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Abstract We implemented a hybrid continuous solver for fluid electrons and kinetic ions. Because the simulation is continuous, numerical noise is not an issue as it is for particle‐in‐cell approaches. Moreover, given that the ion kinetic equation is solved using a characteristic based method, no particle pushes have to be done. Our main goals are to reduce the computational cost of the simulations proposed by Kovalev (Kovalev et al., 2008,https://doi.org/10.5194/angeo2628532008) and reproduce the main experimental features of Farley‐Buneman instabilities measured by radars and rockets. The equations were derived from first principles using the approximations that are satisfied in the auroral E‐region. Various tests will be presented to assess numerical accuracy. With the proposed numerical framework, we are able to recover important nonlinear features associated with Farley‐Buneman instabilities: wave turning of dominant modes, and saturation of density irregularities at values consistent with experiments.