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Acceleration of particles and plasma heating is one of the fundamentalproblems in solar flare physics. An accurate determination of the spectrum offlare energized electrons over a broad energy range is crucial for ourunderstanding of aspects such as the acceleration mechanism and the total flareenergy. Recent years have seen a growing interest in the kappa-distribution asrepresentation of the total spectrum of flare accelerated electrons. In thiswork we present the kappa-distribution as a differential emission measure. Thisallows for inferring the electron distribution from X-ray observations and EUVobservations by simultaneously fitting the proposed function to RHESSI andSDO/AIA data. This yields the spatially integrated electron spectra of acoronal source between less than 0.1 keV up to several tens of keV. The methodis applied to a single-loop GOES C4.1 flare. The results show that the totalenergy can only be determined accurately by combining RHESSI and AIAobservations. Simultaneously fitting the proposed representation of thekappa-distribution reduces the electron number density in the analyzed flare bya factor of ~30 and the total flare energy by a factor of ~5 compared with thecommonly used fitting of RHESSI spectra. The spatially integrated electronspectrum of the investigated flare between 0.043 keV and 24 keV is consistentwith the combination of a low-temperature (~2 MK) component and a hot (~11 MK)kappa-like component with spectral index 4, reminiscent of solar winddistributions.

Multi-thermal representation of the kappa-distribution of solar flare electrons and application to simultaneous X-ray and EUV observations