## 1 Introduction
In the experiment, a comprehensive tuning process for generating bright \(e\) beams was explored elaborately by presenting the baffle at different locations. Initially, the baffle was placed beneath the nozzle (zb \(>\) 2.5 mm) and the laser was focused at the exit of the baffle; no accelerated \(e\) beams were measured in this case when operating the plasma profile with an average density of \((2.6\pm 0.5)\times 10^{18}\)cm\({}^{-3}\), which is lower than the plasma density for self-injection. By moving the baffle backward to the upstream of the gas jet,  
Figure 1: (**a**) Schematic of the experimental setup. (**b**) The diagram of the magnified nozzle and baffle assembly. The driving laser pulse can pass through the hole of the baffle and interact with the gas target to form the plasma. The baffle can be moved forward (along the propagation direction of the laser, i.e., from left to right) or backward (against the propagation direction of the laser) along the optical axis at a minimal step size of 5 \(\upmu\)m. (**c**) The fringe pattern retrieved from the interferometer. The shock wave is circled with a dashed line. (**d**) The density profile along the optical axis. (**e**) A typical and represented spectrum of an \(e\) beam that has an energy peak at 730 MeV. continuously injected \(e\) beams started to appear. When the coverage rate of the baffle over the nozzle was around 12%, which is much smaller than those in [39,40], a relatively large divergence of \(\sim\)1.1 mrad and energy spread of 11.2% were measured for the continuously injected electrons, as shown for case 1 in Figure 2a. The following cases in Figure 2a show shadowgraphs and corresponding typical spectra of \(e\) beams while moving the baffle backward from \(z_{\text{b}}=750\) um to \(z_{\text{b}}=350\) um at a step size of 50 um. It was observed that when moving the baffle backward, the shock wave approached the baffle and the tilt angle between the shock wave and the baffle decreased from 45\({}^{\circ}\) to 33\({}^{\circ}\), but would not affect the electron injection due to the tilt angle, as in [4]. For \(z_{\text{b}}=450\) um, the generated \(e\) beams were already optimized to low-energy spreads of 0.5% and small divergences of 0.25 mrad. As the baffle moved to \(z_{\text{b}}<450\) um, no \(e\) beams were measured over the whole energy spectrum, which indicated that the electron injection did not occur. The overall properties of the \(e\) beams with different plasma-density modulations were measured and are plotted in Figure 2b,c in terms of peak energy, charge, relative energy spread (RES), divergence, and reproducibility. As seen, the peak energy of \(e\) beams increased almost linearly from 400 to 800 MeV, and the RES accordingly decreased from 9.7% to 0.5%. The divergences of the \(e\) beams decreased from 1 to 0.25 mrad, and the reproducibility accordingly decreased from 100% to 85% for \(z_{\text{b}}=450\) um. It was also found that for \(z_{\text{b}}=500\) um, the reproducibility of the measured electron beams was measured to be 95% in a series of 100 continuous shots. The measured average peak energy, root-mean square(rms) energy spread, charge, and divergence were 730 MeV, 0.9%, 34 pC, and 0.3 mrad, respectively. Assuming reasonable values of the \(e\) beam size and the pulse duration at the exit of the LWFA as 2 um and 2.5 fs (FWHM) [42, 43, 44], backed by the PIC simulations, the produced bright beams could be estimated to have a brightness of \(\sim 10^{15}\) A/m\({}^{2}\)/0.1% [27].