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.     

Acceleration of particles by shocks in a cosmic plasma

The theory and observational evidence pertaining to particle acceleration by shock waves in astrophysical objects and in space are systematized. Recent works showing observational and theoretical aspects of the problem dealing with shocks in turbulent media are emphasized. The acceleration of particles by shocks in turbulent media is observed in interplanetary space. This acceleration mechanism is of particular interest from the point of view of the origin of cosmic rays, providing the degree form of the spectrum. The index of the spectrum is close to the observable one for galactic cosmic rays. It depends slightly on specific conditions in the acceleration region. Electron and nucleus acceleration in supernova remnants and in radiogalaxies is discussed, and theory and observational data are compared. The theory of particle acceleration by supersonic turbulence is outlined.     

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.     

Stochastic Acceleration of Energetic Particles in the Heliosphere

In this paper we assess possible roles of stochastic acceleration by random electric field and plasma motion in the production and transport of energetic particles in the heliosphere. Stochastic acceleration can occur in the presence of multiple small-scale magnetohydrodynamic waves propagating in different directions. Usually, this type of stochastic acceleration is closely related to particle pitch angle scattering or parallel diffusion. Given the values of the parallel diffusion coefficient inferred from the observations of cosmic ray modulation or other energetic particle phenomena in the heliosphere, stochastic acceleration by small-scale waves is much slower than acceleration by shock waves and it is also much slower than adiabatic cooling by the expansion of the solar wind; thus it is considered as inefficient for producing heliospheric energetic particles or for the modulation of cosmic rays. Another type of stochastic acceleration occurs when particles go through random compressions or expansions due to large-scale plasma motion. This acceleration mechanism could be very fast when the correlation time of the fluctuations in plasma compression is short compared to the diffusion time. Particle acceleration by an ensemble of small shock waves or intermittent long wavelength compressible turbulence belongs to this category. It tends to establish an asymptotic p ^?3 universal distribution function quickly if there is no or little large-scale adiabatic cooling. Such a particle distribution will contain an infinite amount of pressure. Back reaction from the pressure is expected to modify the amplitude of plasma waves to an equilibrium state. At that point, the pressure of accelerated particles must remain finite and the accelerated particles could approach a p ^?5 distribution function.     

Diffusive Shock Acceleration and Magnetic Field Amplification

Diffusive shock acceleration is the theory of particle acceleration through multiple shock crossings. In order for this process to proceed at a rate that can be reconciled with observations of high-energy electrons in the vicinity of the shock, and for cosmic rays protons to be accelerated to energies up to observed galactic values, significant magnetic field amplification is required. In this review we will discuss various theories on how magnetic field amplification can proceed in the presence of a cosmic ray population. On both short and long length scales, cosmic ray streaming can induce instabilities that act to amplify the magnetic field. Developments in this area that have occurred over the past decade are the main focus of this paper.     

Corotating Particle Events

The corotating particle events give us a unique opportunity to probe the three-dimensional structures of the heliosphere. This is especially true if we have observations over a period of extreme stability of the CIRs, such as existed over the recent solar minimum. We discuss how the observations fit into the context of current heliospheric magnetic field models. The energetic particle signatures of CIRs throughout the regions of the heliosphere covered by the deep-space missions are reviewed. The CIRs accelerate these particles and at the same time modulate both the high energy galactic cosmic rays and the anomalous cosmic rays.     

Shock Acceleration of Ions in the Heliosphere

Energetic particles constitute an important component of the heliospheric plasma environment. They range from solar energetic particles in the inner heliosphere to the anomalous cosmic rays accelerated at the interface of the heliosphere with the local interstellar medium. Although stochastic acceleration by fluctuating electric fields and processes associated with magnetic reconnection may account for some of the particle populations, the majority are accelerated by the variety of shock waves present in the solar wind. This review focuses on “gradual” solar energetic particle (SEP) events including their energetic storm particle (ESP) phase, which is observed if and when an associated shock wave passes Earth. Gradual SEP events are the intense long-duration events responsible for most space weather disturbances of Earth’s magnetosphere and upper atmosphere. The major characteristics of gradual SEP events are first described including their association with shocks and coronal mass ejections (CMEs), their ion composition, and their energy spectra. In the context of acceleration mechanisms in general, the acceleration mechanism responsible for SEP events, diffusive shock acceleration, is then described in some detail including its predictions for a planar stationary shock, shock modification by the energetic particles, and wave excitation by the accelerating ions. Finally, some complexities of shock acceleration are addressed, which affect the predictive ability of the theory. These include the role of temporal and spatial variations, the distinction between the plasma and wave compression ratios at the shock, the injection of thermal plasma at the shock into the process of shock acceleration, and the nonlinear evolution of ion-excited waves in the vicinity of the shock.     

