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This tutorial presents a study of positive and negative corona discharges in dry air at atmospheric pressure. The discharges are sustained within two electrodes in a coaxial configuration by a high voltage DC source applied to the inner electrode. Two different types of models are used: a full self-consistent plasma model and a simplified model. The plasma model solves the electron and ion continuity and momentum equations in the drift-diffusion approximation, self-consistently coupled with Poisson’s equation. The local field approximation is used, which means that transport and source coefficients are assumed to be well parameterized through the reduced electric field. The simplified model uses a simplified charge transport model coupled with electrostatics to provide an approximate method of computing the charge density and the electrostatic field in corona discharges. The space charge density and the electric potential obtained with the simplified model are in good agreement with the simulation results obtained with the self-consistent plasma model.