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To estimate the potential distribution and field-enhancement factor associated with a gated carbon nanotubes array on the planar cathode surface, the image charge model of floated sphere between parallel gate and cathode plates was proposed.The field-enhancement factor for the gated nanotubes array obtained by β =3 + ρ· B + W, in which ρ is the aspect ratio of CNTs, and B and W are a function of the gate-hole radius R, gate-cathode distance d and other geometrical parameters of the gated nanotubes cold cathode.The calculation result has shown that the influence of the aspect ratio of the nanotubes for field-enhancement factor is much remarkable on the gated nanotubes cold cathode.The field-enhancement factor decreases with the increasing of the gate-hole radius as the gate-cathode distance is a finite, and the influence of gate-hole radius for the field-enhancement factor could be neglected when the gate-cathode distance is infinite.Otherwise, the field-enhancement factor increases rapidly with the increasing of intertube distance and trends to a fixed value as the intertube distance is infinite.