Fig. 1. Variation of laser frequency (a) and ramp-up of the laser amplitude against ξ for un-chirped case (b) and four chirped functions (c)–(f). In (c)–(f), the red curve is with c = –0.2, the black curve is with c = –0.5. The curve for each chirped function is shown in the figure.

Fig. 2. The stability phase diagram of electron oscillation in (a₀, ω_p0) plane for different laser frequencies Ω(ξ₀).

Fig. 3. Contour plot of γ_max in (a₀, ω_p0) plane with different chirped laser pulses [linearly chirped laser pulse (the first row), exponential chirped laser pulse (the second row), Gaussian chirped laser pulse (the third row), and sinusoidal chirped laser pulse (the fourth row)]. Initially, the electron is at rest, but it is slightly displaced from the x and y axes of the plasma channel.

Fig. 4. Variation of γ/γ_vac (a), dephasing rate (b) and oscillation displacement in y direction (c) of electron against z/λ for different intensity of Gauss chirped laser under same plasma density (ω_p0 = 0.05, a₀ = 6).

Fig. 5. The effect of Gaussian chirped laser pulse on the trajectory of single electron with different chirped pulse parameters, the amplitude of laser a₀ = 6 and the density of plasma channel ω_p0 = 0.15.

Fig. 6. The single electron is placed in linearly inhomogeneous plasma channel (the first row) and parabolic inhomogeneous plasma channel (the second row) respectively. It is irradiated by four types of chirped laser pulse (linearly chirped laser pulse in (a) and (e), Gaussian chirped laser pulse in (b) and (f), exponential chirped laser pulse in (c) and (g) and sinusoidal chirped laser pulse in (d) and (h)). The intensity of the laser pulse a₀ = 6, the plasma density at the axis of the channel is ω_p0 = 0.05, the density distribution for linearly inhomogeneous and parabolic inhomogeneous case are n(r) = 1 + br and n(r) = 1 + br² (the r is radial direction). The maximum energy of electron is normalized by the maximum energy of electron in vacuum γvac=1+a02/2.