Abstract: The primary arcs on the solar arrays are the main cause of secondary arcs, a serious threat to the safety of spacecraft operation. The primary arcs were widely studied but without a fast assessment model. A 1D model of the primary arcs is developed to explain the experimental results under different discharging conditions. Both effects of the electric field enhanced emission and the electron impact ionization are included by using an equivalent capacity model for the boundary condition. The primary arc characteristics under different conditions can be predicted. The effects of the differential surface potential, the cover glass thickness, and the secondary emission coefficient are studied. It is shown that the onset voltage of the primary arc grows with the increase of cover glass thickness and the solar cell gap distance, the discharging frequency is affected by the bias voltage and the secondary emission coefficient, and the peak current is proportional to the bias voltage and the solar array capacitance. The results are consistent with experiments and can provide a fast assessment of the primary arc in a solar array design.