## 2 Experimental Setup and Experimental Results  
The experiments were carried out on the Ti:sapphire laser system (pulse duration:33 fs FWHM, repetition rate: 1 Hz) based on chirped pulse amplification [20], as shown in Figure 1. Laser pulses with an 800 nm wavelength were focused on a gas target with a 100 TW on-target power and a 32 \(\upmu\)m FWHM spot size using an off-axis parabolic mirror with f/30 optical geometry. The focused peak intensity was estimated to be \(3.6\times 10^{18}\) W/cm\({}^{2}\), corresponding to a normalized vector potential \(a_{0}\) of approximately 1.3. The accelerated \(e\)-beams were deflected by a 90 cm-long tunable dipole electromagnet with a maximum magnetic field of 1.1 T, then imaged onto a Lanex phosphor screen, and finally detected by a 16-bit intensified charge-coupled device (ICCD). The gas target was similar to the one we used in the cascaded LWFA [7; 21], and consisted of two supersonic helium gas nozzles. In the experiments, the diameter of the first gas nozzle (d\({}_{1}\)) was fixed at 2 mm, and that of the second (d\({}_{2}\)) was changed from 3 to 5 mm. By adjusting the gas pressures of the two gas nozzles and optimizing the horizontal span between them, two-color \(e\)-beams could be generated using similar combined injection techniques [21]. Recently, a new scheme involving the combination of shock-front injection with colliding-pulse injection also realized the generation of two-color \(e\)-beams [22]. The density profile was measured using an optical interferometer system in which a probe pulse crossed the gas targets perpendicularly and was then imaged onto a charge-coupled device (CCD). As shown by the white line in Figure 2b, the plasma density of the first gas nozzle was measured to be \(n_{e1}=(5.0\pm 0.1)\times 10^{18}\) cm\({}^{-3}\). After the first nozzle's density plateau, a 200 \(\upmu\)m-long density up-ramp with a maximum density of \((7.5\pm 0.1)\times 10^{18}\) cm\({}^{-3}\) was generated, followed by a 200 \(\upmu\)m-long density downward. Finally, the density profile entered into the second density plateau, which was measured to be \(n_{e2}=(3.5\pm 0.1)\times 10^{18}\) cm\({}^{-3}\). In the experiments, two-color \(e\)-beams with different energy spectra were produced (Figure 2a) by using different diameters (2.0, 3.5 and 5.0 mm) for the second supersonic gas nozzle. Figure 2b shows the corresponding plasma channels with different plasma lengths imaged on the interferometer CCD and the white line represents the measured density profile. As the propagation distance of the laser increased, the width of the plasma channel gradually became larger. Because the on-axis normalized laser amplitude was inversely proportional to the square of the radius of the plasma channel [23], the laser intensity began to decrease, and finally, the pump depleted completely. The pump depletion length can be described as \(L_{pd}=c\tau_{L}\big{(}\omega_{0}/\omega_{p}\big{)}^{2}\), where c is the light speed in vacuum, \(\tau_{L}\) is the laser pulse duration, \(\omega_{0}\) is the laser frequency and \(\omega_{p}\) is the plasma frequency [24]. For example, at a density of 3.5 \(\times 10^{18}\) cm\({}^{-3}\), \(L_{pd}\approx 5\) mm. The corresponding angle-resolved energy spectra are shown in Figure 2c,  
Figure 1: Experimental layout of the hybrid laser-plasma wakefield accelerator. CCD: charge-coupled device; ICCD: intensified charge-coupled device. Figure 2: (**a**) Energy spectra of two-color \(e\)-beams. (**b**) Plasma channel with different plasma length of 4.0, 5.5, and 7.0 mm. (**c**) Corresponding \(e\)-beam angle-resolved energy spectra. (**d**) Statistics of shot-to-shot fluctuations of the energy of the \(e\)-beams and full width at half maximum (FWHM) energy spread when the plasma length was 7.0 mm. and the parameters of the generated \(e\)-beams are listed in Table 1. For the low-charge \(e\)-beam, as the plasma length increased, the energy of the beam increased and its energy spread decreased. For the high-charge \(e\)-beam, the opposite was true.