  Full coherent soft X-ray attosecond pulses are now available through
high-order harmonic generation (HHG); however, its insufficient output energy
hinders various applications, such as attosecond-scale soft X-ray nonlinear
experiments, the seeding of soft X-ray free-electron lasers,
attosecond-pump-attosecond-probe spectroscopies, and single-shot imaging. In
this paper, towards the implementation of these exciting studies, we
demonstrate a soft X-ray harmonic beam that is more than two orders of
magnitudes stronger up to the water window region compared to previous works.
This was achieved by combining a newly developed TW class mid-infrared
femtosecond laser and a loosely focusing geometry for HHG in the mid-infrared
region for the first time. Thanks to a loosely focusing geometry with a neutral
medium target, we achieve a high conversion efficiency, a low beam divergence,
and a significantly reduced medium gas pressure. As the first application of
our nano-joule level water window soft X-ray harmonic source, we demonstrate
near edge X-ray absorption fine structure (NEXAFS) experiments with clear fine
absorption spectra near the K- and L-edges observed in various samples. The
systematic study of a robust energy scaling method on HHG opens the door for
demonstrating single-shot absorption spectrum and live cell imaging with a
femtosecond time resolution.
