TOF-OFF: A method for determining focal positions in tightly focused free-electron laser experiments by measurement of ejected ions

Abstract Pulse intensities greater than 10 17  Watt/cm 2 were reached at the FLASH soft X-ray laser in Hamburg, Germany, using an off-axis parabolic mirror to focus 15 fs pulses of 5–70 μJ energy at 13.5 nm wavelength to a micron-sized spot. We describe the interaction of such pulses with niobium and vanadium targets and their deuterides. The beam produced craters in the solid targets, and we measured the kinetic energy of ions ejected from these craters. Ions with several keV kinetic energy were observed from craters approaching 5 μm in depth when the sample was at best focus. We also observed the onset of saturation in both ion acceleration and ablation with pulse intensities exceeding 10 16  W/cm 2 , when the highest detected ion energies and the crater depths tend to saturate with increasing intensity. A general difficulty in working with micron and sub-micron focusing optics is finding the exact focus of the beam inside a vacuum chamber. Here we propose a direct method to measure the focal position to a resolution better than the Rayleigh length. The method is based on the correlation between the energies of ejected ions and the physical dimensions of the craters. We find that the focus position can be quickly determined from the ion time-of-flight (TOF) data as the target is scanned through the expected focal region. The method does not require external access to the sample or venting the vacuum chamber. Profile fitting employed to analyze the TOF data can extend resolution beyond the actual scanning step size.