Sources of solar energetic particles

Solar energetic particles are an integral part of the physical processes related with space weather. We present a review for the acceleration mechanisms related to the explosive phenomena (flares and/or coronal mass ejections, CMEs) inside the solar corona. For more than 40 years, the main two-dimensional cartoon representing our understanding of the explosive phenomena inside the solar corona remained almost unchanged. The acceleration mechanisms related to solar flares and CMEs also remained unchanged and were part of the same cartoon. In this review, we revise the standard cartoon and present evidence from recent global magnetohydrodynamic simulations that support the argument that explosive phenomena will lead to the spontaneous formation of current sheets in different parts of the erupting magnetic structure. The evolution of the large-scale current sheets and their fragmentation will lead to strong turbulence and turbulent reconnection during solar flares and turbulent shocks. In other words, the acceleration mechanism in flares and CME-driven shocks may be the same, and their difference will be the overall magnetic topology, the ambient plasma parameters, and the duration of the unstable driver. This article is part of the theme issue 'Solar eruptions and their space weather impact'.

Reduction of Thermal Conductive Flux by Non-local Effects in the Presence of Turbulent Scattering

The heat flux in a plasma is determined by the degree of anisotropy in the particle distribution function, which is in turn driven by gradients in the ambient density and temperature. When the mean free path at the thermal speed is substantially smaller than the scale length associated with the temperature variation, the heat flux simply depends on the local value of the temperature gradient. However, when the temperature scale length and mean free path are comparable, heat conduction becomes substantially non-local in character: the magnitude of the heat flux now depends on the overall temperature profile and is generally smaller than the locally determined value. In the presence of angular scattering associated with turbulence, the mean free path (and its velocity dependence) can be significantly smaller than its collisional value; this makes the expression for the heat flux more local in character, but also results in a heat flux that is lower than that obtained through a purely collisional analysis. Therefore, whether or not turbulence is present, the heat flux is generally smaller than the value obtained from a local collisional analysis. We here present an analytic expression for the conductive heat flux in terms of a convolution of the local heat flux with a non-local kernel function that incorporates both Coulomb collisions and turbulent scattering. We comment on the need to include both non-local and turbulent scattering effects in the modeling of quasi-static active region loops and in the conductive cooling of post-flare loops.

Turbulent Kinetic Energy in the Energy Balance of a Solar Flare

The energy released in solar flares derives from a reconfiguration of magnetic fields to a lower energy state, and is manifested in several forms, including bulk kinetic energy of the coronal mass ejection, acceleration of electrons and ions, and enhanced thermal energy that is ultimately radiated away across the electromagnetic spectrum from optical to x rays. Using an unprecedented set of coordinated observations, from a suite of instruments, we here report on a hitherto largely overlooked energy component-the kinetic energy associated with small-scale turbulent mass motions. We show that the spatial location of, and timing of the peak in, turbulent kinetic energy together provide persuasive evidence that turbulent energy may play a key role in the transfer of energy in solar flares. Although the kinetic energy of turbulent motions accounts, at any given time, for only ∼(0.5-1)% of the energy released, its relatively rapid (∼1-10  s) energization and dissipation causes the associated throughput of energy (i.e., power) to rival that of major components of the released energy in solar flares, and thus presumably in other astrophysical acceleration sites.

Particle acceleration by a solar flare termination shock

Solar flares--the most powerful explosions in the solar system--are also efficient particle accelerators, capable of energizing a large number of charged particles to relativistic speeds. A termination shock is often invoked in the standard model of solar flares as a possible driver for particle acceleration, yet its existence and role have remained controversial. We present observations of a solar flare termination shock and trace its morphology and dynamics using high-cadence radio imaging spectroscopy. We show that a disruption of the shock coincides with an abrupt reduction of the energetic electron population. The observed properties of the shock are well reproduced by simulations. These results strongly suggest that a termination shock is responsible, at least in part, for accelerating energetic electrons in solar flares.

