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Context. High energy electrons accelerated during solar flare are abundant inthe solar corona and in the interplanetary space. Commonly, the number and theenergy of non-thermal electrons at the Sun is estimated using hard X-ray (HXR)spectral observations (e.g. RHESSI) and a single-particle collisionalapproximation. Aims. To investigate the role of the spectrally evolvingLangmuir turbulence on the population of energetic electrons in the solarcorona. Methods. We numerically simulate the relaxation of a power-lawnon-thermal electron population in a collisional inhomogeneous plasma includingwave-particle, and wave-wave interactions. Results. The numerical simulationsshow that the long-time evolution of electron population above 20 keV deviatessubstantially from the collisional approximation when wave-particleinteractions in non-uniform plasma are taken into account. The evolution ofLangmuir wave spectrum towards smaller wavenumbers, due to large-scale densityfluctuations and wave-wave interactions, leads to an effective acceleration ofelectrons. Furthermore, the time-integrated spectrum of non-thermal electrons,which is normally observed with HXR above 20 keV, is noticeably increased dueto acceleration of non-thermal electrons by Langmuir waves. Conclusions. Theresults show that the observed HXR spectrum, when interpreted in terms ofcollisional relaxation, can lead to an overestimated number and energy ofenergetic electrons accelerated in the corona.

Wave-particle interactions in non-uniform plasma and the interpretation of Hard X-ray spectra in solar flares