A magnetic horn system to be operated at a pulsed current of 320 kA and to survive high-power proton beam operation at 750 kW was developed for the T2K experiment. The first set of T2K magnetic horns was operated for over 12 million pulses during the four years of operation from 2010 to 2013, under a maximum beam power of 230 kW, and $6.63times10^{20}$ protons were exposed to the production target. No significant damage was observed throughout this period. This successful operation of the T2K magnetic horns led to the discovery of the $ u_{mu}rightarrow u_e$ oscillation phenomenon in 2013 by the T2K experiment. In this paper, details of the design, construction, and operation experience of the T2K magnetic horns are described.
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