The spatial distributions of transverse focusing field E y − cB θ (a) and longitudinal accelerating field E_x (b) at t = 1.23 ps. (c) The transverse (in the center of the self-injected electron bunch) and (d) longitudinal (on the on-axis) distributions of the accelerating field E_x at t = 0.5 ps, 2 ps, 3 ps, and 5 ps, respectively. The dashed and the dot–dashed lines show the boundaries of the hollow plasma and the self-injected electron bunch in panel (a), respectively. The focusing field E y − cB θ at x = 332 μ m is shown by the black line in panel (a). The black rectangles denote the locations of the self-injected electron bunch in panel (d).