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Context: Stochastic acceleration is thought to be a key mechanism in theenergization of solar flare electrons.  Aims: We study whether stochastic acceleration can reproduce the observedsoft-hard-soft evolution of the spectral features of the hard X-ray emitted bysuprathermal electron. We pay special attention to the effects of particletrapping and escape.  Methods: The Fokker-Planck equation for the electron distribution isintegrated numerically using the coefficients derived by Miller et al. fortransit-time damping acceleration. The electron spectra are then converted tophoton spectra for comparison with RHESSI observation of looptop sources.  Results: The presence of particle escape softens the model spectra computedin the stochastic acceleration framework. The ratio between the efficiency oftrapping and acceleration controls the spectral evolution which follows asoft-hard-soft pattern. Furthermore, a pivot point (that is, a common crossingpoint of the accelerated particle spectra at different times) is found ataround 10 keV. It can be brought into agreement with the observed value of 20keV by enhanced trapping through an electric potential.  Conclusions: The model proposed here accounts for the key features observedin the spectral evolution of hard X-ray emission from looptop sources.Comment: expanded in answer to the referee's comments, accepted by Astronomy &  Astrophysic

Electron acceleration in solar flares: theory of spectral evolution