Collisionless Shocks in Partly Ionized Plasma with Cosmic Rays: Microphysics of Non-thermal Components

In this review we discuss some observational aspects and theoretical models of astrophysical collisionless shocks in partly ionized plasma with the presence of non-thermal components. A specific feature of fast strong collisionless shocks is their ability to accelerate energetic particles that can modify the shock upstream flow and form the shock precursors. We discuss the effects of energetic particle acceleration and associated magnetic field amplification and decay in the extended shock precursors on the line and continuum multi-wavelength emission spectra of the shocks. Both Balmer-type and radiative astrophysical shocks are discussed in connection to supernova remnants interacting with partially neutral clouds. Quantitative models described in the review predict a number of observable line-like emission features that can be used to reveal the physical state of the matter in the shock precursors and the character of nonthermal processes in the shocks. Implications of recent progress of gamma-ray observations of supernova remnants in molecular clouds are highlighted.     

GeV Particle Acceleration in Solar Flares and Ground Level Enhancement (GLE) Events

Ground Level Enhancement (GLE) events represent the most energetic class of solar energetic particle (SEP) events, requiring acceleration processes to boost ?1?GeV ions in order to produce showers of secondary particles in the Earth’s atmosphere with sufficient intensity to be detected by ground-level neutron monitors, above the background of cosmic rays. Although the association of GLE events with both solar flares and coronal mass ejections (CMEs) is undisputed, the question arises about the location of the responsible acceleration site: coronal flare reconnection sites, coronal CME shocks, or interplanetary shocks? To investigate the first possibility we explore the timing of GLE events with respect to hard X-ray production in solar flares, considering the height and magnetic topology of flares, the role of extended acceleration, and particle trapping. We find that 50% (6 out of 12) of recent (non-occulted) GLE events are accelerated during the impulsive flare phase, while the remaining half are accelerated significantly later. It appears that the prompt GLE component, which is observed in virtually all GLE events according to a recent study by Vashenyuk et al. (Astrophys. Space Sci. Trans. 7(4):459–463, 2011), is consistent with a flare origin in the lower corona, while the delayed gradual GLE component can be produced by both, either by extended acceleration and/or trapping in flare sites, or by particles accelerated in coronal and interplanetary shocks.     

Stochastic Acceleration by Turbulence

The subject of this paper is stochastic acceleration by plasma turbulence, a process akin to the original model proposed by Fermi. We review the relative merits of different acceleration models, in particular the so called first order Fermi acceleration by shocks and second order Fermi by stochastic processes, and point out that plasma waves or turbulence play an important role in all mechanisms of acceleration. Thus, stochastic acceleration by turbulence is active in most situations. We also show that it is the most efficient mechanism of acceleration of relatively cool non relativistic thermal background magnetized plasma particles. In addition, it can preferentially accelerate electrons relative to protons as is needed in many astrophysical radiating sources, where usually there are no indications of presence of shocks. We also point out that a hybrid acceleration mechanism consisting of initial acceleration by turbulence of background particles followed by a second stage acceleration by a shock has many attractive features. It is demonstrated that the above scenarios can account for many signatures of the accelerated electrons, protons and other ions, in particular ³He and ⁴He, seen directly as Solar Energetic Particles and through the radiation they produce in solar flares.     

Non-Thermal Processes in Cosmological Simulations

Non-thermal components are key ingredients for understanding clusters of galaxies. In the hierarchical model of structure formation, shocks and large-scale turbulence are unavoidable in the cluster formation processes. Understanding the amplification and evolution of the magnetic field in galaxy clusters is necessary for modelling both the heat transport and the dissipative processes in the hot intra-cluster plasma. The acceleration, transport and interactions of non-thermal energetic particles are essential for modelling the observed emissions. Therefore, the inclusion of the non-thermal components will be mandatory for simulating accurately the global dynamical processes in clusters. In this review, we summarise the results obtained with the simulations of the formation of galaxy clusters which address the issues of shocks, magnetic field, cosmic ray particles and turbulence.     

