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.     

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.     

Optical and UV Diagnostics of Supernova Remnant Shocks

The relatively faint optical and UV emission from non-radiative shock waves provides diagnostics for processes related to cosmic ray acceleration in collisionless shocks. Emission line profiles and intensities can be used to determine the efficiencies of electron-ion and ion-ion thermal equilibration, which influence the population of fast particles injected into the acceleration process. It is found that T _e/T _p declines with shock speed and that T _i is roughly proportional to mass in fast shocks. Important information about cosmic ray precursors may be available, but the interpretation is still somewhat ambiguous. The compression ratios in shocks which efficiently accelerate cosmic rays are predicted to be substantially larger than the factor of 4 expected for a strong shock in a = 5/3 perfect gas, and some limits may be available from observations.     

Solar modulation of galactic cosmic radiation

In this review an attempt is made to present an integrated view of the solar modulation process that cause time variation of cosmic ray particles. After briefly surveying the relevant large and small scale properties of the interplanetary magnetic fields and plasma, the motion of cosmic ray particles in the disordered interplanetary magnetic fields is discussed. The experimentally observed long term variations of different species of cosmic ray particles are summarised and compared with the theoretical predictions from the diffusion-convection model. The effect of the energy losses due to decelaration in the expanding solar wind are clearly brought out. The radial density gradient, the modulation parameter and their long term variation are discussed to understand the dynamics of the modulating region. The cosmic ray anisotropy measurements at different energies are summarised. At high energies (E 1 GeV), the average diurnal anisotropy is shown to be energy independent and along the 18.00 h direction consistent with their undergoing partial corotation with the sun. The average semi-diurnal anisotropy seems to vary with energy as E ⁺¹ and incident from a direction perpendicular to the interplanetary field line, consistent with the semi-diurnal component being produced by latitudinal gradients. Both the diurnal and semi-diurnal components are shown to be practically time invariant. On a day to day basis, however, the anisotropy characteristics such as the exponent of variation, the amplitude and the phase show very high variability which are interpreted in terms of convection and variable field aligned diffusion due to the redistribution of the galactic cosmic ray density following transient changes in the interplanetary medium. The anisotropy observation at low energies (E 100 MeV) are, however, not explained by the theory.The rigidity dependence and the anisotropies during short term variations such as Forbush decreases are discussed in terms of the proposed field models for the interplanetary field structure and are compared with the observed rigidity dependence of long term variations. The data pertaining to the 27 day corotating Forbush decreases and their association with enhanced diurnal variation are also presented. The relationship between the energetic storm particle events which are caused by the acceleration of particles in the shock fronts and the Forbush decreases which are caused by the exclusion of galactic particles by the enhanced field structure in the same fronts are clearly brought out. Thus the recurrent increases at low energies and recurrent decreases at high energies may both be caused by the field structure in the shock front. In conclusion, the properties of the very short period fluctuations (18–25 cph) are summarised.     

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.     

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.     

Theoretical studies of interplanetary propagation and acceleration

Studies evaluating the transport coefficients for energetic particles in interplanetary space are described in relation to particle data.In position space, the main mode of propagation is along field lines but perpendicular diffusion and drift motion is also possible. Diffusion coefficients based on interplanetary magnetic field data are either derived from quasi-linear, adiabatic theory or this theory corrected for finite scattering near 90° pitch angle or by numerical techniques. Relevant particle data includes solar proton event time profile and anisotropy measurements. In general, when Fokker-Planck transport equation solutions are fitted to particle data, the parallel diffusion coefficients obtained still appear rather larger than those given by theoretical estimates. Perpendicular diffusion is shown to be due to field line wandering and random drift motion effects. The importance of drift motion in cosmic ray modulation theory is mentioned.Although much emphasis is currently placed upon shock acceleration in CIR's, statistical acceleration in interplanetary space must be considered. Energetic particles may gain energy from longitudinal waves and cyclotron resonance interactions. Analytical and numerical estimates of the energy space diffusion coefficients are considered. Some reveal a surprising importance to this statistical acceleration and can explain a variety of data.Presented at the Fifth International Symposium on Solar-Terrestrial Physics, held at Ottawa, Canada, May 1982.     

Perpendicular Shock Reformation and Ion Acceleration

Kinetic simulations of supercritical, quasi-perpendicular shocks yield time-varying solutions that cyclically reform on proton spatio-temporal scales. Whether a shock solution is stationary or reforming depends upon the plasma parameters which, for SNR shocks and the heliospheric termination shock, are ill defined but believed to be within this time-dependent regime. We first review the time-dependent solutions and the acceleration processes of the ions for a proton–electron plasma. We then present recent results for a three-component plasma: background protons, electrons and a second ion population appropriate for SNR (heavy ions) or the termination shock (pickup protons). This ion acceleration generates a suprathermal “injection” population – a seed population for subsequent acceleration at the shock, which may in turn generate ions at cosmic ray energies.     

Polar rain entry of galactic electrons into the inner heliosphere?

