A capacitive discharge connected through a dielectric or metal slot to a peripheral grounded region is a configuration of both theoretical and practical interest. The configuration is used in commercial dual frequency capacitive discharges, where a dielectric slot surrounding the substrate separates the main plasma from the peripheral grounded pumping region. Ignition of the peripheral plasma produces effects such as poor matching and relaxation oscillations that are detrimental to processing performance. Discharge models are developed for diffusion and plasma maintenance in the slot, and plasma maintenance in the periphery. The theoretical predictions of ignition conditions as a function of voltage and pressure are compared with experimental results for a driving frequency of 27.12 MHz and a gap spacing of 0.635 cm connecting the two regions, giving good agreement.