The observed properties (i.e., source size, source position, time duration, decay time) of solar radio emission produced through plasma processes near the local plasma frequency, and hence the interpretation of solar radio bursts, are strongly influenced by propagation effects in the inhomogeneous turbulent solar corona. In this work, a 3D stochastic description of the propagation process is presented, based on the Fokker-Planck and Langevin equations of radio-wave transport in a medium containing anisotropic electron density fluctuations. Using a numerical treatment based on this model, we investigate the characteristic source sizes and burst decay times for Type III solar radio bursts. Comparison of the simulations with the observations of solar radio bursts shows that predominantly perpendicular density fluctuations in the solar corona are required, with an anisotropy factor ∼ 0.3 for sources observed at around 30 MHz. The simulations also demonstrate that the photons are isotropized near the region of primary emission, but the waves are then focused by large-scale refraction, leading to plasma radio emission directivity that is characterized by a half-width-half-maximum of about 40 degrees near 30 MHz. The results are applicable to various solar radio bursts produced via plasma emission.

The acceleration of electrons and protons caused by a super-Dreicer electric field directed along the longitudinal component B y of the magnetic field is investigated. The three-component magnetic field in a nonneutral current sheet occurring at the top of the reconnecting flaring loops on the charged particle trajectories and energies is considered. Particle trajectories in the reconnecting current sheet (RCS) and their energy spectra at the point of ejection from the RCS are simulated from the motion equation for different sheet thicknesses. A superDreicer electric field of the current sheet is found to accelerate particles to coherent energy spectra in a range of 10-100 keV for electrons and 100-400 keV for protons with energy slightly increasing with the sheet thickness. A longitudinal B y component was found to define the gyration directions of particles with opposite charges toward the RCS midplane, i.e., the trajectory symmetry. For the ratio B y =B z < 10 À6 the trajectories are fully symmetric, which results in particle ejection from an RCS as neutral beams. For the ratio B y =B z > 10 À2 the trajectories completely lose their symmetry toward the RCS midplane, leading to the separation of particles with opposite charges into the opposite halves from an RCS midplane and the following ejection into different legs of the reconnecting loops. For the intermediate values of B y /B z the trajectories are partially symmetric toward the midplane, leading to electrons prevailing in one leg and protons in the other.

The effect of a self-induced electric field is investigated analytically and numerically on differential and mean electron spectra produced by beam electrons during their precipitation into a flaring atmosphere as well as on the emitted hard X-ray (HXR) photon spectra. The induced electric field is found to be a constant in upper atmospheric layers and to fall sharply in the deeper atmosphere from some ''turning point'' occurring either in the corona (for intense and softer beams) or in the chromosphere (for weaker and harder beams). The stronger and softer the beam, the higher the electric field before the turning point and the steeper its decrease after it. Analytical solutions are presented for the electric fields, which are constant or decreasing with depth, and the characteristic ''electric'' stopping depths are compared with the ''collisional'' ones. A constant electric field is found to decelerate precipitating electrons and to significantly reduce their number in the upper atmospheric depth, resulting in their differential spectra flattening at lower energies (<100 keV). While a decreasing electric field slows down the electron deceleration, allowing them to precipitate into deeper atmospheric layers than for a constant electric field, the joint effect of electric and collisional energy losses increases the energy losses by lower energy electrons compared to pure collisions and results in maxima at energies of 40-80 keV in the differential electron spectra. This, in turn, leads to the maxima in the mean source electron spectra and to the ''double power law'' HXR photon spectra (with flattening at lower energies) similar to those reported from the RHESSI observations. The more intense and soft the beams are, the stronger is the lower energy flattening and the higher is the ''break'' energy where the flattening occurs.

Context. Twisted coronal loops should be ubiquitous in the solar corona. Twisted magnetic fields contain excess magnetic energy, which can be released during magnetic reconnection, causing solar flares. Aims. The aim of this work is to investigate magnetic reconnection, and particle acceleration and transport in kink-unstable twisted coronal loops, with a focus on the effects of resistivity, loop geometry and atmospheric stratification. Another aim is to perform forward-modelling of bremsstrahlung emission and determine the structure of hard X-ray sources. Methods. We use a combination of magnetohydrodynamic (MHD) and test-particle methods. First, the evolution of the kinking coronal loop is considered using resistive MHD model, incorporating atmospheric stratification and loop curvature. Then, the obtained electric and magnetic fields and density distributions are used to calculate electron and proton trajectories using a guiding-centre approximation, taking into account Coulomb collisions. Results. It is shown that electric fields in twisted coronal loops can effectively accelerate protons and electrons to energies up to 10 MeV. High-energy particles have hard, nearly power-law energy spectra. The volume occupied by high-energy particles demonstrates radial expansion, which results in the expansion of the visible hard X-ray loop and a gradual increase in hard X-ray footpoint area. Synthesised hard X-ray emission reveals strong footpoint sources and the extended coronal source, whose intensity strongly depends on the coronal loop density.

Abstract. The numerical solutions of the time-dependent kinetic Fokker-Planck equation are presented for fast electrons injected from the solar corona into a flaring atmosphere and precipitating with energy and pitch-angle diffusion into a loop with a converging magnetic field. The electrons are assumed to lose their energy in Coulomb collisions with particles of the partially ionised ambient plasma and Ohmic heating owing to the electric field induced by the precipitating beam. The electric field induced by a precipitating electron beam is found to cause a return current beam, which comes back to the source in the corona with a wide pitch angle distribution. The return current is assumed to arise from the ambient plasma and from beam electrons scattered into negative pitch-angles. Energy and pitch-angle distributions of precipitating and return current electron beams at various atmospheric depths are presented along with the precipitating beam abundances, energy fluxes and resulting hard X-ray bremsstrahlung (photon) spectra for electron beams with power law energy spectra with spectral indices of 3, 5, 7 and initial energy fluxes of 10 8 , 10 10 , 10 12 erg cm −2 s −1 . Energy distributions of the return current cover energies lower than 60 keV for weaker soft beams and increase to 65 keV for moderate soft beams, or to 70-75 keV for more intense and hard beams. The maxima are at 30 keV for weaker soft beams and are shifted towards higher energies, up to 50 keV, for harder and more intense beams. As a result, the photon spectra of hard X-ray emission emitted from a flaring atmosphere are found to have a broken power-law (elbow-type) shape with a higher energy part retaining the spectral index δ high associated with the electron beam's initial index and varying slightly with the beam parameters. However, the lower energy part of the X-ray photon spectra shows a much smaller increase or even a substantial decrease of its spectral index δ low for more intense or harder beams. These simulated broken power-law photon spectra produced by precipitating electron beams with a single spectral index agree reasonably well with the photon energy spectra from the flares of 20 and 23 July, 2002 observed by the RHESSI payload.