Homogeneous non-thermal plasma at atmospheric pressure is highly effective for surface treatment of various polymeric substrates. We propose a dielectric barrier discharge (DBD) reactor consisting of two back-to-back L-shaped electrodes, driven by bipolar voltage pulses of opposite polarity. This structure and driving scheme allow the discharge to be initiated earlier inside the reactor than outside the reactor. The plasma formed inside the reactor is ejected through a slit and moves toward the substrate. As a result, an abundance of electrons is provided to the outside region of the reactor at its breakdown stage. These electrons play a role in suppressing the filamentary mode, and hence, homogeneous discharge in He and Ar can be achieved under an open air configuration. The discharge characteristics inside and outside the reactor are analyzed by using the discharge current and the temporal evolution of emission intensity, respectively. The importance of seed electrons available at the gas breakdown stage in achieving a homogeneous discharge is discussed together with the differences between the discharge characteristics of helium and argon gases.