Influence of surface processes on surface discharges generated on borosilicate glass barriers in high-pressure CO$_{2}$ up to supercritical conditions

Surface dielectric barrier discharges (DBDs) generated in CO$_{2}$ from atmospheric pressure up to supercritical conditions ($T_{c} = $ 304.13 K, $p_{c} = $ 7.4 MPa) using 10-kHz AC excitation are investigated experimentally using current-voltage and charge-voltage measurements, imaging, and optical emission spectroscopy. Surface processes are investigated to resolve unexplained phenomena from related work on the ``standard'' and ``field-emitting Townsend'' discharge regimes. Variations in the energy, residual or ``memory'' charge, and spatial homogeneity of the field-emitting Townsend regime are shown to depend on the duration that the discharge runs continuously. The memory charge is positive for the field-emitting Townsend regime but negative for the standard regime. It is demonstrated that high discharge homogeneity and low variation in the discharge energy is correlated with the maximization of positive memory charge. Charge neutralization of plasma ions and electrons by anions and cations in the borosilicate glass is proposed as the process responsible for the presence of nanosecond current pulses in the field-emitting Townsend regime.