## 2 Results and Discussion  
### Optimization of the Laser-Plasma-Based Hard X-ray Pulse Source  
As shown in Figure 1a,b, the prototype table-top plasma X-ray source consists of a U-shaped steel vacuum chamber operating at a pressure of 10\({}^{-4}\) mbar (the size is 67 cm \(\times\) 55 cm \(\times\) 15 cm) and a commercial 1 kHz Ti: sapphire femtosecond laser system which provides \(p\)-polarized 35 fs laser pulses with a center wavelength of 800 nm and a maximum pulse energy output up to 13 mJ. The output beam from the laser system is divided into two pulses by the beam splitter with an intensity ratio of 1:9. The weak pulse at 800 nm (the wavelength can be tuned from the ultraviolet to the mid-infrared by nonlinear frequency conversion based on experimental requirements) is utilized as the pump beam to initiate the dynamics in the sample under concern, while the strong one is focused on the 20 \(\upmu\)m-thickness Cu foil target (moving at a speed of 40 mm/s) by an off-axis parabolic mirror (OAP, which is out of the chamber with an effective focal length of 101.2 mm) to generate X-ray pulses. The laser focal spot is measured by the beam profiler (see Figure 1c), indicating that the vertical and horizontal Full-Width Half-Maximum (FWHM) is 7.8 \(\upmu\)m and 8.1 \(\upmu\)m, respectively. As shown in Figure 1d, the spectrum of the generated X-ray pulse is measured with a silicon-based pin photon detector with a 300 \(\upmu\)m diameter lead aperture and a 400 \(\upmu\)m thick aluminum foil is placed in front of the detector to ensure that the data acquisition is under the single-photon counting mode. As expected, the spectrum with a high signal-to-noise ratio is obtained, which is dominated by Cu characteristic radiations (K\({}_{\alpha}\) and K\({}_{\beta}\)) superimposed on a small bremsstrahlung background. To monochromize the X-ray pulse, one can use a nickel foil (8 \(\upmu\)m) to filter the Cu-K\({}_{\beta}\) line with a 40% loss in intensity (the red curve in Figure 1d). As mentioned above, a key issue in hard X-ray sources is flux instability. Although sources with a solid target tape are relatively simple to operate in comparison with the liquid target, they generate metallic debris. A continuously moving plastic tape is thus required to take away the generated debris to maintain the optical transmittance of the chamber entrance. On the other hand, it is well known that the moving speed of the copper tape also affects the conversion efficiency from laser to X-ray [12]. Therefore, it is critical to maintain the copper tape at a constant moving speed. To reach this aim, we have introduced several rotatable deflection rolls to hold the target tape as stable as possible, which combines static and rolling friction to keep the tightness of the target tape to avoid any sudden change in the rotating speed. Additionally, then, similar to the cassette player, a pinch roller in the reaction chamber is used to maintain the surface stability of the copper tape. Moreover, we redesigned the driving system to include a high-precision laser displacement sensor with an accuracy of 2.5 \(\upmu\)m and a sampling period of 200 \(\upmu\)s. This sensor is installed inside the vacuum chamber to measure the radius of the active copper tape reel during the moving process. Based on the conversion relation between the line speed and the angular velocity, we obtain the real-time radius value change and then determine the number of rotation pulses at a unit time of the stepping motor using home-built software. In such a way, we can actively control the moving speed of the copper tape. Besides the mechanical factors, the fluctuation of the laser pulse itself cannot be ignored. To reduce the laser pointing drift on the copper tape due to the temperature or other environmental changes, we use two pairs of diaphragms placed in the optical path to confine the laser beam direction actively. Benefitting from these optimizations, we have successfully obtained a relatively stable X-ray flux in a long term.