Effects of front-surface target structures on properties of relativistic laser-plasma electrons

We report the results of a study of the role of prescribed geometrical structures on the front of a target in determining the energy and spatial distribution of relativistic laser-plasma electrons. Our three-dimensional particle-in-cell simulation studies apply to short-pulse, high-intensity laser pulses, and indicate that a judicious choice of target front-surface geometry provides the realistic possibility of greatly enhancing the yield of high-energy electrons while simultaneously confining the emission to narrow ($<$$5^{\circ }$) angular cones.

Figure 1

Schematic diagram of one target structure investigated and a flat target with corresponding fast electron distributions. The colored cones on the backside of the target represent the angular distributions of electrons with different energies. Blue, green, yellow, and red cones (from wider to narrower) indicate energies from low to high. (For example, for target and laser parameters we describe in Sec. 2a, the four colors indicate 1–10, 50–60, 80–100, and $>$150 MeV, respectively.) The figure in the upper left is the simulation setup for a 2D simulation; the shaded yellow outer contour is modeled as a conductor.

Figure 2

Electron spectrum for different targets from 3D simulations. There are three types of targets: (a) A flat target with 1 $\mu$m preplasma. (b) A target with slab structures on the front; the depth and width of the slabs are 10 $\mu$m and 1 $\mu$m. The spacing between the slabs is 2 $\mu$m. (c) A target with tower structures on the front; the depth and width of the towers are also 10 $\mu$m and 1 $\mu$m. The spacing between towers in both transverse directions is 2 $\mu$m. (d) shows the electron energy spectra of targets (a)–(c). The blue (bottom) curve for target (a) is commonly observed in experiments on flat targets. The green (middle) and orange (top) curves for targets (b) and (c) show substantial increases in the yield of electrons above 50 MeV.

Figure 3

Angular distribution of fast electrons ($>$1 MeV). The top three graphs are fast electron number distributions (on a color log scale) as a function of kinetic energy and angle $\theta$ with respect to the forward ($z$) direction. The bottom three graphs are fast electron number distributions as a function of direction in the $xz$ and $yz$ planes. (a1), (a2) correspond to the flat target in Fig. 2. An overall divergence angle of about ${60}^{\circ }$ is seen. (b1), (b2) correspond to the slab-structured target in Fig. 2. The overall divergence angle is about ${40}^{\circ }$. (c1), (c2) correspond to the tower-structured target in Fig. 2. The distribution shows two peaks at ${\theta }_y\approx \pm 4^{\circ }–5^{\circ }$. For electrons $>$100 MeV, each cone angle is about $4^{\circ }–5^{\circ }$.

Figure 4

Electron injection and acceleration mechanisms as revealed in a 2D simulation. (a) is a plot of electron density on a log scale when the peak of the laser pulse is located at $Z=-4$ $\mu$m. Electron bunches are pulled out from the structure surfaces by the laser $E_L$ field. (b) is a cartoon showing the accelerating and guiding mechanisms of the electrons pulled out into the gaps. The red ellipse represents the laser pulse. The black dots are the electrons. $E_S$ and $B_S$ are the quasistatic surface fields induced by the structures (different from the laser fields $E_L$ and $B_L$). The trajectories shown here are substantially different from those revealed using fully 3D simulations (see Fig. 5).

Figure 5

Trajectories of the higher-energy hot electrons ($>$120 MeV) from 3D simulations. (a1), (a2), (a3) correspond to the slab target Fig. 2. (a2), (a3) are side views while looking along either the $y$ or $x$ axis. Red curves indicate electrons with initial positions $X>0$, while blue are those from $X<0$. In the case of slabs, electrons bounce back and forth between the structure surfaces in the $x$ direction, and are bent towards the center in the $y$ direction. (b1), (b2), (b3) correspond to the tower target Fig. 2. Electrons are guided by the structure surfaces in the $x$ direction, and pinch in the $y$ direction. These trajectories are considerably different from those predicted using 2D simulations (see Fig. 4).

Figure 6

Guiding mechanisms in 3D slabs. In (a), in the $x$ direction, electrons are bounced back and forth between surfaces, while in the $y$ direction, they are guided towards the center. (b) is a plot of the $B_S$ field perpendicular to the laser direction at $Z=-5$ $\mu$m, where the peak of the laser pulse is located. A spatial average over $\lambda$ in the $z$ direction is applied to minimize the oscillating $B_{Ly}$ field from the laser. $B_{S\perp }$ is normalized by the peak $B_L$ field of the laser $B_{L0}$. The color scheme indicates the magnitude while the arrows point out the directions. The lengths of the arrows are proportional to the magnitude of $B_{S\perp }$.

Figure 7

Guiding mechanisms in 3D towers. In (a), the quasistatic $B_S$ field induced by the hot electron current and the return current is indicated by the green arrows. Since the laser polarization is in the $x$ direction, the electrons pulled out by the laser $E_L$ field mainly fill in the gaps in the XZ plane rather than the YZ plane. The $B_{Sx}$ field that dominates in the gaps pulls the electrons along $y$ towards the center. In the $x$ direction near the surfaces, the $E_{Sx}$ and $B_{Sy}$ fields still balance out. So electrons are constrained in the $x$ direction and pinched in the $y$ direction. Similar to Fig. 6, (b) is a plot of $B_{S\perp }$ at $Z=-5$ $\mu$m where the peak of the laser pulse is located.