The acceleration of quasi-thermal particles by an electric field, whose velocity is greater than the thermal velocity, is considered in various interpretations for the dynamic brake force of electrons arising due to Coulomb collisions. It is shown that if the velocity of electrons exceeds the thermal velocity by a factor of two, then the forces of dynamic braking, taking into account electron-electron collisions (Spitzer approximation), and changes in the distribution function of background electrons under the influence of an electric field (Dreicer approximation), practically coincide. If the electric field is much smaller than the Dreicer field, then the Spitzer and Harrison (accounting both for electron-electron collisions and changes in the background electron distribution function) approaches match to within a coefficient. The implications of these results for the acceleration of quasi-thermal electrons in solar flares are discussed.
Yu. T. Tsap (2025) studied this question.