Laser-plasma lens for laser-wakefield accelerators

Thanks to their compactness and unique properties, laser-wakefield accelerators are currently considered for several innovative applications. However, many of these applications—and especially those that require beam transport—are hindered by the large divergence of laser-accelerated beams. Here we propose a collimating concept that relies on the strong radial electric field of the laser-wakefield to reduce this divergence. This concept utilizes an additional gas jet, placed after the laser-wakefield accelerator. When the laser pulse propagates through this additional gas jet, it drives a wakefield which can refocus the trailing electron bunch. Particle-in-cell simulations demonstrate that this approach can reduce the divergence by at least a factor of 3 for realistic electron bunches.

Figure 1

Evolution of the propagation angle of individual electrons, as predicted by Eq. (4) for several ($x_0$, ${\theta }_0$), and for $\gamma =400$, $Z_R=180\mu \mathrm{m}$, $a_0(0)=5$, $w(0)=6.7\mu \mathrm{m}$, and $\eta =1$. In the drift space ($z<L_d$), Eq. (4) does not apply, and instead ${\theta }_x$ remains constant.

Figure 2

Upper panel: density profile (blue), laser waist (red), and trajectories of a few injected electrons (black) in the PIC simulation. Lower panel: RMS divergence of the bunch in the $x$ and $y$ directions. (The laser is polarized along $x$.)

Figure 3

Aspect of the wakefield in the second jet, during a PIC simulation with (left panel) and without (right panel) a second laser pulse. The electron density and the laser intensity are represented in blue and red respectively. The dark blue spot represents the electron bunch.

Figure 4

Upper panel: density profile (blue), waists of the first (red, solid) and second (orange, dashed) laser pulse, and trajectories of a few injected electrons (black) in the PIC simulation. Lower panel: divergence of the bunch.

Figure 5

Results of a standard PIC simulation for the laser-plasma lens. Upper panels: Density profile of the two jets (blue curves) and evolution of the transverse coordinates $x$ (left panel) and $y$ (right panel) for some of the accelerated electrons (black lines). (In the simulation the laser is polarized along $x$.) Lower panels: Evolution of the transverse momenta $p_x$ (left panel) and $p_y$ (right panel) for the same electrons. For more clarity, the trajectory of one of these electrons has been singled out and colored in red.

Figure 6

Top panel: Snapshot of the simulation at $z=550\mu \mathrm{m}$ (i.e., inside the drift space), showing the laser pulse (red and blue) and the trailing electron bunch (black dots). Bottom panel: Zoom on the electron bunch. (Notice that the electric field $E_x$ has also been rescaled.)

Figure 7

Schematic evolution of the $E_x$ and $B_y$ fields for a sinusoidal wave, in a PIC simulation. On the Yee lattice, the discrete fields $E_x^n/c$ (red dots) and $B_y^{n+\frac{1}{2}}$ (blue dots) lie exactly on the same sinusoid. However, when interpolating the $B_y$ field to an integer time (dashed red line), the interpolated field $B_y^n$ is not on the sinusoid (green dot), and thus the $E_x$ and $B_y$ fields do not cancel exactly when computing the Lorentz force.

Figure 8

Schematic representation of the third-order accurate interpolation method. This method is more accurate than the standard second-order accurate interpolation method, and thus the interpolated field lies closer to the sinusoid than in Fig. 7.

Figure 9

Comparison of the simulation results with second-order accurate interpolation (top panels) and with third-order accurate interpolation (lower panels). The plots show the evolution of the transverse momenta $p_x$ (left panels) and $p_y$ (right panels) of the accelerated electrons throughout the simulation.

Figure 10

Snapshot of the simulation at $z=550\mu \mathrm{m}$ with the second-order accurate (top panel) and third-order accurate (bottom panel) methods. The electric field of the laser is virtually unchanged with the third-order method, but the electrons (black dots) experience a weaker force.