A transverse beam profile monitor that visualizes a two-dimensional beam-induced fluorescent image was developed. The monitor employs a sheet-shaped gas flow formed by a technique of rarefied gas dynamics. A simplified analysis method was developed to reconstruct the beam intensity profile from the obtained image. The developed profile monitor and the analysis method were applied to measure the J-PARC 3 MeV H^{-} beam profile. The root mean square values of the profiles were consistent with the ones obtained by a wire-scanning-type beam profile monitor. The beam loss due to the gas sheet injection was measured as a beam-current reduction. The amount of the beam current decreased in proportion to the gas sheet flux and the reduction ranged from 0.004 to 2.5%. The assembled system was capable of reconstructing a beam profile from a single shot beam pulse (1.7×10^{13} protons in 50 μs).
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