High-Intensity-Laser--Solid Interactions in the Refluxing Limit

Small mass targets are of interest in high-intensity-laser--solid interactions due to their unique fast-electron transport properties.\footnote{ S. P. Hatchett \textit{et al}., Phys. Plasmas \textbf{7}, 2076 (2000).}$^{,}$\footnote{ R. A. Snavely\textit{ et al}., Phys. Rev. Lett. \textbf{85}, 2945 (2000).} Electron refluxing in solid-density matter by the Debye sheath fields that are set up at the target surfaces provide a unique environment for the determination of the conversion efficiency of laser energy into fast electrons.\footnote{ W. Theobald\textit{ et al}., Phys. Plasmas \textbf{13}, 043102 (2006).} Previous measurements of the absolute K$_{\alpha }$ yield from copper foils as a function of laser intensity demonstrate excellent agreement with electron refluxing models.$^{3,}$\footnote{ J. Myatt\textit{ et al}., Phys. Plasmas \textbf{14}, 056301 (2007).}$^{ }$In particular, fast-electron conversion efficiencies of around 10{\%} to 20{\%} have been inferred by fitting the absolute K$_{\alpha }$ yields to semi-analytical modeling. It is well known that ionization of the M shell during volumetric heating within such small mass copper targets can cause a deviation in the ratio of the number of emitted K$_{\beta }$ and K$_{\alpha }$ photons below the cold material limit.$^{4}$ This is a direct consequence of bulk target heating due to fast-electron energy loss. Such a deviation could provide a useful code benchmarking parameter on the energy content of the fast electrons and a consistency check on the laser-electron conversion efficiency. This consistency check, however, has proven elusive experimentally. We demonstrate here for the first time the consistency between the fast-electron conversion efficiencies predicted by these two methods using small mass targets. It is demonstrated that a 3.5$\times $ reduction in the ratio of the number of emitted K$_{\beta }$ and K$_{\alpha }$photons is achievable below the cold material limit using 20 $\times $ 20 $\times $ 2 \textit{$\mu $}m copper targets at laser intensities of 2 $\times $ 10$^{19}$ W cm$^{-2}$. These results provide a comparison in preparation for the higher energy-density environments that will be accessible using the future OMEGA EP Laser Facility.\footnote{ C. Stoeckl\textit{ et al}., Fusion Sci. Technol. \textbf{49}, 367 (2006)} This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreements DE-FC52-92SF19460 and DE-FC02-04ER54789. Contributors: W. Theobald, J. Myatt, M. Storm, O.V. Gotchev, C. Mileham, C. Stoeckl, R. Betti,$^{\ast }$ D.D. Meyerhofer,$^{\ast }$ and T.C. Sangster. $^{\ast }$Also at the Fusion Science Center for Extreme States of Matter and Fast Ignition.