A strongly-ionized plasma generator includes a chamber for confining a feed gas. An anode is positioned inside the chamber. A cathode assembly is positioned adjacent to the anode inside the chamber. An output of a pulsed power supply is electrically connected between the anode and the cathode assembly. The pulsed power supply comprising solid state switches that are controlled by micropulses generated by drivers. At least one of a pulse width and a duty cycle of the micropulses is varied so that the power supply generates a multi-step voltage waveform at the output having a low-power stage including a peak voltage and a rise time that is sufficient to generate a plasma from the feed gas and a transient stage including a peak voltage and a rise time that is sufficient to generate a more strongly-ionized plasma.