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.     

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.     

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.     

Energy Release and Particle Acceleration in Flares: Summary and Future Prospects

RHESSI measurements relevant to the fundamental processes of energy release and particle acceleration in flares are summarized. RHESSI??s precise measurements of hard X-ray continuum spectra enable model-independent deconvolution to obtain the parent electron spectrum. Taking into account the effects of albedo, these show that the low energy cut-off to the electron power-law spectrum is typically ?tens of keV, confirming that the accelerated electrons contain a large fraction of the energy released in flares. RHESSI has detected a high coronal hard X-ray source that is filled with accelerated electrons whose energy density is comparable to the magnetic-field energy density. This suggests an efficient conversion of energy, previously stored in the magnetic field, into the bulk acceleration of electrons. A new, collisionless (Hall) magnetic reconnection process has been identified through theory and simulations, and directly observed in space and in the laboratory; it should occur in the solar corona as well, with a reconnection rate fast enough for the energy release in flares. The reconnection process could result in the formation of multiple elongated magnetic islands, that then collapse to bulk-accelerate the electrons, rapidly enough to produce the observed hard X-ray emissions. RHESSI??s pioneering ??-ray line imaging of energetic ions, revealing footpoints straddling a flare loop arcade, has provided strong evidence that ion acceleration is also related to magnetic reconnection. Flare particle acceleration is shown to have a close relationship to impulsive Solar Energetic Particle (SEP) events observed in the interplanetary medium, and also to both fast coronal mass ejections and gradual SEP events. New instrumentation to provide the high sensitivity and wide dynamic range hard X-ray and ??-ray measurements, plus energetic neutral atom (ENA) imaging of SEPs above ??2 R_??, will enable the next great leap forward in understanding particle acceleration and energy release is large solar eruptions??solar flares and associated fast coronal mass ejections (CMEs).     

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.     

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.     

Reconnective release of magnetic energy in astrophysical plasmas

Two particular examples are considered of astrophysical objects containing a highly conducting tenuous plasma with an excess magnetic energy supplied by an external source. The first example is the solar corona, whose magnetic field is continuously distorted by footpoint shuffling due to photospheric motions. The second case it an extragalactic jet extending from a galactic nucleus with an immersed magnetic field, and which is perturbed by variations in the pressure of the external medium. In both cases it is assumed that the system tends towards its lowest magnetic energy equilibrium via magnetic reconnection, thus providing a fast release of injected magnetic energy. Explicit relations between the characteristics of the external driver and the magnetic energy dissipation rate in these objects have been obtained. The relevance of this mechanism for heating the solar corona and maintaining radio emission from extragalactic jets is then. discussed by comparing these results with observational data.     

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.     

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.     

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.     

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.     

The Magnetic Field Pile-up and Density Depletion in the Martian Magnetosheath: A Comparison with the Plasma Depletion Layer Upstream of the Earth's Magnetopause

Using magnetometer and electron observations from the Mars Global Surveyor (MGS) and the Wind spacecraft we show that the region of magnetic field pile-up and density decrease located between the Martian ionosphere and bow shock exhibit strong similarities with the plasma depletion layer (PDL) observed upstream of the Earth's magnetopause in the absence of magnetic reconnection when the magnetopause is a solid obstacle in the solar wind. A PDL is formed upstream of the terrestrial magnetopause when the magnetic field piles up against the obstacle and particles in the pile-up region are squeezed away from the high magnetic pressure region along the field lines as the flux tubes convect toward the magnetopause. We here discuss the possibility that at least part of the region of magnetic field pile-up and density depletion upstream of Mars may be formed by the same physical processes which generate the PDL upstream of the Earth's magnetopause. More complete ion, electron, and neutral measurements are needed to conclusively determine the relative importance of the plasma depletion process versus exospheric processes.     

