Enhanced Relativistic-Electron-Beam Energy Loss in Warm Dense Aluminum

Energy loss in the transport of a beam of relativistic electrons in warm dense aluminum is measured in the regime of ultrahigh electron beam current density over $2\times {10}^{11}\mathrm{A}/{\mathrm{cm}}^2$ (time averaged). The samples are heated by shock compression. Comparing to undriven cold solid targets, the roles of the different initial resistivity and of the transient resistivity (upon target heating during electron transport) are directly observable in the experimental data, and are reproduced by a comprehensive set of simulations describing the hydrodynamics of the shock compression and electron beam generation and transport. We measured a 19% increase in electron resistive energy loss in warm dense compared to cold solid samples of identical areal mass.

Figure 1

(a) Measured (full symbols) and simulated (empty symbols) absolute $\mathrm{Sn}\text{−}{K}_{\alpha }$ yields as a function of the Al sample areal density. Simulation results obtained with ${\eta }_{\text{laser}\to \mathrm{e}}=25\%$ (the shaded area corresponds to $\pm 5\%$ variations). (b) Measured and simulated $\mathrm{Sn}\text{−}{K}_{\alpha }/\mathrm{Ag}\text{−}{K}_{\alpha }$ ratio as a function of the Al sample areal density.

Figure 2

(a) REB spectrum obtained from the PIC simulations (solid grey line) and its analytical fit [Eq. (1), dashed red line] injected into hybrid transport simulations. The Sn tracer $K$-shell ionization cross section is also represented (solid green line). (b) Bremsstrahlung spectra results from the MC simulations: experimental spectrum deduced from matching the x-ray detection simulation to the dosimeter layer data (first step, blue solid line) compared to the spectrum generated during the fast electron propagation through the target (second step, dashed red line).

Figure 3

(a) Hydrodynamic simulation results for the density and temperature axis profiles at the SP injection time (focused on the left-hand side), in the Al sample solid (top) and compressed (bottom) cases. (b) Corresponding REB transport simulation results of the time-integrated collisional (left-hand-side plots) and resistive (right-hand-side plots) REB energy loss per unit mass (in logarithmic scale), extracted 2.1 ps after REB injection. All the figures correspond to the thickest targets ($L_0=80\mu \mathrm{m}$).

Figure 4

Results from the hybrid transport simulations assuming ${\eta }_{\text{laser}\to \mathrm{e}}=25\%$: (a) Time-integrated collisional (squares) and resistive (triangles) energy losses in solid (full symbols) and compressed (open symbols) Al samples, as a function of areal density $\rho L$. (b) Time evolution of the resistivity of cold solid (blue squares) and of warm compressed (circles) Al samples, as well as the current beam density (triangles) averaged over a thickness of $L=35\mu \mathrm{m}$ and a radius of $25\mu \mathrm{m}$ around the REB propagation axis, calculated from hybrid simulations.