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Minimization of the power required to sustain weakly ionized plasmas can be achieved if the energy of ionizing electrons is high, from tens to thousands of electronvolts. These electrons spend about a half of their energy on ionization cascades, in contrast to low-energy (1-3 eV) electrons in conventional discharges that dissipate most of their energy in nonionizing inelastic collisions. High-energy electrons can be injected into the gas as beams. Alternatively, they can be created in situ by applying a very strong electric field for a short time, with a repetition rate matching the rate of recombination. Analytical calculations show that the power budget in the high-voltage, repetitive pulse mode can be significantly lower than in the dc regime, but still much higher than in the case of electron beam ionization. For each pulse length, there exists an optimum electric field that minimizes the power budget. A detailed modeling of spatio-temporal dynamics of pulsed discharges reveal that voltage displacement into the cathode sheath plays a critical role. Fully coupled modeling of nonlocal kinetics of high- and low-energy electrons, ionization processes, charge particle transport, and electrodynamics was performed for a high-voltage pulse developing with a substantial pre-existing plasma. The kinetic modeling shows formation of a large group of high-energy electrons in high-voltage nanosecond pulse and dramatic increase in ionization rate. New effects are indicated, such as field reversal, "two-cathode" effect, and interpulse ionization.