Controlling the fast electron divergence in a solid target with multiple laser pulses

Controlling the divergence of laser-driven fast electrons is compulsory to meet the ignition requirements in the fast ignition inertial fusion scheme. It was shown recently that using two consecutive laser pulses one can improve the electron-beam collimation. In this paper we propose an extension of this method by using a sequence of several laser pulses with a gradually increasing intensity. Profiling the laser-pulse intensity opens a possibility to transfer to the electron beam a larger energy while keeping its divergence under control. We present numerical simulations performed with a radiation hydrodynamic code coupled to a reduced kinetic module. Simulation with a sequence of three laser pulses shows that the proposed method allows one to improve the efficiency of the double pulse scheme at least by a factor of 2. This promises to provide an efficient energy transport in a dense matter by a collimated beam of fast electrons, which is relevant for many applications such as ion-beam sources and could present also an interest for fast ignition inertial fusion.

Figure 1

Dependence of the HWHM of the Cu $K_{\alpha }$ (red squares) and thermal emission images (black dots) from the rear target surface on the time delay compared with (green diamonds) numerical simulations. Copied with permission from Scott [7].

Figure 2

Spatial distribution of the magnetic field $B_{\theta }$ for the values of the parameter $b$ increasing from the left ($b=1.2$) to the right ($b=2.0$) at the time of the magnetic-field maximum.

Figure 3

(a) Temporal evolution of the maximum magnetic field at various time delays between the first and the second laser pulse. The blue line (first from left) $\Delta t=0$ ps represents the second pulse alone. The azure line (the line arriving till 18 ps) represents (up to 10 ps) the maximum magnetic field of the first pulse which is amplified by the injection of the second pulse at different time delays, green line (second from left) $\Delta t=3$ ps, red line (third from left) $\Delta t=4$ ps, and azure line (fourth from left) $\Delta t=8$ ps. The diffusion time of the magnetic field depends only on the beam radius and on the target resistivity ${\tau }_{B_{\theta }}\sim w_e^2/\eta$. (b) Temporal evolution of the maximum magnetic field (continuous line) and of the laser-pulse intensity (dotted line) for the time delay $\Delta t=4$ ps for the triple pulses scheme.

Figure 4

Distribution of the electron-beam density ($\text{log}{n}_e$) at the end of the process for the double pulse scheme at $t=10$ ps (case A, center) and for the triple pulses scheme at $t=13$ ps (case B, right). In the left panel is shown the case C with the energy $E=40$ J. Other parameters are shown in Table 1.

Figure 5

Distribution of the resistive magnetic field ($\text{log}{B}_{\theta }$; top line from left $t=6$,10 ps) and the $K_{\alpha }$ emission ($\text{log}{K}_{\alpha }$; bottom line from left $t=6$,10 ps) for the case A.

Figure 6

Distribution of the resistive magnetic field ($\text{log}{B}_{\theta }$; top line from left $t=6$,14 ps) and the $K_{\alpha }$ emission ($\text{log}{K}_{\alpha }$; bottom line from left $t=6$,14 ps) for the case B.

Figure 7

(left) Scheme of a “typical” experiment with the target having two tracer layers at the front and at the rear side. (Right) Radial line out of the $K_{\alpha }$ signal coming from the tracer layers.

Figure 8

Magnetic field (in arbitrary units) radial profile as obtained from Eq. (A8) for two cases $\tau =17$ (max $B\sim -4$) (no hollowing) and $\tau =100$ (max $B\sim -11$).