Particle Acceleration in a Three-Dimensional Model of Reconnecting Coronal Magnetic Fields

Particle acceleration in large-scale turbulent coronal magnetic fields is considered. Using test particle calculations, it is shown that both cellular automata and three dimensional MHD models lead to the production of relativistic particles on sub-second timescales with power law distribution functions. In distinction with the monolithic current sheet models for solar flares, particles gain energy by multiple interactions with many current sheets. Difficulties that need to be addressed, such as feedback between particle acceleration and MHD, are discussed.     

The Observational Motivation for Computational Advances in Solar Flare Physics

A solar flare is a violent and transient release of energy in the corona of the Sun, associated with the reconfiguration of the coronal magnetic field. The major mystery of solar flare physics is the precise nature of the conversion of stored magnetic energy into the copious accelerated particles that are observed indirectly by the radiation that they produce, and also directly with in situ detectors. This presents a major challenge for theory and modeling. Recent years have brought significant observational advances in the study of solar flares, addressing the storage and release of magnetic energy, and the acceleration and propagation of fast electrons and ions. This paper concentrates on two topics relevant to the early phase of a flare, magnetic reconnection and charged particle acceleration and transport. Some recent pertinent observations are reviewed and pointers given for the directions that, this reviewer suggests, computational models should now seek to take.     

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.     

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).     

Plasma populations in a simple open model magnetosphere

The acceleration of charged particles in the magnetic current sheets downstream from magnetic neutral lines is discussed and related to the plasma populations expected to be formed in a simple open model magnetosphere. A simple model of plasma acceleration in the dayside current sheet is set up, and it is shown that magnetospheric particles may take up a considerable fraction of the electromagnetic energy dissipated in the sheet even though they may represent only a small fraction of the total particle influx. The process should result in energetic ring current and ionospheric particles being found in boundary layers on either side of the magnetopause, and accelerated ionospheric particles in the plasma mantle. Acceleration of magnetosheath plasma in the dayside current sheet should result in enhanced flow speeds in these boundary layers, but the process may amount to little more than a return to the sheath plasma of energy previously extracted from it during its inflow on the dayside and stored in the compressed sheath field, due to the appreciable energy take-up from the current sheet by magnetospheric particles. The energy separation between ionospheric plasma and magnetosheath plasma on cusp field lines is shown to result in a spatial separation of polar wind and plasma mantle populations in the tail, the polar wind ions usually reaching out to only a few tens of R _E down-tail such that they usually remain on closed field lines, forming a wedge-shaped region within the mantle shadow-zone. Polar wind ions are then convected back towards the Earth and thus their major sink is via the dayside current sheet rather than outflow into the tail. The major source for the plasmasheet depends upon the location of the neutral line, but mantle ions may usually be dominant. However, with a near-Earth neutral line during disturbed periods ionospheric plasma will be the sole ring-current source. Under usual conditions with a more distant neutral line the spatial separation of the two plasma sources in the tail may result in an energy separation in the inner ring current, with ionospheric particles dominant up to 2 to 20 keV and mantle ions dominant at higher energies. Formation of the plasmasheet is discussed, and it is shown that a layer of ions unidirectionally streaming towards the Earth should be formed on its outer boundary, due to current sheet acceleration of lobe particles and inward convection of the field lines. A similar process leads to earthward flows on the inner layer of the dayside cusp. Finally, the region tailward of the nightside neutral line is discussed and it is shown that a thin tailward flowing two-stream plasma band should be formed across the centre plane of the tail. The slow-speed stream corresponds to incoming lobe ions, the faster stream to the current sheet accelerated ions.     