Astrophysical Hydromagnetic Turbulence

Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich–Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered.     

Development and Effects of Turbulence in Connection with CIRs

We present an overview of the properties of magnetohydrodynamic turbulence within corotating interaction regions (CIRs) and its effects on energetic particles. We stress the importance of both the population of fluctuations in the inner heliosphere and the changing local environment in determining their properties at larger heliospheric distances. We present observations from two typical CIRs, one at 0.3 AU before compression regions have formed and the other well developed at 5.1 AU, and discuss the properties of fluctuations within them and show that it is possible to distinguish different regions of the CIR on the basis of the turbulence itself. The strength of the turbulence varies strongly within and close to the CIRs, explaining changes in the mean free path of energetic particles of several orders of magnitude with implications for the modulation of cosmic rays and for diffusive acceleration of particles. The mechanisms by which turbulent fluctuations within interaction regions scatter energetic particles are briefly discussed on a theoretical basis. This revised version was published online in August 2006 with corrections to the Cover Date.     

Particle Acceleration and Nonthermal Phenomena in Superbubbles

Models of nonthermal particle acceleration in the vicinity of active star forming regions are reviewed. We discuss a collective effect of both stellar winds of massive stars and core collapsed supernovae as particle acceleration agents. Collective supernova explosions with great energy release in the form of multiple interacting shock waves inside the superbubbles are argued as a favourable site of nonthermal particle acceleration. The acceleration mechanism provides efficient creation of a nonthermal nuclei population with a hard low-energy spectrum, containing a substantial part of the kinetic energy released by the winds of young massive stars and supernovae. We discuss a model of temporal evolution of particle distribution function accounting for the nonlinear effect of the reaction of the accelerated particles on the shock turbulence inside the superbubble. The model illustrates that both the low-energy metal-rich nonthermal component and the standard galactic cosmic rays could be efficiently produced by superbubbles at different evolution stages.     

Cross Field Diffusion of Cosmic Rays in a Two-Dimensional Magnetic Field Turbulence

Cross field diffusion of energetic particles (cosmic rays) in a two-dimensional static magnetic field turbulence is studied performing test particle simulations. Qualitatively different diffusion processes are observed depending on the ratio of Larmor radius (ρ) to the correlation length (λ) of the magnetic field fluctuations. The diffusion is found to be composed of several regimes with distinct statistical properties, which can be characterized using Levy statistics. This revised version was published online in August 2006 with corrections to the Cover Date.     

ICMEs at High Latitudes and in the Outer Heliosphere

Interplanetary coronal mass ejections (ICMEs) propagate into the outer heliosphere, where they can have a significant effect on the structure, evolution, and morphology of the solar wind, particularly during times of high solar activity. They are known to play an important role in cosmic ray modulation and the acceleration of energetic particles. ICMEs are also believed to be associated with the large global transient events that swept through the heliosphere during the declining phases of solar cycles 21 and 22. But until recently, little was known about the actual behavior of ICMEs at large heliographic latitudes and large distances from the Sun. Over the past decade, the Ulysses spacecraft has provided in situ observations of ICMEs at moderate heliographic distances over a broad range of heliographic latitudes. More recently, observations of alpha particle enhancements, proton temperature depressions, and magnetic clouds at the Voyager and Pioneer spacecraft have begun to provide comparable information regarding the behavior of ICMEs at extremely large heliocentric distances. At the same time, advances in modeling have provided new insights into the dynamics and evolution of ICMEs and their effects on cosmic rays and energetic particles.     

Particle Scattering by Magnetic Fields

The need for a correct quantitative treatment of the interactions between cosmic rays and turbulent magnetic fields continues to be one of the fundamental problems of modern astrophysics. It is the aim of this paper to review new developments in the understanding of mechanisms involved in the scattering of charged particles by magnetic field fluctuations. Special emphasis is given to a comparison of transport parameters determined from the modeling of spacecraft and neutron monitor observation of solar particle events, with theoretical predictions derived from a spectral analysis of simultaneously measured fluctuation spectra. It appears that the traditional quasi-linear theory of particle scattering requires only a slight modification, and the major problem still is our lack of knowledge of the three-dimensional structure of the magnetic turbulence. Possibilities to better reconcile the theory with observations by properly taking into account the microphysics of wave and turbulence aspects of the fluctuations, and to use energetic particles as probes to study certain properties of the magnetic turbulence, are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.