Time dependence of fast electron beam divergence in ultraintense laser-plasma interactions

We report on the measurement and computer simulation of the divergence of fast electrons generated in an ultraintense laser-plasma interaction (LPI) and the subsequent propagation in a nonrefluxing target. We show that, at $I{\lambda }^2$ of ${10}^{20}$ Wcm${}^{-2}\mu$m${}^2$, the time-integrated electron beam full divergence angle is ${(60\pm 5)}^{\circ }$. However, our time-resolved 2D particle-in-cell simulations show the initial beam divergence to be much smaller ($\le {30}^{\circ }$). Our simulations show the divergence to monotonically increase with time, reaching a final value of ${(68\pm 7)}^{\circ }$ after the passage of the laser pulse, consistent with the experimental time-integrated measurements. By revealing the time-dependent nature of the LPI, we find that a substantial fraction of the laser energy ($\sim 7\%$) is transported up to $100\mu$m with a divergence of 32${}^{\circ }$.

Figure 1

Experimental setup: A 50 J, 250 fs laser pulse incident on Al-Cu-Al-C target. The $K_{\alpha }$ photons induced by electrons in Cu are collected using a spherically bent Bragg crystal.

Figure 2

(a) Typical experimental data: A $K_{\alpha }$ image with Cu tracer at a depth of 15 $\mu$m (inset); a horizontal lineout of the image showing an 80-$\mu$m spot size full width at half intensity. (b) Experimental $K_{\alpha }$ radius as a function of Cu depth. Full divergence angle of ${(60\pm 5)}^{\circ }$ is determined by weighted least square fit.

Figure 3

Time evolution of $K_{\alpha }$ emission at a depth of 15 $\mu$m. The red band represents the range of the time-integrated experimental data. Black curves are the $K_{\alpha }$ profiles obtained from simulations at 0.50, 0.75, and 8.00 ps from bottom to top, respectively.

Figure 4

Time evolution of $K_{\alpha }$ spot size at 0-, 15-, 50-, and 100-$\mu$m depths. The shaded area is the region of monotonically increasing $K_{\alpha }$ spot size. In the nonshaded area, the spot size becomes constant.

Figure 5

Time-dependent beam divergence from LSP simulations (solid circles). Time-integrated experimental measurement (square).