Life science and biology have advanced with the progress of microscope technology. A strong desire of life scientists is
to observe live cells with high spatial resolution. The development of soft x-ray microscopy using a special wavelength
called the water window started in the 1970s in order to fulfill this desire. However, the photon fluxes realized so far are
still insufficient for this application. Here, we demonstrate the generation of a coherent water window x-ray by extending
the plateau region of high-order harmonics under a neutral-medium condition. The observed maximum harmonic photon
energy attained are 300 eV and 450 eV in Ne and He, respectively. Our proposed generation scheme, combining a 1.6
mm laser driver and a neutral Ne gas medium, is efficient and scalable in output yields of the water window x-ray. This
powerful concept is expected to boost the development of soft x-ray microscopes based on high-order harmonics.