In this study, the charge trapping effect in alumina dielectric surfaces has been deeply investigated by means of a dedicated dielectric barrier discharge apparatus in different discharge regimes and gas mixtures. This work further validates our previous findings in the case of air discharges in a filamentary regime. Long lasting charge trapping has been evidenced by ex situ thermoluminescence characterizations of alumina dielectric barrier plates exposed to a plasma. The density of trapped surface charges was found to be higher in the glow discharge with respect to pseudo-glow and filamentary regimes, and for all regimes the minimum trap activation temperature was 390 K and the trap energy was less than or around 1 eV. This implies that in the case of glow discharges a higher reservoir of electrons is present. Also, the effect was found to persist for several days after running the discharge.