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Pulsed power technology has been used in many applications such as control of NOx and SOx from exhaust gases, treatment of dioxins, removal of volatile organic compounds, and generation of ozone. Since the pulse width of the applied voltage has a strong influence on the energy efficiency of the removal of pollutants, the development of a short pulse generator is of paramount importance for practical applications. The observation of discharges created by short duration pulsed voltage is an essential aspect for understanding the plasma physics of this growing field. In the present work, a nano-second pulse generator (NS-PG) that has a pulse duration of less than 10 ns is presented. The NS-PG consists of a high-pressure spark gap switch as a low inductance self-closing switch and a triaxial Blumlein line as a pulse-forming line. The Blumlein line consists of an outer conductor, a middle conductor, and an inner conductor, and is filled up with transformer oil as an insulation medium. The outer conductor is grounded, and the nano-second pulse is generated between the inner and outer conductors. The characteristics of the NS-PG are also reported. The propagation images of the pulsed streamer discharge in a coaxial reactor were taken by a high speed streak camera. The propagation of the streamers was observed for both positive and negative polarities of the applied voltages to the reactor. From the results, for both polarities, the primary streamer propagated from the inner wire electrode to the outer cylinder electrode, and the maximum propagation velocity of the streamer was in the range 6.0 - 8.0 mm/ns over the voltage 67 - 93 kV of the absolute value of peak applied voltage. The results also showed that the propagation velocity of the streamers was strongly influenced by the voltage rise time and to a lesser extent by the voltage polarity.