Electron Acceleration in the Heliosphere

We review the evidence for electron acceleration in the heliosphere putting emphasis on the acceleration processes. There are essentially four classes of such processes: shock acceleration, reconnection, wave particle interaction, and direct acceleration by electric fields. We believe that only shock and electric field acceleration can in principle accelerate electrons to very high energies. The shocks known in the heliosphere are coronal shocks, traveling interplanetary shocks, CME shocks related to solar type II radio bursts, planetary bow shocks, and the termination shock of the heliosphere. Even in shocks the acceleration of electrons requires the action of wave particle resonances of which beam driven whistlers are the most probable. Other mechanisms of acceleration make use of current driven instabilities which lead to electron and ion hole formation. In reconnection acceleration is in the current sheet itself where the particles perform Speiser orbits. Otherwise, acceleration takes place in the slow shocks which are generated in the reconnection process and emanate from the diffusion region in the Petschek reconnection model and its variants. Electric field acceleration is found in the auroral zones of the planetary magnetospheres and may also exist on the sun and other stars including neutron stars. The electric potentials are caused by field aligned currents and are concentrated in narrow double layers which physically are phase space holes in the ion and electron distributions. Many of them add up to a large scale electric field in which the electrons may be impulsively accelerated to high energies and heated to large temperatures.     

Coronal streamers' theories

Some theoretical aspects of solar coronal streamers are discussed with emphasis on the current sheet and reconnection processes going on along the axis of the streamer. The dynamics of the streamer is a combination of MHD and transport, with acceleration of particles due to reconnection and leakage of plasma outwards as a slow solar wind as the observable results. The presence of the almost-closed magnetic bottles of streamers that can store high-energy particles for significant times provides the birdcage for solar cosmic rays, the reconnection in the sheet feeds medium-energy protons into the corona for the large-scale storage needed for certain flare models, and the build-up of excess density sets the stage for coronal mass ejections.     

Particle Acceleration by the Sun: Electrons, Hard X-rays/Gamma-rays

Observations of hard X-ray (HXR)/γ-ray continuum and γ-ray lines produced by energetic electrons and ions, respectively, colliding with the solar atmosphere, have shown that large solar flares can accelerate ions up to many GeV and electrons up to hundreds of MeV. Solar energetic particles (SEPs) are observed by spacecraft near 1 AU and by ground-based instrumentation to extend up to similar energies, but it appears that a different acceleration process, one associated with fast Coronal Mass Ejections (CMEs) is responsible. Much weaker SEP events are observed that are generally rich in electrons, ³He, and heavy elements. The energetic particles in these events appear to be similar to those accelerated in flares. The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) mission provides high-resolution spectroscopy and imaging of flare HXRs and γ-rays. The observations of the location, energy spectra, and composition of the flare accelerated energetic particles at the Sun strongly imply that the acceleration is closely related to the magnetic reconnection that releases the energy in solar flares. Here preliminary comparisons of the RHESSI observations with observations of both energetic electrons and ions near 1 AU are reviewed, and the implications for the particle acceleration and escape processes are discussed.     

The Localization of Particle Acceleration Sites in Solar Flares and CMES

We review the particular aspect of determining particle acceleration sites in solar flares and coronal mass ejections (CMEs). Depending on the magnetic field configuration at the particle acceleration site, distinctly different radiation signatures are produced: (1) If charged particles are accelerated along compact closed magnetic field lines, they precipitate to the solar chromosphere and produce hard X-rays, gamma rays, soft X-rays, and EUV emission; (2) if they are injected into large-scale closed magnetic field structures, they remain temporarily confined (or trapped) and produce gyrosynchrotron emission in radio and bremsstrahlung in soft X-rays; (3) if they are accelerated along open field lines they produce beam-driven plasma emission with a metric starting frequency; and (4) if they are accelerated in a propagating CME shock, they can escape into interplanetary space and produce beam-driven plasma emission with a decametric starting frequency. The latter two groups of accelerated particles can be geo-effective if suitably connected to the solar west side. Particle acceleration sites can often be localized by modeling the magnetic topology from images in different wavelengths and by measuring the particle velocity dispersion from time-of-flight delays.     

The Origin of Solar Energetic Particle Events: Coronal Acceleration versus Shock Wave Acceleration

We review evidence that led to the view that acceleration at shock waves driven by coronal mass ejections (CMEs) is responsible for large particle events detected at 1 AU. It appears that even if the CME bow shock acceleration is a possible model for the origin of rather low energy ions, it faces difficulties on account of the production of ions far above 1 MeV: (i) although shock waves have been demonstrated to accelerate ions to energies of some MeV nucl^–1 in the interplanetary medium, their ability to achieve relativistic energies in the solar environment is unproven; (ii) SEP events producing particle enhancements at energies 100 MeV are also accompanied by flares; those accompanied only by fast CMEs have no proton signatures above 50 MeV. We emphasize detailed studies of individual high energy particle events which provide strong evidence that time-extended particle acceleration which occurs in the corona after the impulsive flare contributes to particle fluxes in space. It appears thus that the CME bow shock scenario has been overvalued and that long lasting coronal energy release processes have to be taken into account when searching for the origin of high energy SEP events.     

