ejected into Plasma Sheet Boundary Layer (PSBL) and stream towards the Earth. Numerical simulations performed as part of a Large-Scale Kinetic Model have shown the multiplet ion structure of the PSBL is formed by a set of ion beams (beamlets) localized both in physical and velocity space. This structure of the PSBL is quite different from the one produced by CS acceleration near a magnetic reconnection region in which more energetic ion beams are generated with a broad range of parallel velocities. Multi-point Cluster observations in the magnetotail PSBL not only showed that non-adiabatic ion acceleration occurs on closed magnetic field lines with at least two CS sources operating simultaneously, but also allowed an estimation of their spatial and temporal characteristics. In this paper we discuss and compare the PSBL manifestations of both mechanisms of CS particle acceleration: one based on the peculiar properties of non-adiabatic ion trajectories which operates on closed magnetic field lines and the other representing the well-explored mechanism of particle acceleration during the course of magnetic reconnection. We show that these two mechanisms supplement each other and the first operates mostly during quiescent magnetotail periods.     

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.     

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.     

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.     

Several recent findings concerning the dynamics of the Earth's magnetotail

Several recent results concerning the nature of the Earth's magnetotail are briefly reviewed. These observational findings include: (1) the three-dimensional character of the plasma sheet via a comprehensive survey of proton bulk flows, (2) a region of earthward flowing plasmas at the interfaces of the plasma sheet and magnetotail lobes during magnetic substorm recovery, and (3) the signature of electrostatic acceleration for protons within the jetting plasmas from magnetotail fireballs.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

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.     

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.     

The Induced Magnetospheres of Mars, Venus, and Titan

This article summarizes and aims at comparing the main features of the induced magnetospheres of Mars, Venus and Titan. All three objects form a well-defined induced magnetosphere (IM) and magnetotail as a consequence of the interaction of an external wind of plasma with the ionosphere and the exosphere of these objects. In all three, photoionization seems to be the most important ionization process. In all three, the IM displays a clear outer boundary characterized by an enhancement of magnetic field draping and massloading, along with a change in the plasma composition, a decrease in the plasma temperature, a deflection of the external flow, and, at least for Mars and Titan, an increase of the total density. Also, their magnetotail geometries follow the orientation of the upstream magnetic field and flow velocity under quasi-steady conditions. Exceptions to this are fossil fields observed at Titan and the near Mars regions where crustal fields dominate the magnetic topology. Magnetotails also concentrate the escaping plasma flux from these three objects and similar acceleration mechanisms are thought to be at work. In the case of Mars and Titan, global reconfiguration of the magnetic field topology (reconnection with the crustal sources and exits into Saturn??s magnetosheath, respectively) may lead to important losses of plasma. Finally, an ionospheric boundary related to local photoelectron signals may be, in the absence of other sources of pressure (crustal fields) a signature of the ultimate boundary to the external flow.     

Basic Physical Mechanism of Fast Reconnection Evolution in Space Plasmas

Large dissipative events, such as solar flares and geomagnetic substorms, may result from sudden onset of fast (explosive) magnetic reconnection. Hence, it is a long-standing problem to find the physical mechanism that makes magnetic reconnection explosive; in particular, how can the fast magnetic reconnection explosively evolve in space plasmas? In this respect, we have proposed the spontaneous fast reconnection model as a nonlinear instability that grows by the positive feedback between plasma microphysics (anomalous resistivity) and macrophysics (global reconnection flow). On the basis of MHD simulations, we demonstrate for a variety of physical situations that the fast reconnection mechanism involving slow shocks in fact evolves explosively as a nonlinear instability and is sustained quasi-steadily on the nonlinear saturation phase. Also, distinct plasma processes, such as large-scale plasmoid propagation, magnetic loop development and loop-top heating, and asymmetric fast reconnection evolution, directly result from the spontaneous fast reconnection model. Obviously, MHD simulations are very useful in understanding the basic physics of explosive fast reconnection evolution in space plasmas. However, they cannot treat the details of microphysics near an X neutral point, which should be precisely studied in the coming 21st century.     

