The acceleration of protons and electrons in a reconnecting current sheet (RCS) is simulated with a particle-in-cell (PIC) 2D3V code for the proton-to-electron mass ratio of 100. The electro-magnetic configuration forming the RCS incorporates all three components of the magnetic field (including the guiding field) and a drifted electric field. PIC simulations reveal that there is a polarisation electric field that appears during acceleration owing to a separation of electrons from protons towards the midplane of the RCS. If the plasma density is low, the polarisation field is weak and the particle trajectories in the PIC simulations are similar to those in the test particle (TP) approach. For the higher plasma density the polarisation field is stronger and it affects the trajectories of protons by increasing their orbits during acceleration. This field also leads to a less asymmetrical abundances of ejected protons towards the midplane in comparison with the TP approach. For a given magnetic topology electrons in PIC simulations are ejected to the same semispace as protons, contrary to the TP results. This happens because the polarisation field extends far beyond the thickness of a current sheet. This field decelerates the electrons, which are initially ejected into the semispace opposite to the protons, returns them back to the RCS, and, eventually, leads to the electron ejection into the same semispace as protons. Energy distribution of the ejected electrons is rather wide and single-peak, contrary to the two-peak narrow-energy distribution obtained in the TP approach. In the case of a strong guiding field, the mean energy of the ejected electrons is found to be smaller than it is predicted analytically and by the TP simulations.Comment: 12 pages, 11 figures, J. Plasma Physics (accepted

Aims. We study time-dependent precipitation of an electron beam injected into a flaring atmosphere with a converging magnetic field by considering collisional and Ohmic losses with anisotropic scattering and pitch angle diffusion. Two injection regimes are investigated: short impulse and stationary injection. The effects of converging magnetic fields with different spatial profiles are compared and the energy deposition produced by the precipitating electrons at different depths and regimes is calculated. Methods. The time dependent Fokker-Planck equation for electron distribution in depth, energy and pitch angle was solved numerically by using the summary approximation method. Results. Steady state injection was found to be established for beam electrons 0.07-0.2 s after the injection onset depending on the initial beam parameters. Energy deposition by a stationary beam is strongly dependent on a self-induced electric field but more weakly dependent on a magnetic field convergence. Energy depositions by short electron impulses are found to be insensitive to the self-induced electric field but are strongly affected by magnetic convergence. Short beam impulses are shown to produce sharp asymmetric hard X-ray bursts on a timescale of the order of tens of milliseconds, often observed in solar flares.

Aims. The paper aims are to simulate steady-state distributions of electrons beams precipitating in collisional and Ohmic losses with pitch angle anisotropy into a flaring atmosphere with converging magnetic field and to apply these to the interpretation of HXR photon spectra, directivity and polarization observed for different photon energies and flare positions on the solar disk. Methods. Summary approximation method is applied to a time-dependent Fokker-Planck equation by splitting the temporal derivative equally between the derivatives in depth, energy and pitch angles and finding the solutions in forward and backward directions for each variable. Results. For softer beams, there is a noticeable flattening of the photon spectra at lower energies caused by the self-induced electric field that increases for larger viewing angles. For the models with an electric field, the HXR emission with lower energies (30 keV) becomes directed mainly upwards at upper atmospheric levels owing to the increased number of particles moving upwards, while in deeper layers it again becomes directed downwards. The polarization maximum shifts to higher energies with every precipitation depth approaching 25 keV for the models with pure collisions and 100 keV for the models with return currents. At deeper layers, the polarization decreases because of the isotropization of electrons by collisions. The maximum polarization is observed at the viewing angle of 90 • , becoming shifted to lower angles for softer beams. The integrated polarization and directivity shows a dependence on a magnetic field convergence for harder beams, while for softer beams the directivity is strongly affected by the self-induced electric field changing from a downward motion to an upward one at upper atmospheric depths. Conclusions. The proposed precipitation model for an electron beam with wider pitch angle dispersion of 0.2 taking into account collisional and Ohmic losses allowed us to fit the double power law HXR photon spectra with a spectrum flattening at lower energies observed in the flares of 20 and 23 July 2002. The observed directivity of HXR photons of 20 keV derived for a large number of flares located from the disk center to limb is also reproduced well by the theoretical directivity calculated for an electron beam with a very narrow pitch angle dispersion of 0.02. The simulated polarization of this narrowly-directed electron beam fits up to 90% of all the available polarimetric observations carried out at various locations across the solar disk.

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We study instabilities driven by a sheared plasma flow in the low-frequency domain. Two unstable branches are found: the ion-sound mode and the kinetic Alfvén mode. Both instabilities are aperiodic. The ion-sound instability does not depend on the plasma β (gas/magnetic pressure ratio) and has a maximum growth rate of about 0.1 of the velocity gradient dV 0 /dx. On the other hand, the kinetic Alfvén instability is stronger for larger β and dominates the ion-sound instability for β > 0.05. Possible applications for space plasmas are shortly discussed.