| Abstract
| - Context. High-energy electrons accelerated during solar flares are abundant in the solar corona and in interplanetary space. Commonly, the number and energy of non-thermal electrons at the Sun is estimated through hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims. We aim to investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods. We numerically simulated the relaxation of a power-law non-thermal electron population in a collisional inhomogeneous plasma, including wave-particle and wave-wave interactions. Results. The numerical simulations show that the long-time evolution of electron population above 20 keV deviates substantially from the collisional approximation when wave-particle interactions in non-uniform plasma are taken into account. The evolution of the Langmuir wave spectrum towards smaller wavenumbers, caused by large-scale density fluctuations and wave-wave interactions, leads to an effective acceleration of electrons. Furthermore, the time-integrated spectrum of non-thermal electrons, which is normally observed with HXR above 20 keV, is noticeably increased because of acceleration of non-thermal electrons through Langmuir waves. Conclusions. The results show that the observed HXR spectrum, when interpreted in terms of collisional relaxation, can lead to an overestimated number and energy of energetic electrons accelerated in the corona.
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