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In this paper, we present a model (which is structured as an equivalent electric circuit whose elements are identified and deducted from the nature of the medium, the ionization and expansion process of the streamers that convey the prebreakdown current, and the energy associated to the electric breakdown in water) and a simulation of a pulsed corona discharge (PCD). Considering this, a coaxial reactor and an inexpensive and compact high-voltage pulsed-power supply (PPS) system were designed and constructed with the purpose of carrying out the PCD experimentally. The simulation results enable the prediction of the behavior of the discharge. The coaxial reactor is constituted by a cylindrical chamber and a straight central rod. The PPS operates within the 100-2000-Hz repetition rate and 0-30-kV amplitude ranges. All the system has been tested, and the first electrical results, voltage, and current waveforms, are presented.