A method of generating a fast-rise time voltage step to produce an overvoltage condition for a dielectric barrier plasma discharge involves providing a pair of electrodes spaced apart by an electrode gap and at least one dielectric disposed in the gap; generating fast-rise time voltage step such that the rise time to achieve said overvoltage condition is equal to or less than the time required to generate the plasma thereby establishing the overvoltage condition prior to current flow across said electrode gap. Power from storage capacitor banks discharge into the electrode gap through a switch. The switch is capable of standing-off voltage sufficient to create the overvoltage condition when the switch is open. The discharge current pulse across the said electrode gap is terminated by charging properties of the said dielectric(s) in the said electrode gap. This abstract is not to be considered limiting, since other embodiments may deviate from the features described in this abstract.