Diagnostic studies of an rf-capacitvely coupled plasma driven by ring-shaped electrodes are performed with the focus of the investigation on the unintentional peripheral region breakdown. Upon this peripheral region breakdown, the radial profile of the electron density changes significantly from center-high to edge-high, as confirmed by the plasma appearance and by the surface temperature measurements. It is found that this breakdown is controlled by the gas type, pressure, power, and the gap between the grounding sample stage and the glass chamber wall. Among the factors, the gap appears to be the most critical one that controls this breakdown. The voltage at which this breakdown occurs increases with the decrease in the pressure and the gap size. In addition, argon plasmas show the lowest breakdown voltage, followed by nitrogen, oxygen, and helium plasmas. The above trends follow the left branch of the Paschen curve. We show that with a proper modification of the sample stage, a well-confined peripheral breakdown region with a high plasma density and a high degree of dissociation in O 2 plasmas can be formed.