Towards Attosecond High-Energy Electron Bunches: Controlling Self-Injection in Laser-Wakefield Accelerators Through Plasma-Density Modulation

Self-injection in a laser-plasma wakefield accelerator is usually achieved by increasing the laser intensity until the threshold for injection is exceeded. Alternatively, the velocity of the bubble accelerating structure can be controlled using plasma density ramps, reducing the electron velocity required for injection. We present a model describing self-injection in the short-bunch regime for arbitrary changes in the plasma density. We derive the threshold condition for injection due to a plasma density gradient, which is confirmed using particle-in-cell simulations that demonstrate injection of subfemtosecond bunches. It is shown that the bunch charge, bunch length, and separation of bunches in a bunch train can be controlled by tailoring the plasma density profile.

Figure 1

Bubble phase velocity ${\beta }_b$ from PIC data (green) and calculated using (4) (black dashed), for the density profile (1) (red). Chosen parameters were $a_0=4$, $\lambda =800\mathrm{nm}$, and ${\eta }_0^2=0.001$. After a linear ramp of $r=300\mu \mathrm{m}$, a density peak with amplitude $\alpha =0.1$ and width $w=50\mu \mathrm{m}$ is located at $z_i=500\mu \mathrm{m}$.

Figure 2

Trajectories of a random selection of sheath electrons for ${\eta }_0^2=0.001$ and $\alpha =0$ [$\alpha =0.15$ for panel (d)] and laser parameters as in Fig. 1. Panel (a) shows the spatial trajectories of electrons in the frame comoving with the bubble, and panel (b) the variation of their longitudinal velocities ${\beta }_z$. Red and blue lines highlight typical trajectories. Panels (c) and (d) show the evolution of the longitudinal electron velocities. In the latter, the injected population is shown in red. Orange lines show the bubble phase velocity, and horizontal black lines denote the threshold velocity.

Figure 3

Variation of the average plasma density gradient for the density profile (1) with $\alpha \in [0.05,0.3]$. The region for which self-injection can occur, as described by (6), is shaded grey. ${\mathrm{\Gamma }}_e=6$ corresponding to $a_0=4$.

Figure 4

Injected bunch length (square, circle) and charge (times, plus) for simulations with plasma density parameters as in Fig. 3 for 2D and 3D cases. Injected bunch length predicted by the model is shown for comparison with solid (2D) and dashed (3D) lines. The 2D case differs due to the geometric dependence of ${\mathrm{\Gamma }}_e$. The 2D charge density is scaled by a factor of $1.2\times {10}^{-5}\mathrm{m}$.

Figure 5

Comparison of injected bunches from 3D simulations in Fig. 4: (a) $\alpha =0.10$, just exceeding the injection threshold, and (b) $\alpha =0.25$, significantly exceeding the injection threshold.