Locating Current Sheets in the Solar Corona

Current sheets are essential for energy dissipation in the solar corona, in particular by enabling magnetic reconnection. Unfortunately, sufficiently thin current sheets cannot be resolved observationally and the theory of their formation is an unresolved issue as well. We consider two predictors of coronal current concentrations, both based on geometrical or even topological properties of a force-free coronal magnetic field. First, there are separatrices related to magnetic nulls. Through separatrices the magnetic connectivity changes discontinuously. Coronal magnetic nulls are, however, very rare. Second, inspired by the concept of generalized magnetic reconnection without nulls, quasi-separatrix layers (QSL) were suggested. Through QSL the magnetic connectivity changes continuously, though strongly. The strength of the connectivity change can be quantified by measuring the squashing of the flux tubes which connect the magnetically conjugated photospheres. We verify the QSL and separatrix concepts by comparing the sites of magnetic nulls and enhanced squashing with the location of current concentrations in the corona. Due to the known difficulties of their direct observation, we simulated coronal current sheets by numerically calculating the response of the corona to energy input from the photosphere, heating a simultaneously observed Extreme Ultraviolet Bright Point. We did not find coronal current sheets at separatrices but at several QSL locations. The reason is that, although the geometrical properties of force-free extrapolated magnetic fields can indeed hint at possible current concentrations, a necessary condition for current sheet formation is the local energy input into the corona.     

Large solar event of September 29, 1989: ten years after

Out of the 56 Ground Level Enhancements (GLEs) of solar cosmic rays (SCRs) observed since 1942 until the present, 15 events were recorded in the 22nd cycle of solar activity (1986–1996). Solar proton events (SPEs) in that cycle displayed some peculiarities, which may need an interpretation on a new concept base. The event of September 29, 1989 is of special interest. Since the well-known event of February 23, 1956, it proved to be the most intense in the relativistic range of proton energies. This GLE affords a unique opportunity to study the propagation of SCRs over a wide range of rigidity.In spite of its occurrence behind the western solar limb, the originating major flare could be observed over a wide range of the wavelengths and particle energy spectra – from gamma rays to decametric radio waves, from >2 MeV electrons to multi-GeV protons; there were also measurements of the energy spectra and charge states of solar heavy nuclei. The flare was followed by some energetic solar phenomena (large magnetic loops, coronal eruptions and mass ejections, shocks, etc.). Due to the very hard rigidity spectrum, this was the first GLE recorded by underground muon detectors. The event also has a number of other unusual features, for example, an extended component of gamma-ray emission and the change in direction of the probable particle source during the event's initial stage. In addition, the intensity-time profile of the GLE is notable for its non-classic shape, showing a two-peak structure. The latter implies the possibility of a two-component (or two-source) ejection of accelerated particles from the Sun.The available observational data for the event is described in detail, the main focus of this paper is concentrated on different attempts to interpret the data within the framework of traditional and non-traditional concepts: shock and/or post-eruption acceleration, two-component (dual) ejection, two-source model of particle acceleration in large (extended) coronal structures, etc. None of the models put forward for explaining this event is exhaustive. The rigidity spectrum of ejected protons is estimated and the problem of the maximum rigidity, R _m, of the accelerated particles is discussed. In the relativistic range, this event proved to be by 1–2 orders less intense than the event of February 23, 1956. It is also shown that the event of September 29, 1989 could not have been recorded with the present-day neutrino detectors.     

