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The surface electric field (SEF) for the quasi-static negative corona discharge in atmospheric pressure air is investigated by the general fluid model which contains the continuity equations of electrons, positive ions, and negative ions coupled with Gauss' equation, considering the secondary electron emission. The SEF for the monopolar ion flow, which assumes that the whole interelectrode gap is filled with monopolar ions, is also investigated by the simplified model under the same boundary conditions at the anode. The results predict that the SEF remains constant at the onset value for both the negative corona plasma and the monopolar ion flow under a low corona current. With the increase of the corona current, the SEF is slightly strengthened for the negative corona plasma and significantly weakened for the monopolar ion flow in a wide range of conductor radii. The results for the monopolar ion flow are consistent with those deduced from the experimental data in the literature.