Extreme focusing of high power x-ray lasers to relativistic intensity with a concave plasma lens

The intensity of present x-ray lasers is still far from relativistic due to equipment damage by the powerful radiation involved in the generation process. We propose to use a microscopic concave plasma lens to tightly focus terawatt x-ray pulses to relativistic intensity by avoiding the destructive instabilities arising from the laser-plasma interaction in the focusing process. Three-dimensional particle-in-cell simulations show that an intense x-ray laser pulse can be focused to a tiny spot of the wavelength scale at ultrahigh intensity while well preserving its original spatiotemporal profile. The resulting pulse can exceed the relativistic intensity threshold [(1.37×10^{24}/λ_{nm}^{2})W/cm^{2}, with λ_{nm} being the wavelength normalized by nanometers] by two orders of magnitude. Such intense nano-sized x-ray pulses can be useful for exploring nonlinear phenomena in the strong-field quantum electrodynamics regime, as well as in high-energy-density science and astrophysics.