Journal Article Research Support, Non-U.S. Gov't Elettra synchrotron FEL diagnostics FERMI free-electron laser Hertz–Knudsen equations X-ray absorption spectroscopy beam diagnosis cross correlation detector extreme ultra-violet four-wave mixing four-wave-mixing free-electron laser free-electron lasers high-vacuum environments liquid flat jets liquid sample delivery non-linear optics optical impulse force phosphors pixelated phosphor detector pump–probe timing transient grating ultra-fast soft X-ray experiments ultrafast dynamics warm dense matter water droplets