A dielectric barrier plasma discharge device consistent with certain embodiments of the present invention has a pair of electrodes spaced apart by an electrode gap. A dielectric is disposed between the electrodes. The electrode gap is provided with a gas at a specified pressure. A rapid rise time voltage pulse generator produces a voltage pulse across the electrodes to cause an extreme overvoltage condition, wherein the rapid rise time is less than a plasma generation time so that the extreme overvoltage condition occurs prior to current flow across the electrode gap. Due to the high voltages and high current densities, the product yields an extremely high instantaneous power density. This extreme overvoltage condition is also believed to lead to production of shock waves and runaway free electrons. The resulting plasma can be utilized to carry out many potential tasks including, but not limited to etching, deposition, and sterilization. This abstract is not to be considered limiting, since other embodiments may deviate from the features described in this abstract.