Particle-in-cell simulations of return current in solar flares

Aims. We numerically study a formation of the return current generated in solar flares. Methods. For simulations of the return current in the beam-plasma system, a 3D particle-in-cell electromagnetic code is used. Results. In conditions of solar flares with the electron beam fluxes of E-F = 9.1 x 10(9)-4.55 x 10(10) erg s(-1) cm(-2), the beam-plasma interaction with the return current is studied. We found that the electron beam relaxes to the plateau distribution function as known from electrostatic simulations. Simultaneously, due to electromagnetic effects and the Buneman instability of the prescribed Maxwell-shifted return current, the electron distribution function evolves to a new stationary state with a new form of the return current. In this final state the return current is formed not only by electrons in the bulk of the electron distribution function, but also by electrons in the extended tail. We use the results of simulations to estimate the critical beam fluxes for the processes under study in the low corona, the transition region and the upper chromosphere.