We study a model of particle acceleration coupled with an MHD model of magnetic reconnection in unstable twisted coronal loops. The kink instability leads to the formation of helical currents with strong parallel electric fields resulting in electron
acceleration. The motion of electrons in the electric and magnetic fields of the reconnecting loop is investigated using a test-particle approach taking into account collisional scattering. We discuss the effects of Coulomb collisions and magnetic convergence near loop footpoints on the spatial distribution and energy spectra of high-energy electron populations and possible implications on the hard X-ray emission in solar flares.
X-radiation from energetic electrons is the prime diagnostic of flare-accelerated electrons. The observed X-ray flux (and polarization state) is fundamentally a convolution of the cross-section for the hard X-ray emission process(es) in question with
the electron distribution function, which is in turn a function of energy, direction, spatial location and time. To address the problems of particle propagation and acceleration one needs to infer as much information as possible on this electron distribution function, through a deconvolution of this fundamental relationship. This review presents recent progress toward this goal using spectroscopic, imaging and polarization measurements, primarily from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Previous conclusions regarding the energy, angular (pitch angle) and spatial distributions of energetic electrons in solar flares are critically reviewed. We discuss the role and the observational evidence of several radiation processes: free-free electron-ion, free-free electron-electron, free-bound electron-ion bremsstrahlung, photoelectric absorption and Compton back-scatter (albedo), using both spectroscopic and imaging techniques. This unprecedented quality of data allows for the first time inference of the angular distributions of the X-ray-emitting electrons using albedo, improved model-independent inference of electron energy spectra and emission measures of thermal plasma. Moreover, imaging spectroscopy has revealed hitherto unknown details of solar flare morphology and detailed spectroscopy of coronal, footpoint and extended sources in flaring regions. Additional attempts to measure hard X-ray polarization were not sufficient to put constraints on the degree of anisotropy of electrons, but point to the importance of obtaining good quality polarization data.
Plasma turbulence is thought to be associated with various physical processes involved in solar flares, including magnetic reconnection, particle acceleration and transport. Using Ramaty High Energy Solar Spectroscopic Imager ({it RHESSI}) observatio
ns and the X-ray visibility analysis, we determine the spatial and spectral distributions of energetic electrons for a flare (GOES M3.7 class, April 14, 2002 23$:$55 UT), which was previously found to be consistent with a reconnection scenario. It is demonstrated that because of the high density plasma in the loop, electrons have to be continuously accelerated about the loop apex of length $sim 2times 10^9$cm and width $sim 7times 10^8$cm. Energy dependent transport of tens of keV electrons is observed to occur both along and across the guiding magnetic field of the loop. We show that the cross-field transport is consistent with the presence of magnetic turbulence in the loop, where electrons are accelerated, and estimate the magnitude of the field line diffusion coefficient for different phases of the flare. The energy density of magnetic fluctuations is calculated for given magnetic field correlation lengths and is larger than the energy density of the non-thermal electrons. The level of magnetic fluctuations peaks when the largest number of electrons is accelerated and is below detectability or absent at the decay phase. These hard X-ray observations provide the first observational evidence that magnetic turbulence governs the evolution of energetic electrons in a dense flaring loop and is suggestive of their turbulent acceleration.
{This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvenic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare pla
sma conditions.} {We consider anisotropic Alfvenic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-$beta$ limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfven waves, from the large magnetohydrodynamics (MHD) scales with $k_{perp}rho_{s}ll 1$ down to the small kinetic scales with $k_{perp}rho_{s} gg 1$, $rho_{s}$ being the ion sound gyroradius.} {Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of $k_{perp}$ and $k_{parallel}$, showing that the electric field develops a component parallel to the magnetic field at large MHD scales.} {The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfven waves in solar flare plasma conditions}
Anisotropic Alfv{e}nic fluctuations with $k_{parallel}/k_{perp}ll 1$ remain at frequencies much smaller than the ion cyclotron frequency in the presence of a strong background magnetic field. Based on the simplest truncation of the electromagnetic gy
rofluid equations in a homogeneous plasma, a model for the energy cascade produced by Alfv{e}nic turbulence is constructed, which smoothly connect the large magnetohydrodynamics (MHD) scales and the small kinetic scales. Scaling relations are obtained for the electromagnetic fluctuations, as a function of $k_{perp}$ and $k_{parallel}$. Moreover, a particular attention is paid to the spectral structure of the parallel electric field which is produced by Alfv{e}nic turbulence. The reason is the potential implication of this parallel electric field in turbulent acceleration and transport of particles. For electromagnetic turbulence, this issue was raised some time ago in [A. Hasegawa, K. Mima, J. Geophys. Res. {bf 83} 1117 (1978)].
Impulsive solar energetic electrons are often observed in the interplanetary space near the Earth and have an attractive diagnostic potential for poorly understood solar flare acceleration processes. We investigate the transport of solar flare energe
tic electrons in the heliospheric plasma to understand the role of transport to the observed onset and spectral properties of the impulsive solar electron events. The propagation of energetic electrons in solar wind plasma is simulated from the acceleration region at the Sun to the Earth, taking into account self-consistent generation and absorption of electrostatic electron plasma (Langmuir) waves, effects of non-uniform plasma, collisions and Landau damping. The simulations suggest that the beam-driven plasma turbulence and the effects of solar wind density inhomogeneity play a crucial role and lead to the appearance of a) spectral break for a single power-law injected electron spectrum, with the spectrum flatter below the break, b) apparent early onset of low-energy electron injection, c) the apparent late maximum of low-energy electron injection. We show that the observed onsets, spectral flattening at low energies, and formation of a break energy at tens of keV is the direct manifestation of wave-particle interactions in non-uniform plasma of a single accelerated electron population with an initial power-law spectrum.
