## 1 Introduction  
Laser-wakefield acceleration (LWFA) is an aspirational technology in the acceleration community for producing compact, bright, and highly relativistic \(e\) beams. These LWFA-based \(e\) beams can act as potential drivers of free-electron lasers (FELs) [1, 2], sources of table-top X-rays and Gamma-rays [3, 4], and even candidates for healthcare [5, 6]. High-quality \(e\) beams can be achieved with a variety of injection techniques, such as self-injection [7, 8], ionization-induced injection [9, 10, 11, 12], density down-ramp injection [13, 14], or colliding-pulse injection [10, 15]. However, some of these methods demand sophisticated configurations, and the produced \(e\) beams are deficient in charge, energy spread, or peak energy, which hinder their practical applications. Recently, some significant studies have been reported to improve the specific qualities of \(e\) beams, including the peak energy [16, 17, 18, 19, 20], the energy spread [21, 22, 23, 24, 25, 26], the brightness [24, 27, 28], the reproducibility [29, 30, 31], etc. More considerable research efforts, however, are still needed to focus on generating reproducible high-quality electrons for table-top light sources, which should have a broad-ranging impact across multiple scientific fields. Of particular interest is that for high-quality and stable \(e\) beams, the shock-induced density down-ramp injection [32, 33] is the most prominent technique. Usually, a thin blade is placed at the exit of a supersonic nozzle. When the gas flow from the nozzle impinges on the blade, a shock wave is generated, and the injection process can thus be tuned, where the phase velocity of the wake is temporarily reduced to trap the electrons through a density down-ramp or a sharp density transition. The density transition length \(\delta_{1}\) with respect to  
interferometer using a 4\(f\) optical imaging system was set up for measuring the plasma density, as shown in Figure 1c,d. The desired density shock front was manipulated with a perforated baffle and a pulsed gas valve connected to a nozzle with a 6-mm bore diameter. Different from the previous structures [32; 39; 40], a 2.5-mm-thick perforated copper baffle was inserted parallelly along the nozzle in the upstream of the supersonic flow, and could thus produce a slanted shock wave much farther away from the baffle compared with the previous thin blade (i.e., the right wall of the first segment gas cell). This specifically designed structure may also benefit the required evolution of the bubble and electron injections with a larger charge. It acts as a specially designed structure to form the required plasma density distribution with only one gas jet, resulting in less airflow disturbance and more stable abrupt density transitions. The distance between the exit of the baffle and the left inner wall of the nozzle is defined as zb, as shown in Figure 1b, and the structured gas profile with a stable shock wave is induced with different zb by adjusting the horizontal span along the optical axis. The generated \(e\) beams were deflected by a 90-cm-long tunable dipole electromagnet with a maximum magnetic field of 1.1 T and measured with a Lanex phosphor screen imaged with an intensified charge-coupled device (ICCD) camera in a single shot (Figure 1e), which was cross-calibrated by using a calibrated imaging plate and an integrating current transformer (ICT) to measure the charge of the \(e\) beams [41]. The collimator was used to shield the low-energy and large-divergence \(e\) beams and to minimize the irrelevant signal on the profile during the measurement [4; 27; 37]. The energy spectrometer had a resolution of 0.2% at 800 MeV and 0.1 mrad divergence, and the uncertainty of the measured peak energy was calculated as \(\pm\)2% considering the \(e\) beam's pointing stability of 1 mrad. The uncertainty of the measured \(e\) beam charge was estimated to be within \(\pm\)6%.