Particle Acceleration in the Magnetotail and Aurora

This paper deals with acceleration processes in the magnetotail and the processes that enhance particle precipitation from the tail into the ionosphere through electric fields in the auroral acceleration region, generating or intensifying discrete auroral arcs. Particle acceleration in the magnetotail is closely related to substorms and the occurrence, and consequences, of magnetic reconnection. We discuss major advances in the understanding of relevant acceleration processes on the basis of simple analytical models, magnetohydrodynamic and test particle simulations, as well as full electromagnetic particle-in-cell simulations. The auroral acceleration mechanisms are not fully understood, although several, sometimes competing, theories and models received experimental support during the last decades. We review recent advances that emphasize the role of parallel electric fields produced by quasi-stationary or Alfvénic processes.     

Relativistic Reconnection and Particle Acceleration

This chapter mainly deals with magnetic reconnection and particle acceleration in relativistic astrophysical plasmas, where the temperature of the current sheet exceeds the rest mass energy and the Alfvén velocity is close to the speed of light. Magnetic reconnection now receives a great deal of interest for its role in many astrophysical systems such as pulsars, magnetars, galaxy clusters, and active galactic nucleus jets. We review recent advances that emphasize the roles of reconnection in high-energy astrophysical phenomena.     

Magnetic reconnection,merging, and viscous interaction in the magnetosphere

Two ideas were advanced for the process of solar wind-magnetospheric interaction in the same year 1961. Dungey suggested that the interplanetary magnetic field (IMF), although weak, might determine the nature of this process by magnetic reconnection as the solar wind plasma flows across the separatrix surface which divides the IMF from the geomagnetic field. Axford and Hines pointed out that the flow inside the magnetopause is in the same sense as the magnetosheath flow and appears to be viscously coupled. Within a few years the dependence of geomagnetic activity on the IMF predicted by Dungey's mechanism was observed, and reconnection began to dominate current theories. One difficulty, that of the implied dissipation at the magnetopause, was troublesome; however, the ISEE-1/2 observations of the predicted high speed flows on several occasions was enough to convince many persons that reconnection ideas were basically correct. Several investigators found some evidence in the ISEE-3 data in the distant magnetotail for the steady-state reconnection line, as demanded by the Dungey model, in the form of a southward sense of the magnetic field through the current sheet. Here, again, there is some hard contrary evidence when the data are analyzed exactly at the cross-tail current sheet: the instantaneous values show a northward sense, even at high values of auroral activity. Coupled with the anti-Sunward plasma flow, this repudiates the steady-state Dungey model. On the other hand, it lends strong support to some kind of viscous effect through the medium of the magnetospheric boundary layer. This is not a semantic problem, as the sense of the electric field (as well as the magnetic field) is opposite for the two cases. The downfall of the reconnection model is its implicit use of frozen-field convection; this problem is obvious when the problem is viewed in three dimensions. Instead, the view is taken that the relevant process must be essentially time-dependent, three-dimensional, and localized. It is proposed that the term merging be used for this generalized timedependent form of reconnection. The merging process (whatever it is) must permit solar wind plasma to cross the magnetopause onto closed field lines of the boundary layer. Once it is there, it provides the viscous-like effect that Axford and Hines had envisaged.     

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.     

