Efficiency Enhancement for $K_{\alpha }$ X-Ray Yields from Laser-Driven Relativistic Electrons in Solids

High-irradiance short-pulse lasers incident on solid density thin foils provide high-energy, picosecond-duration, and monochromatic $K_{\alpha }$ x-ray sources, but with limited conversion efficiency $ϵ$ of laser energy into $K_{\alpha }$ x-ray energy. A novel two-stage target concept is proposed that utilizes ultrahigh-contrast laser interactions with primary ultrathin foils in order to efficiently generate and transport in large quantities only the most effective $K_{\alpha }$-producing high-energy electrons into secondary x-ray converter foils. Benchmarked simulations with no free numerical parameters indicate an $ϵ$ enhancement greater than tenfold over conventional single targets may be possible.

Figure 1

The quantities $\xi$ (left) and ${ϵ}_{\mathrm{ideal}}$ (right) versus projectile energy for $e^{-}$ (solid line), ${\mathrm{H}}^{+}$ (dashed line), and ${\mathrm{C}}^{+6}$ (dotted line) in Sn, with $e^{-}$ its results (squares), assuming ${\rho }_{\mathrm{Sn}}=7.3\mathrm{g}{\mathrm{cm}}^{-3}$. The gray bands illustrate the range a cumulative uncertainty factor of only 2 would introduce.

Figure 2

Integrated simulation of two-stage concept for increasing $ϵ$. From top to bottom: electric field magnitude; ultrathin-foil electron density, average electron energy $k{T}_e=\frac{2}{3}{E}_{\mathrm{av}}$, and ion beam density; and converter foil average electron energy are shown at $t=0.46$, 0.66, 0.80, and 1.10 ps.

Figure 3

Ultrathin-foil electron phase space densities (normalized to Sn) at $t=0.46$, 0.66, 0.80, and 1.10 ps. Energies $E_e$ of 5, 10, 20, and 50 MeV are about ${\gamma }_e{\beta }_e=10.7$, 20.5, 40.1, and 98.8. Note the nonthermal beamlike distribution.

Figure 4

Laser (gray) and $K_{\alpha }$ x-ray (black) power in $\mathrm{J}{\mathrm{fs}}^{-1}$ (solid lines) and energy in J (dotted lines). The dashed line denotes ${10}^{-4}$ efficiency relative to the laser energy. By $t=2.6\mathrm{ps}$, the efficiency is tenfold higher than direct-foil irradiation.