The cell structure of surface discharge ACPDPs with a long gap between the sustaining electrodes achieves high luminous efficiency. However, the long gap cell structure causes high firing voltage and thus makes driving more difficult than with the conventional gap cell structure. The rise in firing voltage in the long gap cell structure could not be explained by Paschen's scaling law. We derived a new governing equation for firing voltage, involving the influence of a non-uniform electric field, to investigate this deviation from Paschen's law. From the calculated results we found that changing the gap length corresponds to the change in the degree of distortion of the electric field between the sustaining electrodes.