Diagnostics of electron beam properties from the simultaneous hard X-ray and microwave emission in the 2001 March 10 flare

Context. Microwave (MW) and hard X-ray (HXR) data are thought to be powerful means of investigating the mechanisms of particle acceleration and precipitation in solar flares, reflecting different aspects of electron interaction with ambient particles in the presence of a magnetic field. Simultaneous simulation of HXR and MW emission with the same populations of electrons is still a big challenge for interpreting observations of real events. Recent progress in simulations of particle kinetics with the time-dependent Fokker-Planck (FP) approach offers an opportunity to produce this interpretation. Aims. In this paper we apply the FP kinetic model of precipitation of electron beam with energy range from 12 keV to 1.2 MeV to the interpretation of X-ray and MW emissions observed in the flare of 2001 March 10. Methods. The theoretical HXR and MW emissions were calculated by using the distribution functions of electron beams found by solving time-dependent approach in a converging magnetic field for anisotropic scattering of beam electrons on the ambient particles in Coloumb collisions and Ohmic losses. Results. The simultaneously observed HXR photon spectra and frequency distribution of MW emission and polarization were fit by those simulated from FP models that include the effects of electric field induced by beam electrons and precipitation onto a converging magnetic loop. Magnetic field strengths in the footpoints on the photosphere were updated with newly calibrated SOHO/MDI data. The observed HXR energy spectrum above 10 keV is shown to be a double power law that was precisely fit by the photon HXR spectrum simulated for the model including the self-induced electric field but without magnetic convergence. The MW emission simulated for different models of electron precipitation revealed a better fit (above 90% confidence level) to the observed distribution at higher frequencies for the models combining collisions and electric field effects with a moderate magnetic field convergence of two. The MW simulations were able to reproduce closely the main features of the MW emission observed at higher frequencies: the spectral index, the frequency of peak intensity and the frequency of the MW polarization reversal, while at lower frequencies the simulated MW intensities are lower than the observed ones