A one-dimensional longitudinal model including the cathode sheath, the drift region and the external circuit has been used for conditions close to experiments of a corona discharge in liquid Ar. The model provides the space and time variations of the electric field, electron and positive ion densities in the cathode region, as well as the time variations of the electric current through the discharge. The cathode electric field can reach values as high as several MV/cm. The influence of secondary electron emission due to ion impact has been taken into account. Creation of the cathode sheath occurs rapidly due to the multiplication of cathode-emitted electrons in the strong electric field near the cathode, leading to a fast increase in the ion density in this region.
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