Observed Aspects of Reconnection in Solar Eruptions

The observed magnetic field configuration and signatures of reconnection in the large solar magnetic eruptions that make major flares and coronal mass ejections and in the much smaller magnetic eruptions that make X-ray jets are illustrated with cartoons and representative observed eruptions. The main reconnection signatures considered are the imaged bright emission from the heated plasma on reconnected field lines. In any of these eruptions, large or small, the magnetic field that drives the eruption and/or that drives the buildup to the eruption is initially a closed bipolar arcade. From the form and configuration of the magnetic field in and around the driving arcade and from the development of the reconnection signatures in coordination with the eruption, we infer that (1) at the onset of reconnection the reconnection current sheet is small compared to the driving arcade, and (2) the current sheet can grow to the size of the driving arcade only after reconnection starts and the unleashed erupting field dynamically forces the current sheet to grow much larger, building it up faster than the reconnection can tear it down. We conjecture that the fundamental reason the quasi-static pre-eruption field is prohibited from having a large current sheet is that the magnetic pressure is much greater than the plasma pressure in the chromosphere and low corona in eruptive solar magnetic fields.     

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.     

Influence of the Interplanetary Magnetic Field on the Solar Wind Flow about Planetary Obstacles

The main effects caused by the interplanetary magnetic field (IMF) are analyzed in cases of supersonic solar wind flow around magnetized planets (like Earth) and nonmagnetized (like Venus) planets. The IMF has a relatively weak strength in the solar wind but it is enhanced considerably in the so-called plasma depletion layer or magnetic barrier in the vicinity of the streamlined obstacle (magnetopause of a magnetized planet, or ionopause of a nonmagnetized planet). For magnetized planets, the magnetic barrier is a source of free magnetic energy for magnetic reconnection in cases of large magnetic shear at the magnetopause. For nonmagnetized planets, mass loading of the ionospheric particles is very important. The new created ions are accelerated by the electric field related to the IMF, and thus they gain energy from the solar wind plasma. These ions form the boundary layer within the magnetic barrier. This mass loading process affects considerably the profiles of the magnetic field and plasma parameters in the flow region.     

Microphysics in Astrophysical Plasmas

Although macroscale features dominate astrophysical images and energetics, the physics is controlled through microscale transport processes (conduction, diffusion) that mediate the flow of mass, momentum, energy, and charge. These microphysical processes manifest themselves in key (all) boundary layers and also operate within the body of the plasma. Crucially, most plasmas of interest are rarefied to the extent that classical particle collision length- and time-scales are long. Collective plasma kinetic phenomena then serve to scatter or otherwise modify the particle distribution functions and in so-doing govern the transport at the microscale level. Thus collisionless plasmas are capable of supporting thin shocks, current sheets which may be prone to magnetic reconnection, and the dissipation of turbulence cascades at kinetic scales. This paper lays the foundation for the accompanying collection that explores the current state of knowledge in this subject. The richness of plasma kinetic phenomena brings with it a rich diversity of microphysics that does not always, if ever, simply mimic classical collision-dominated transport. This can couple the macro- and microscale physics in profound ways, and in ways which thus depend on the astrophysical context.     

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.     

Global Properties of Solar Flares

This article broadly reviews our knowledge of solar flares. There is a particular focus on their global properties, as opposed to the microphysics such as that needed for magnetic reconnection or particle acceleration as such. Indeed solar flares will always remain in the domain of remote sensing, so we cannot observe the microscales directly and must understand the basic physics entirely via the global properties plus theoretical inference. The global observables include the general energetics—radiation in flares and mass loss in coronal mass ejections (CMEs)—and the formation of different kinds of ejection and global wave disturbance: the type II radio-burst exciter, the Moreton wave, the EIT “wave”, and the “sunquake” acoustic waves in the solar interior. Flare radiation and CME kinetic energy can have comparable magnitudes, of order 10³² erg each for an X-class event, with the bulk of the radiant energy in the visible-UV continuum. We argue that the impulsive phase of the flare dominates the energetics of all of these manifestations, and also point out that energy and momentum in this phase largely reside in the electromagnetic field, not in the observable plasma.