Ion runaway in lightning discharges

Runaway ions can be produced in plasmas with large electric fields, where the accelerating electric force is augmented by the low mean ionic charge due to the imbalance between the number of electrons and ions. Here we derive an expression for the high-energy tail of the ion distribution function in lightning discharges and investigate the energy range that the ions can reach. We also estimate the corresponding energetic proton and neutron production due to fusion reactions.

Solar flares and energetic particles

Solar flares are now observed at all wavelengths from γ-rays to decametre radio waves. They are commonly associated with efficient production of energetic particles at all energies. These particles play a major role in the active Sun because they contain a large amount of the energy released during flares. Energetic electrons and ions interact with the solar atmosphere and produce high-energy X-rays and γ-rays. Energetic particles can also escape to the corona and interplanetary medium, produce radio emissions (electrons) and may eventually reach the Earth's orbit. I shall review here the available information on energetic particles provided by X-ray/γ-ray observations, with particular emphasis on the results obtained recently by the mission Reuven Ramaty High-Energy Solar Spectroscopic Imager. I shall also illustrate how radio observations contribute to our understanding of the electron acceleration sites and to our knowledge on the origin and propagation of energetic particles in the interplanetary medium. I shall finally briefly review some recent progress in the theories of particle acceleration in solar flares and comment on the still challenging issue of connecting particle acceleration processes to the topology of the complex magnetic structures present in the corona.

Super-Alfvénic propagation of substorm reconnection signatures and Poynting flux

The propagation of reconnection signatures and their associated energy are examined using kinetic particle-in-cell simulations and Cluster satellite observations. It is found that the quadrupolar out-of-plane magnetic field near the separatrices is associated with a kinetic Alfvén wave. For magnetotail parameters, the parallel propagation of this wave is super-Alfvénic (V(∥) ∼ 1500-5500 km/s) and generates substantial Poynting flux (S ∼ 10(-5)-10(-4) W/m(2)) consistent with Cluster observations of magnetic reconnection. This Poynting flux substantially exceeds that due to frozen-in ion bulk outflows and is sufficient to generate white light aurora in Earth's ionosphere.

Anisotropic magnetohydrodynamic spectral transfer in the diffusion approximation

A theoretical model of spectral transfer for anisotropic magnetohydrodynamic (MHD) turbulence is introduced, approximating energy transport in wave vector (k) space as a nonlinear diffusion process, extending previous isotropic k -space diffusion theories for hydrodynamics and MHD. This formal closure at the spectral equation level may be useful in space and astrophysical applications.

Beamlets from stochastic acceleration

We investigate the dynamics of a realization of the stochastic Fermi acceleration mechanism. The model consists of test particles moving between two oscillating magnetic clouds and differs from the usual Fermi-Ulam model in two ways. (i) Particles can penetrate inside clouds before being reflected. (ii) Particles can radiate a fraction of their energy during the process. Since the Fermi mechanism is at work, particles are stochastically accelerated, even in the presence of the radiated energy. Furthermore, due to a kind of resonance between particles and oscillating clouds, the probability density function of particles is strongly modified, thus generating beams of accelerated particles rather than a translation of the whole distribution function to higher energy. This simple mechanism could account for the presence of beamlets in some space plasma physics situations.

Flare Observations

Solar flares are observed at all wavelengths from decameter radio waves to gamma-rays at 100 MeV. This review focuses on recent observations in EUV, soft and hard X-rays, white light, and radio waves. Space missions such as RHESSI, Yohkoh, TRACE, and SOHO have enlarged widely the observational base. They have revealed a number of surprises: Coronal sources appear before the hard X-ray emission in chromospheric footpoints, major flare acceleration sites appear to be independent of coronal mass ejections (CMEs), electrons, and ions may be accelerated at different sites, there are at least 3 different magnetic topologies, and basic characteristics vary from small to large flares. Recent progress also includes improved insights into the flare energy partition, on the location(s) of energy release, tests of energy release scenarios and particle acceleration. The interplay of observations with theory is important to deduce the geometry and to disentangle the various processes involved. There is increasing evidence supporting reconnection of magnetic field lines as the basic cause. While this process has become generally accepted as the trigger, it is still controversial how it converts a considerable fraction of the energy into non-thermal particles. Flare-like processes may be responsible for large-scale restructuring of the magnetic field in the corona as well as for its heating. Large flares influence interplanetary space and substantially affect the Earth's lower ionosphere. While flare scenarios have slowly converged over the past decades, every new observation still reveals major unexpected results, demonstrating that solar flares, after 150 years since their discovery, remain a complex problem of astrophysics including major unsolved questions.

