Electron Acceleration in Solar Flares: Theory of Spectral Evolution
  Context: Stochastic acceleration is thought to be a key mechanism in the energization of solar flare electrons.   Aims: We study whether stochastic acceleration can reproduce the observed soft-hard-soft evolution of the spectral features of the hard X-ray emitted by suprathermal electron. We pay special attention to the effects of particle trapping and escape.   Methods: The Fokker-Planck equation for the electron distribution is integrated numerically using the coefficients derived by Miller et al. for transit-time damping acceleration. The electron spectra are then converted to photon spectra for comparison with RHESSI observation of looptop sources.   Results: The presence of particle escape softens the model spectra computed in the stochastic acceleration framework. The ratio between the efficiency of trapping and acceleration controls the spectral evolution which follows a soft-hard-soft pattern. Furthermore, a pivot point (that is, a common crossing point of the accelerated particle spectra at different times) is found at around 10 keV. It can be brought into agreement with the observed value of 20 keV by enhanced trapping through an electric potential.   Conclusions: The model proposed here accounts for the key features observed in the spectral evolution of hard X-ray emission from looptop sources. 
Paolo C. Grigis, Arnold O. Benz