Measurements of Ion Stopping Around the Bragg Peak in High-Energy-Density Plasmas

For the first time, quantitative measurements of ion stopping at energies around the Bragg peak (or peak ion stopping, which occurs at an ion velocity comparable to the average thermal electron velocity), and its dependence on electron temperature ($T_e$) and electron number density ($n_e$) in the range of 0.5–4.0 keV and $3\times {10}^{22}$ to $3\times {10}^{23}{\mathrm{cm}}^{-3}$ have been conducted, respectively. It is experimentally demonstrated that the position and amplitude of the Bragg peak varies strongly with $T_e$ with $n_e$. The importance of including quantum diffraction is also demonstrated in the stopping-power modeling of high-energy-density plasmas.

Figure 1

CPS2-measued spectra of DD tritons, $\mathrm{D}{}^3\mathrm{He}$ alphas, DD protons, and $\mathrm{D}{}^3\mathrm{He}$ protons produced in implosions 29828 (blue) and 43233 (red). These experiments were designed to generate similar total $\rho R$ values but to have most of the ion energy loss taking place in the cold remaining shell for implosion 29828 (blue spectra) and in the hot fuel for implosion 43233 (red spectra).

Figure 2

Brown-Preston-Singleton (BPS) and Li-Petrasso (LP) modeling of proton stopping in a uniform plasma with a $T_e$ of 1.0 keV and $n_e$ of $5\times {10}^{22}{\mathrm{cm}}^{-3}$. The BPS quantum (dotted black) and BPS classical stopping (dashed black) are also shown.

Figure 3

Stopping-power data illustrating $T_e$ dependence. Measured and modeled $-\mathrm{\Delta }{E}_i/Z_i^2$ versus $E_i/A$ for a low-temperature experiment (a), and for a high-temperature experiment (b). Inferred $\rho R$ was similar in these experiments. The data were determined directly from the spectra shown in Fig. 1. The black (green) curves represent the BPS (LP) modeling. For the low-temperature experiment, the reduced ${\chi }^2$ [36] is 2.1 for LP and 0.2 for BPS, and for the high-temperature experiment, the reduced ${\chi }^2$ is 1.5 for LP and 1.5 for BPS. The errors on the inferred $T_e$ and $\rho R$ values were determined from the reduced ${\chi }^2$ fit.

Figure 4

Stopping-power data illustrating $\rho R$ (or $n_e$) dependence. Measured and modeled $-\mathrm{\Delta }{E}_i/Z_i^2$ versus $E_i/A$ for a low-$\rho R$ experiment ($n_e\sim 3\times {10}^{22}{\mathrm{cm}}^{-3}$) (a), and for a high-$\rho R$ experiment ($n_e\sim 3\times {10}^{23}{\mathrm{cm}}^{-3}$) (b). The experimental and modeled data shown in (a) have been multiplied with a factor of 5 to put the information on the same scale as used in (b). Inferred $T_e$ was similar in these experiments. The black (green) curves represent the BPS (LP) modeling. For the low-$\rho R$ experiment, the reduced ${\chi }^2$ is 0.4 for LP and 0.2 for BPS, and for the high-$\rho R$ experiment, the reduced ${\chi }^2$ is 2.3 for LP and 0.7 for BPS. The errors on the inferred $T_e$ and $\rho R$ values were determined from the reduced ${\chi }^2$ fit.

Figure 5

Measured and modeled $-\mathrm{\Delta }{E}_i/Z_i^2$ versus $E_i/A$ for implosion 27814. In the modeling of the energy-loss data, $\rho R$ was fixed to $8.1\mathrm{mg}/{\mathrm{cm}}^2$ while $T_e$ was allowed to vary. The reduced ${\chi }^2$ is 10.1 for BPS-classical (dashed black), 0.7 for BPS (solid black) and 1.7 for LP (solid green). The errors on the inferred $T_e$ values were determined from the reduced ${\chi }^2$ fit.