Fig. 1. Schematic of the experimental setup for generating a betatron X-ray source via the LWFA and X-ray phase-contrast imaging. A high-power laser (red) was focused at the entrance of a helium gas jet, producing high-energy electron and X-ray beams. A tungsten collimator positioned behind the gas jet effectively blocked bremsstrahlung radiation, whereas the depleted laser pulse was filtered out using either a 50-μm-thick Kapton or 200-μm-thick Al foil. The electron beam (cyan) was deflected using a 180-cm-long dipole magnet with a maximum magnetic field of 1.5 T onto a Lanex PS, where it was imaged using a 14-bit optical camera to measure the electron spectrum. The X-ray beam (yellow) passed through the sample located 40 cm downstream and was imaged onto an X-ray detector, positioned an additional 470 cm away.

Fig. 2. Characterization of high-charge GeV-class electron beams. (a) Raw electron energy spectra of 20 shots at an electron density of n_e = 6 × 10¹⁸ cm⁻³. The corresponding charge for each shot is indicated in white above the spectra. (b) Electron spectra angularly resolved in the laser polarization plane, within the range of 0.5–2.5 GeV. (c) Statistical analysis of the peak energy and (d) charge of the electron beam for 100 shots under the same conditions (n_e = 6 × 10¹⁸ cm⁻³).

Fig. 3. Characterization of betatron radiation. (a) Radiation intensity distribution (black squares) measured through calibrated metallic cut-off filters made from varying thicknesses of Al and Cu foils (see inset). The filters, labeled from 1 to 8, consisted of blank, 400 μm Al foil, and 40, 70, 120, 150, 300 and 500 μm Cu foils, respectively. The calculated intensity distributions are shown using the synchrotron spectra with critical energies E_c of 15 keV (circle), 20 keV (diamond) and 25 keV (triangle). (b) Single-shot normalized betatron spectrum with E_c = 23 keV, corresponding to the radiation intensity distribution (green stars) through the filters shown in (a). The gray shaded area represents the transmission threshold for the Kapton foil, Al and Be window and air. (c) Betatron radiation divergence with an FWHM of 12.1 mrad × 7.0 mrad. (d) Statistical analysis of the photon counts from X-ray beams for 100 shots, based on the divergence angle shown in (c), corresponding to the electron beams in Figures 2(c) and 2(d).

Fig. 4. Peak brightness, photon number and critical energy of the betatron X-ray source described in this work compared with the results in Refs. [2, 16, 17, 21, 22, 25, 26, 28, 29, 33–37].

Fig. 5. Simulation of betatron radiation. (a) Energy evolution of the electron beam within the plasma simulated using the FBPIC code. (b) Trajectories of the 20,000 tracked electrons. (c) Betatron X-ray spectrum calculated using the SynchRad code. (d) Angularly and spectrally resolved X-ray flux, exhibiting a peak on-axis at 5 keV with a tail extending to 100 keV. (e) X-ray beam profile of spectral integration, revealing an elliptical shape aligned with the direction of laser polarization.

Fig. 6. Measurement of the X-ray source size using the shadow of a half-plane on the detector. The measured intensity distribution (black squares) is integrated along the edge of the half-shadow (inset), and the error bars represent the SD of intensity at different positions. The simulated intensity distributions used Fresnel diffraction modeling for a source with a synchrotron spectrum critical energy of E_c = 22 keV and Gaussian intensity distributions with rms radii of ω_rms = 2 μm (solid red), 4 μm (dashed green) and 6 μm (dotted blue). Gray shading indicates critical energy error.

Fig. 7. Imaging of samples using betatron radiation. (a) X-ray image of the Gilder fine square mesh grids (1000-mesh). (b) Optical microscope image of the mesh grids, showing 19-μm grid holes and 6-μm grid ribs. (c) Intensity distribution within the red box in (a), demonstrating that the imaging system resolution is better than 6 μm. (d) X-ray image of an electronic chip. (e) Partially enlarged view of the red box in (d). (f) Line-out from the region of interest marked by the red line in (e).