Computer modeling of test particle acceleration at oblique shocks

We review the basic techniques and results of numerical codes used to model the acceleration of charged particles at oblique, fast-mode, collisionless shocks. The emphasis is upon models in which accelerated particles (ions) are treated as test particles, and particle dynamics is calculated by numerically integrating along exact phase-space orbits. We first review the case where ions are sufficiently energetic so that the shock can be approximated by a planar discontinuity, and where the electromagnetic fields on both sides of the shock are defined at the outset of each computer run. When the fields are uniform and static, particles are accelerated by the scatter-free drift acceleration process at a single shock encounter. We review the characteristics of scatter-free drift acceleration by considering how an incident particle distribution is modified by interacting with a shock. Next we discuss drift acceleration when magnetic fluctuations are introduced on both sides of the shock, and compare these results with those obtained under scatter-free conditions. We describe the modeling of multiple shock encounters, discuss specific applications, and compare the model predictions with theory. Finally, we review some recent numerical simulations that illustrate the importance of shock structure to both the ion injection process and to the acceleration of ions to high energies at quasi-perpendicular shocks.     

Particle Acceleration in the Heliosphere: Implications for Astrophysics

There has been a remarkable discovery concerning particles that are accelerated in the solar wind. At low energies, in the region where the particles are being accelerated, the spectrum of the accelerated particles is always the same: when expressed as a distribution function, the spectrum is a power law in particle speed with a spectral index of ?5, and a rollover at higher particle speeds that can often be described as exponential. This common spectral shape cannot be accounted for by any conventional acceleration mechanism, such as diffusive shock acceleration or traditional stochastic acceleration. It has thus been necessary to invent a new acceleration mechanism to account for these observations, a pump mechanism in which particles are pumped up in energy through a series of adiabatic compressions and expansions. The conditions under which the pump acceleration is the dominant acceleration mechanism are quite general and are likely to occur in other astrophysical plasmas. In this paper, the most compelling observations of the ?5 spectra are reviewed; the governing equation of the pump acceleration mechanism is derived in detail; the pump acceleration mechanism is applied to acceleration at shocks; and, as an illustration of the potential applicability of the pump acceleration mechanism to other astrophysical plasmas, the pump mechanism is applied to the acceleration of galactic cosmic rays in the interstellar medium.     

Long-Duration Solar Gamma-Ray Flares

Long-duration solar -ray flares are those in which high-energy photon emission is present well beyond the impulsive phase, indicating the presence of either stored or continuously accelerated ions. We review both the observations and the current theories or models that can explain this unusual phenomenon. The present situation favors either acceleration of protons and ions for long periods of time by second order Fermi acceleration in large coronal loops or acceleration in large-scale, CME-associated reconnection sheets. Observations in the upcoming solar maximum may resolve this problem.     

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.     

Theory of fragmented energy release in the Sun

The magnetic energy released inside an active region is closely related to its formation and evolution. Following the evolution of a collection of flux tubes inside the convection zone and above the photosphere we can show that many nonlinear structures (current sheets, shock waves, double layers etc.) are formed. We propose in this review that coronal heating, flares and particle acceleration are due to the interaction of the plasma with these nonlinear structures. Approaching active regions as a driven complex dynamical system we can show that several coherent ensembles of the nonlinear structures will appear spontaneously. The statistical analysis of these structures is a major problem in solar physics. We can also show that many observed large scale structures are the result of the convolution of non-observable fragmentation in the energy release process.     

Heliospheric Lessons for Galactic Cosmic-ray Acceleration

The heliosphere is bathed in the supersonic solar wind, which generally creates shocks at any obstacles it encounters: magnetic structures such as coronal mass ejections and planetary magnetospheres, or fast-slow stream interactions such as corotating interaction regions (CIRs) or the termination shock. Each of these shock structures has an associated energetic particle population whose spectra and composition contain clues to the acceleration process and the sources of the particles. Over the past several years, the solar wind composition has been systematically studied, and the long-standing gap between high energy (>1 MeV amu^–1) and the plasma ion populations has been closed by instruments capable of measuring the suprathermal ion composition. In CIRs, where it has been possible to observe all the relevant populations, it turns out that the suprathermal ion population near 1.8–2.5 times the solar wind speed is the seed population that gets accelerated, not the bulk particles near the solar wind peak. These new results are of interest to the problem of Galactic Cosmic-Ray (GCR) Acceleration, since the injection and acceleration of GCRs to modest energies is likely to share many features with processes we can observe in detail in the heliosphere.