Cause and Effect At the Magnetopause

Recent analyses of spacecraft data, especially AMPTE/IRM data, provide a test of reconnection theory; an analysis for the signature of a local tangential stress balance in a one-dimensional time-stationary rotational discontinuity has left crucial questions unanswered. A key result is that the electron temperature profile inward through the magnetopause current sheet shows heating followed by cooling. Electrons must be one of the carriers of the current; hence this result reflects the sign of E · J in the frame of reference of the magnetopause current carriers. Since the current is directed from dawn to dusk, the inescapable conclusion is that the electric field must reverse within the current sheet. This is direct evidence of a load–dynamo combination; in that dynamo, energy is transferred from the solar wind plasma to the electromagnetic field. A dynamo is not included in the reconnection model which includes only the electrical load; therefore, we argue that the reconnection problem is improperly posed. A second compelling observation is a remarkable difference of the normal component of the plasma velocity between inbound and outbound crossings. For an inbound crossing (outward current meander) this component does reverse, but not quite as assumed in the reconnection model; on the other hand, for outbound crossings of the spacecraft (corresponding to erosion) there is no reversal at all. The normal component is approximately constant at 20 km s^-1, anti-Sunward throughout. Since the typical motion of the magnetopause is 10 km s^-1 this revealing result shows that solar wind plasma can go across the magnetopause, even onto closed field lines to feed the low latitude boundary layer. This is in stark contrast to the reconnection model where the plasma goes to open field lines. The interaction can be understood by appealing to Poynting's theorem, where E · J describes the net effect on or by the plasma. Time-dependent terms (even in the initial conditions) must be used so that it is possible to draw upon energy which has been stored locally in both electrical and magnetic forms. An extended discussion of observational results from ground-based, rocket, and satellite instruments indicate the impulsive nature of the solar wind–magnetospheric interaction. There is a lot of plasma involved in this interaction, over 10²⁷ ions electrons^-1 per second; the anti-Sunward flow takes place in the low latitude boundary layer. There is no flux catastrophe produced by this flow since the frozen-field theorem does not hold for plasma transfer across the magnetopause. The LLBL completely envelops the plasma sheet; the LLBL is the source of its plasma, not the plasma mantle as hypothesized in the reconnection model of the magnetotail. A number of serious errors have occurred in some articles in the literature on reconnection, and we list and discuss the most important of these. In the conclusion it is emphasized that the failure to provide a viable energy source, within the necessary spatial and temporal constraints, is responsible for the failure of reconnection model. This does not mean that the state of interconnection between the geomagnetic field and the interplanetary magnetic field can not change, but it does mean that the advocated process is not relevant to such changes. True reconnection requires that the electric field has a curl so that an electromotive force = E · dl = -d_Mdt exists through which energy can be interchanged with stored magnetic energy.     

Auroral Plasma Acceleration Above Martian Magnetic Anomalies

Aurora is caused by the precipitation of energetic particles into a planetary atmosphere, the light intensity being roughly proportional to the precipitating particle energy flux. From auroral research in the terrestrial magnetosphere it is known that bright auroral displays, discrete aurora, result from an enhanced energy deposition caused by downward accelerated electrons. The process is commonly referred to as the auroral acceleration process. Discrete aurora is the visual manifestation of the structuring inherent in a highly magnetized plasma. A strong magnetic field limits the transverse (to the magnetic field) mobility of charged particles, effectively guiding the particle energy flux along magnetic field lines. The typical, slanted arc structure of the Earth’s discrete aurora not only visualizes the inclination of the Earth’s magnetic field, but also illustrates the confinement of the auroral acceleration process. The terrestrial magnetic field guides and confines the acceleration processes such that the preferred acceleration of particles is frequently along the magnetic field lines. Field-aligned plasma acceleration is therefore also the signature of strongly magnetized plasma. This paper discusses plasma acceleration characteristics in the night-side cavity of Mars. The acceleration is typical for strongly magnetized plasmas – field-aligned acceleration of ions and electrons. The observations map to regions at Mars of what appears to be sufficient magnetization to support magnetic field-aligned plasma acceleration – the localized crustal magnetizations at Mars (Acuña et al., 1999). Our findings are based on data from the ASPERA-3 experiment on ESA’s Mars Express, covering 57 orbits traversing the night-side/eclipse of Mars. There are indeed strong similarities between Mars and the Earth regarding the accelerated electron and ion distributions. Specifically acceleration above Mars near local midnight and acceleration above discrete aurora at the Earth – characterized by nearly monoenergetic downgoing electrons in conjunction with nearly monoenergetic upgoing ions. We describe a number of characteristic features in the accelerated plasma: The “inverted V” energy-time distribution, beam vs temperature distribution, altitude distribution, local time distribution and connection with magnetic anomalies. We also compute the electron energy flux and find that the energy flux is sufficient to cause weak to medium strong (up to several tens of kR 557.7 nm emissions) aurora at Mars. Monoenergetic counterstreaming accelerated ions and electrons is the signature of field-aligned electric currents and electric field acceleration. The topic is reasonably well understood in terrestrial magnetospheric physics, although some controversy still remains on details and the cause-effect relationships. We present a potential cause-effect relationship leading to auroral plasma acceleration in the nightside cavity of Mars – the downward acceleration of electrons supposedly manifesting itself as discrete aurora above Mars.