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At the Nevada Terawatt Facility, experiments are developed to investigate matter in extreme conditions, which is created by the interaction of intense laser-produced plasma with a strong magnetic field. A fast-pulsed-power generator, Zebra, is used to drive coils with megaampere current pulses. Two coil geometries were investigated: two-turn helical coils and horseshoe coils. Finite-element modeling and analytical calculations were used to design the coils, taking into account the magnetic- and electric-field distributions, the coil heating, and its deformation. The magnetic flux density was measured using Faraday rotation in glass probes situated inside or in the immediate vicinity of the coils. Several failure modes of the magnets were observed. In addition, the survivability of the laser target and issues that are particular to the coupling of a terawatt-class short-pulse laser, with a terawatt-pulsed-power generator, are discussed.