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During solar flares a large amount of electrons are accelerated within theplasma present in the solar atmosphere. Accurate measurements of the motion ofthese electrons start becoming available from the analysis of hard X-rayimaging-spectroscopy observations. In this paper, we discuss the linearizedperturbations of the Boltzmann kinetic equation describing an ensemble ofelectrons accelerated by the energy release occurring during solar flares.Either in the limit of high energy or at vanishing background temperature suchan equation reduces to a continuity equation equipped with an extra force ofstochastic nature. This stochastic force is actually described by the wellknown energy loss rate due to Coulomb collision with ambient particles, but, inorder to match the collision kernel in the linearized Boltzmann equation itneeds to be treated in a very specific manner. In the second part of the paperthe derived continuity equation is solved with some hyperbolic techniques, andthe obtained solution is written in a form suitable to be compared with datagathered by hard X-ray imaging-spectroscopy telescopes. Finally, a firstvalidation of the model with NASA Reuven Ramaty High Energy Solar SpectroscopicImager spectrometer measurements is provided.

Interplay of Boltzmann equation and continuity equation for accelerated electrons in solar flares