## 2 Materials and Methods
The position of the target with respect to the focus was initially optimized to the highest radiation dose measured with a dosimeter and then tuned to the maximum of the X-ray signal on spectrometers. Figure 1: **(a)** the scheme of the experimental setup (not to scale). All the diagnostics (except the focal spot imaging system) are shown. The charge-coupled device (CCD3) recording the X-rays reflected from the quartz (SiO\({}_{2}\)) crystal also detected signals not reflected from the crystal. Scanning electron microscope (SEM) images of the investigated targets: **(b)** the ordered nanowire (NW) target; **(c)** the disordered NW target. Figure 2: Schematic illustration of the laser field polarization with respect to the target geometry in the case of the ordered NW **(a)** and disordered NW **(b)** samples. \(\overrightarrow{E_{p}}\) and \(\overrightarrow{E_{s}}\) represent the electric fields of the p- and s- polarized light, respectively. \(\overrightarrow{n}\) represents the vector normal to the target, and \(\overrightarrow{k}\) the wave vector of the incident beam. The interaction of the laser pulse with the nanostructured and flat targets took place inside a vacuum chamber pumped down to \(10^{-4}\) mbar. The diagnostic setup was placed outside the chamber in ambient air. The expected line emission and, especially, the hard X-rays were not strongly absorbed on their propagation in air to the detectors at a distance below \(1\) m. For the line spectrum measurements, two bent crystals were set up. The first one, based on a toroidal quartz (40-4) crystal (2d = 1.672 nm), measured spectra in a narrow spectral window. The spectral resolution was limited by the CCD spatial resolution \(\lambda/\delta\lambda<1500\). This spectrometer enabled a high-resolution investigation of the K\({}_{\alpha}\) doublet from zinc. The second spectrometer, with a cylindrical LiF (220) crystal (2d = 2.848 nm), works in a wide range of energies (from K\({}_{\alpha}\) to K\({}_{\beta}\) emission lines of Zn), with a resolution of \(\lambda/\delta\lambda<2000\). The detection of the spectra reflected by the bent crystals was realized by cooled, back-illuminated X-ray CCD cameras (Roper Scientific and Andor, CCD2 and CCD3 in Figure 1a, respectively) with their own vacuum-supporting containers. For detecting the bremsstrahlung emission, another Andor X-ray CCD camera (CCD1 in Figure 1a), sensitive to photons with energies up to 20 keV, and a Timepix detector were installed. The Timepix detector is based on a 1 mm thick CdTe chip and can register photons with energies from 30 keV to 800 keV [27]. The distance of 45 cm from the target was roughly the same for both detectors. Reliable measurements of bremsstrahlung spectra over a broad range taken with the same CCD camera require correction due to the abruptly decreasing quantum efficiency for higher energies. Additionally, the Compton scattering becomes more important for higher energies, enhancing the count rate. Therefore, for higher energy X-rays, these two counter-acting processes must be carefully considered. The obtained spectra must not only be corrected for absorption in air and the Kapton window but also require additional Monte Carlo simulations considering the two above-mentioned efficiencies scaling with the photon energy (e.g., [28; 29]). For our setup, simulations showed that for the given experimental parameters and detected spectra, the introduced correction for the absorption would be sufficient to obtain reliable data. As we used no wavelength dispersive elements for measuring the continuous X-ray spectra, we had to ensure that our detectors operated in the \"single-photon counting regime\" [30; 31], implying, in any case, that the ratio of the number of photons divided by the number of pixels must be \(\leq\)0.15.