The understanding of the relative intensity variations in cosmic ray ions and electrons with respect to solar modulation is a grand challenge for cosmic ray modulation theory. Although effects of the heliospheric neutral sheet, gradient-curvature drifts, and merged interaction regions provide qualitative explanations for observed solar cycle variations of high energy protons and ions, these effects do not account for the anomalously high intensities of high energy galactic electrons at 22-year intervals of the solar magnetic solar cycle. From the similar modulation responses of protons and heavy ions it does not appear that cosmic ray pressure effects, dominated by protons, can account for the chargesign asymmetry of cosmic ray modulation. External factors including modulation in the heliosheath and polar linkage to the interstellar magnetic field are examined as potential causes of symmetry breaking for electron modulation with respect to the solar magnetic polarity at solar minimum.     

Cosmic Ray Production in Supernovae

We give a brief review of the origin and acceleration of cosmic rays (CRs), emphasizing the production of CRs at different stages of supernova evolution by the first-order Fermi shock acceleration mechanism. We suggest that supernovae with trans-relativistic outflows, despite being rather rare, may accelerate CRs to energies above \(10^{18}\mbox{ eV}\) over the first year of their evolution. Supernovae in young compact clusters of massive stars, and interaction powered superluminous supernovae, may accelerate CRs well above the PeV regime. We discuss the acceleration of the bulk of the galactic CRs in isolated supernova remnants and re-acceleration of escaped CRs by the multiple shocks present in superbubbles produced by associations of OB stars. The effects of magnetic field amplification by CR driven instabilities, as well as superdiffusive CR transport, are discussed for nonthermal radiation produced by nonlinear shocks of all speeds including trans-relativistic ones.     

Galactic Cosmic Rays in the Outer Heliosphere: Theory and Models

We review recent advances in the field of galactic cosmic ray transport in the distant heliosphere. The advent of global MHD models brought about a better understanding of the three-dimensional structure of the interface between the solar system and the surrounding interstellar space, and of the magnetic field topology in the outer heliosphere. These results stimulated a development of galactic cosmic ray transport models taking the advantage of the available detailed plasma backgrounds and of the new Voyager results from the heliosheath. It emerges that the heliosheath plays a prominent role in the process of modulation and filtration of low-energy galactic ions and electrons. The heliosheath stores particles for a duration of several years thus acting as a large reservoir of galactic cosmic rays. Cosmic-ray trajectories, transit times, and entry locations across the heliopause are discussed. When compared to observations model calculations of low energy electrons show almost no radial gradient up to the termination shock, irrespective of solar activity, but a large gradient in the inner heliosheath. Intensities are however sensitive to heliospheric conditions such as the location of the heliopause and shock. In contrast, high energy proton observations by both the Voyager spacecraft show a clear solar cycle dependence with intensities also increasing with increasing distance. By comparing these observations to model calculations we can establish whether our current understanding of long-term modulation result in computed intensities compatible to observations.     

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.     

The Solar Wind in the Outer Heliosphere and Heliosheath

The solar wind environment has a large influence on the transport of cosmic rays. This chapter discusses the observations of the solar wind plasma and magnetic field in the outer heliosphere and the heliosheath. In the supersonic solar wind, interaction regions with large magnetic fields form barriers to cosmic ray transport. This effect, the “CR-B” relationship, has been quantified and is shown to be valid everywhere inside the termination shock (TS). In the heliosheath, this relationship breaks down, perhaps because of a change in the nature of the turbulence. Turbulence is compressive in the heliosheath, whereas it was non-compressive in the solar wind. The plasma pressure in the outer heliosphere is dominated by the pickup ions which gain most of the flow energy at the TS. The heliosheath plasma and magnetic field are highly variable on scales as small as ten minutes. The plasma flow turns away from the nose roughly as predicted, but the radial speeds at Voyager 1 are much less than those at Voyager 2, which is not understood. Despite predictions to the contrary, magnetic reconnection is not an important process in the inner heliosheath with only one observed occurrence to date.     

Shock Wave Interaction with the Magnetopause

The magnetopause is in continuous motion and shock waves and impulsive acceleration events can occur. As an example, we show that the interaction of an interplanetary shock with the bow shock can generate a shock wave that after passing through the magnetosheath can interact with the magnetopause. In fluid dynamics, when a shock wave encounters a fluid discontinuity, the interface may become unstable and form bubbles and spikes. We consider this Richtmyer-Meshkov instability in magnetohydrodynamics. At the dayside magnetopause, the instability tends to be stabilized by the magnetic field. However, the shock wave interaction can initiate magnetic field reconnection for the southward IMF, which may be important in strong interplanetary shock events. This revised version was published online in August 2006 with corrections to the Cover Date.     

Microphysics of Cosmic Ray Driven Plasma Instabilities

Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.     

