Scaling of resistive guiding of laser-driven fast-electron currents in solid targets

The resistive magnetic field plays a crucial role in determining the laser produced fast-electron transport in solid targets. The scaling of the resistive guiding is derived and benchmarked against two-dimensional collisional particle-in-cell simulations. We study the impact of the initial state of the material ($Z$ dependence, conductor, or insulator) on global electron-transport patterns, and conclude that the initial state of a conductor or insulator is not important. Instead, global transport patterns depend on the material $Z$. The fast-electron transport seen in the simulations is consistent with the derived scaling rule. Previous experimental observations [e.g., R. B. Stephens et al., Phys. Rev. E 69, 066414 (2004) and Y. Sentoku et al., Phys. Rev. Lett. 107, 135005 (2011)] that show confinement or divergence in various regimes are also explained by our scaling. The presented scaling then becomes a useful tool to design compact radiation sources or fast ignitor experiments.

Figure 1

2D contour plots of the normalized electron energy density for (a)–(c) aluminum, and (d)–(f) plastic at $t=250$, 500, and 1000 fs. A white bar in each plot indicates 50 $\mu$m scale. The time integrated flux of forward going hot electrons over 2 ps at 125 $\mu$m deep inside the target for (g) aluminum and (h) plastic. $K_{\alpha }$ images taken at 125 $\mu$m inside the target for (i) aluminum and (j) plastic from Ref. [9]. (k) The electron energy density for silicon at 500 fs. The contour levels of this plot are the same as plots (a)–(f).

Figure 2

Quasitatic magnetic field observed at $t=500$ fs for Al (a) and plastic (b). The peak value for aluminum at this time was 7 MG, while only 3 MG for plastic. The resistivity calculated in Al (c) and plastic (d) at the same time of (a) and (b). A bar in each plot indicates 50 $\mu$m scale.

Figure 3

(a) Average ionization degree of aluminum at the same time of Fig. 2. (b) The ionization profile 5 $\mu$m inside the target. (c) Carbon ionization contour in plastic at 175 fs. (d) Carbon ionization profile 2 $\mu$m inside the target at 175 fs and 250 fs.

Figure 4

Resistive guiding condition $\Gamma \left(t\right)$ with snapshots of the electron energy density in simulations. Snapshots shown for 250 fs and 500 fs from which 185 fs must be subtracted to account for laser travel time and peak intensity ramp up. The electron divergence and the absorption coefficient set to $\langle \theta \rangle ={30}^{\circ }$ and $\chi =0.3$ in this plot, respectively.

Figure 5

Critical parameter ${\Gamma }_s$ for various laser intensities and materials. Circles are for CH and crosses are for Al. The gold simulation result is from Ref. [11]. The values are evaluated with $\langle \theta \rangle ={30}^{\circ }$ and $\chi$ in each simulation.