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Low-pressure dielectric barrier discharge (DBD) alkali vapour lamps are of particular interest for portable atomic clocks because they (1) could enable low-power operation, (2) generate the precise required wavelength, (3) are planar simplifying chip-level integration and (4) use external electrodes, which increases the lifetime. Given the stringent requirements on lamps for atomic clocks, it is important to identify the parameters that can be optimized to meet these performance requirements (size, power consumption, stability, reliability). We report on the electrical and optical characteristics of dielectric barrier plasma discharges observed in two configurations: (1) in a vacuum chamber over a wide low-pressure range (2-100 mbar) for three different buffer gases (He, Ar, N-2) driven at different frequencies between 2 and 500 MHz and (2) on microfabricated hermetically sealed Rb vapour cells filled with 30 and 70 mbar of Ar. We discuss the optimum conditions for a low-power and stable operation of a Rb vapour DBD lamp, aimed at chip-scale atomic clocks. We also present the electrical modelling of the discharge parameters to understand the power distribution mechanisms and the input power to discharge power coupling efficiency.