The Two Sources of Solar Energetic Particles

Evidence for two different physical mechanisms for acceleration of solar energetic particles (SEPs) arose 50 years ago with radio observations of type III bursts, produced by outward streaming electrons, and type II bursts from coronal and interplanetary shock waves. Since that time we have found that the former are related to “impulsive” SEP events from impulsive flares or jets. Here, resonant stochastic acceleration, related to magnetic reconnection involving open field lines, produces not only electrons but 1000-fold enhancements of ³He/⁴He and of (Z>50)/O. Alternatively, in “gradual” SEP events, shock waves, driven out from the Sun by coronal mass ejections (CMEs), more democratically sample ion abundances that are even used to measure the coronal abundances of the elements. Gradual events produce by far the highest SEP intensities near Earth. Sometimes residual impulsive suprathermal ions contribute to the seed population for shock acceleration, complicating the abundance picture, but this process has now been modeled theoretically. Initially, impulsive events define a point source on the Sun, selectively filling few magnetic flux tubes, while gradual events show extensive acceleration that can fill half of the inner heliosphere, beginning when the shock reaches ～2 solar radii. Shock acceleration occurs as ions are scattered back and forth across the shock by resonant Alfvén waves amplified by the accelerated protons themselves as they stream away. These waves also can produce a streaming-limited maximum SEP intensity and plateau region upstream of the shock. Behind the shock lies the large expanse of the “reservoir”, a spatially extensive trapped volume of uniform SEP intensities with invariant energy-spectral shapes where overall intensities decrease with time as the enclosing “magnetic bottle” expands adiabatically. These reservoirs now explain the slow intensity decrease that defines gradual events and was once erroneously attributed solely to slow outward diffusion of the particles. At times the reservoir from one event can contribute its abundances and even its spectra as a seed population for acceleration by a second CME-driven shock wave. Confinement of particles to magnetic flux tubes that thread their source early in events is balanced at late times by slow velocity-dependent migration through a tangled network produced by field-line random walk that is probed by SEPs from both impulsive and gradual events and even by anomalous cosmic rays from the outer heliosphere. As a practical consequence, high-energy protons from gradual SEP events can be a significant radiation hazard to astronauts and equipment in space and to the passengers of high-altitude aircraft flying polar routes.     

Magnetospheric Models and Trajectory Computations

The calculation of particle trajectories in the Earth's magnetic field has been a subject of interest since the time of Störmer. The fundamental problem is that the trajectory-tracing process involves using mathematical equations that have `no solution in closed form'. This difficulty has forced researchers to use the `brute force' technique of numerical integration of many individual trajectories to ascertain the behavior of trajectory families or groups. As the power of computers has improved over the decades, the numerical integration procedure has grown more tractable and while the problem is still formidable, thousands of trajectories can be computed without the expenditure of excessive resources. As particle trajectories are computed and the characteristics analyzed we can determine the cutoff rigidity of a specific location and viewing direction and direction and deduce the direction in space of various cosmic ray anisotropies. Unfortunately, cutoff rigidities are not simple parameters due to the chaotic behavior of the cosmic-ray trajectories in the cosmic ray penumbral region. As the computational problem becomes more manageable, there is still the issue of the accuracy of the magnetic field models. Over the decades, magnetic field models of increasing complexity have been developed and utilized. The accuracy of trajectory calculations employing contemporary magnetic field models is sufficient that cosmic ray experiments can be designed on the basis of trajectory calculations. However, the Earth's magnetosphere is dynamic and the most widely used magnetospheric models currently available are static. This means that the greatest uncertainly in the application of charged particle trajectories occurs at low energies.     

Insights into Cosmic-Ray Acceleration from the Study of Anomalous Cosmic Rays

Cosmic rays from many sources and in many locations exhibit similar, inverse-power-law energy spectra, which suggests a common origin for most cosmic rays. Diffusive shock acceleration appears at present to be this common accelerator. Hence, anomalous cosmic rays, thought to be accelerated at the solar-wind termination shock, provide a relatively accessible laboratory for the study of the mechanism of cosmic-ray acceleration. Observations showing a transition from singly-charged anomalous cosmic-ray oxygen to multiply-charged at an energy of some 250 MeV support the picture of acceleration at the quasi-perpendicular termination shock. Such acceleration may be important in other sources, as well. The basic physics of this acceleration process is discussed in some detail. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cosmic Ray Isotopic Composition Studies with the Ulysses High Energy Telescope: Implications for Origin and Distribution in the Galaxy

The isotopic abundances of the Galactic cosmic radiation measured in the Heliosphere provide unique information on acceleration, propagation modes and containment times in the Galactic magnetic fields. Nuclear interactions with interstellar matter lead to observable γ-radiation production and, thus, to direct information on cosmic ray distribution throughout the Galaxy and its magnetic halo. The COSPIN High Energy Telescope (HET) has excellent isotopic resolution from hydrogen to nickel over the ten year period of Ulysses in space. Based on our recent work, we discuss the implications for modeling the acceleration and propagation of the cosmic radiation. This revised version was published online in August 2006 with corrections to the Cover Date.