A two-dimensional (axially symmetric) computational model of the microdischarge formation in a barrier discharge for short (1–2 mm) gaps in air at atmospheric pressure is proposed. A non-homogeneous electric field, caused by a residual non-uniform charging of the dielectric barriers, is considered as an important reason for the filament formation by a Townsend mechanism. The ion–electron emission from the dielectric covering the cathode is treated as the principal secondary process; the secondary emission coefficient in the model is selected to be consistent with the Paschen voltage. For an applied sinusoidal voltage, this follows the microdischarge development on a microsecond scale. It is shown that even a slight inhomogeneity of the initial electric field leads to the formation of a narrow microdischarge channel.The two-dimensional dynamics of the radiation from a microdischarge for the case of the second positive and the first negative systems of nitrogen is simulated and compared with recent experimental data. The effects of the secondary emission coefficient and of a distribution of residual surface charges are investigated. It is shown that the level of inhomogeneity of the residual surface charge distribution does not affect the radius of the microdischarge channel, but affects its two-dimensional structure.The proposed model explains satisfactorily the experimental results for the velocity of the cathode-directed ionizing wave and the emission of the N2 second positive system from a microdischarge.
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