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A minimally invasive transverse beam profile monitor based on supersonic gas curtain technology and beam-induced fluorescence has been developed and demonstrated. The concept presented can be used to measure both the profile of the proton beam in the Large Hadron Collider (LHC) and the concentricity of the electron and the proton beams in the LHC hollow electron lens. In this Letter, the performance of such a monitor for a low energy electron beam is discussed, which paves the way for its wider implementation.