Fig. 1. (a) Schematic illustration of laser pulse propagation in a typical density-tailored plasma with three down-slope distributions, where L_d1, L_d2, and L_d3 represent the injection stage, acceleration stage, and transportation stage, respectively. (b) Evolution of normalized laser intensity and wake phase velocity in the plasma. (c)–(e) 3D views of TW laser-driven wakefield acceleration using FBPIC simulations, for three segments at t = 1.46, 1.93, and 3.11 ps, respectively.

Fig. 2. (a)–(c) Plasma density, longitudinal acceleration field, and trajectory of injected electrons at different times t = 1.40, 1.46, and 1.51 ps, respectively. (d) The e-beam energy spectrum at injection time t = 1.46 ps. (e) Corresponding transverse density distribution of e-beam (blue shading), focusing field (green curve), and transverse momentum distribution (orange shading). (f) Longitudinal velocity distribution (red curve) and observed longitudinal acceleration field (green curve) of e beam at t = 1.51 ps after L_d1.

Fig. 3. Evolution of transverse position [(a) and (d)], transverse momentum [(b) and (e)], and emittance [(c) and (f)] of e beams for longitudinal injection in a weakly nonlinear LWFA [(a)–(c)], as compared with the transverse injection case for the bubble regime [(d)–(f)].

Fig. 4. (a) Evolution of energy peak value (blue curve) and energy spread (red curve) during the acceleration stage L_d2 (blue shading) and transport stage L_d3 (yellow shading). (b) Energy spectra for different times t = 1.46 ps (black), 1.93 ps (blue), 2.50 ps (green), and 3.11 ps (red). (c)–(f) Corresponding electron phase spatial distribution, energy spectrum (orange shading), and charge current (blue shading). The inset in (f) shows the energy angular distribution of the e beam.

Fig. 5. (a) and (b) Charge (black curve) and energy (blue curve) as functions of the injection distance L_d1 and the peak density n_peak. (c) and (d) Corresponding energy spread (black curve) and emittance (red curve). The blue shading corresponds to the case shown in Figs. 2 and 4.