Field-emitting Townsend regime of surface dielectric barrier discharges generated in CO$_{2}$ emerging at high pressure

Surface dielectric barrier discharges (DBDs) in CO$_{2}$ from atmospheric pressure up to supercritical conditions ($T_{c} = $ 304.13 K, $p_{c} =$7.4 MPa) generated using 10-kHz ac excitation are studied experimentally. Two discharge regimes are obtained: the standard and field-emitting Townsend regimes. The former resembles typical surface DBDs that have streamer-like characteristics, but the latter has not been reported previously. Here we present an analysis of the electrical and optical diagnostics of the field-emitting Townsend discharge regime using current-voltage and charge-voltage measurements, imaging, optical emission spectroscopy, and spontaneous Raman spectroscopy. Using an electrical model, it is possible to calculate the discharge-induced capacitances of the plasma and the dielectric, as well as the space-averaged values of the surface potential and the potential drop across the discharge. The model also accounts for the space-averaged Laplacian field by including the capacitance due to the fringe electric field from the electrode edge. The electrical characteristics are similar to those of atmospheric-pressure Townsend DBDs, i.e. self-sustained DBDs with minimal space-charge effects. The purely continuum emission spectrum is due to electron-neutral bremsstrahlung, with a corresponding average electron temperature of 2600 K. Raman spectra of CO$_{2}$ near the critical point demonstrate that the discharge increases the average gas temperature by less than 1 K.