ELECTRONIC SUPPLEMENTARY MATERIAL

Supplementary material is available for this article at 10.12942/lrsp-2008-1.

Spectral energy transfer and dissipation of magnetic energy from fluid to kinetic scales

We investigate the magnetic energy transfer from the fluid to kinetic scales and dissipation processes using three-dimensional fully kinetic particle-in-cell plasma simulations. The nonlinear evolution of a sheet pinch is studied where we show that it exhibits both fluid scale global relaxation and kinetic scale collisionless reconnection at multiple resonant surfaces. The interactions among collisionless tearing modes destroy the original flux surfaces and produce stochastic fields, along with generating sheets and filaments of intensified currents. In addition, the magnetic energy is transferred from the original shear length scale both to the large scales due to the global relaxation and to the smaller, kinetic scales for dissipation. The dissipation is dominated by the thermal or pressure effect in the generalized Ohm's law, and electrons are preferentially accelerated.

Electron acceleration from contracting magnetic islands during reconnection

A long-standing problem in the study of space and astrophysical plasmas is to explain the production of energetic electrons as magnetic fields 'reconnect' and release energy. In the Earth's magnetosphere, electron energies reach hundreds of thousands of electron volts (refs 1-3), whereas the typical electron energies associated with large-scale reconnection-driven flows are just a few electron volts. Recent observations further suggest that these energetic particles are produced in the region where the magnetic field reconnects. In solar flares, upwards of 50 per cent of the energy released can appear as energetic electrons. Here we show that electrons gain kinetic energy by reflecting from the ends of the contracting 'magnetic islands' that form as reconnection proceeds. The mechanism is analogous to the increase of energy of a ball reflecting between two converging walls--the ball gains energy with each bounce. The repetitive interaction of electrons with many islands allows large numbers to be efficiently accelerated to high energy. The back pressure of the energetic electrons throttles reconnection so that the electron energy gain is a large fraction of the released magnetic energy. The resultant energy spectra of electrons take the form of power laws with spectral indices that match the magnetospheric observations.

Catastrophe model for fast magnetic reconnection onset

A catastrophe model for the onset of fast magnetic reconnection is presented that suggests why plasma systems with magnetic free energy remain apparently stable for long times and then suddenly release their energy. For a given set of plasma parameters there are generally two stable reconnection solutions: a slow (Sweet-Parker) solution and a fast (Alfvénic) Hall reconnection solution. Below a critical resistivity the slow solution disappears and fast reconnection dominates. Scaling arguments predicting the two solutions and the critical resistivity are confirmed with two-fluid simulations.

Production of energetic electrons during magnetic reconnection

The production of energetic electrons during magnetic reconnection is explored with full particle simulations and analytic analysis. Density cavities generated along separatrices bounding growing magnetic islands support parallel electric fields that act as plasma accelerators. Electrons because of their low mass are fast enough to make multiple passes through these acceleration cavities and are therefore capable of reaching relativistic energies.

Radiative intermittent events during Fermi's stochastic acceleration

We investigate the dynamics of a realization of Fermi's relativistic acceleration mechanism that is a charged test particle oscillating between two reflecting plates that move stochastically. By allowing the charge to radiate energy during each collision, we find that the main features of the system are (1) due to the radiation drag the energy gained by the particle is bounded, and (2) the radiated energy represents a typical realization of an on-off intermittent process, due to numerous continuous encounters with a very small emission, interrupted by short and intense bursts of radiation. This intermittent radiative process exhibits non-Gaussian statistical features.