Measurement of Charged-Particle Stopping in Warm Dense Plasma

We measured the stopping of energetic protons in an isochorically heated solid-density Be plasma with an electron temperature of $\sim 32\mathrm{eV}$, corresponding to moderately coupled $[(e^2/a)/(k_B{T}_e+E_F)\sim 0.3]$ and moderately degenerate $[k_B{T}_e/E_F\sim 2]$ “warm-dense matter” (WDM) conditions. We present the first high-accuracy measurements of charged-particle energy loss through dense plasma, which shows an increased loss relative to cold matter, consistent with a reduced mean ionization potential. The data agree with stopping models based on an ad hoc treatment of free and bound electrons, as well as the average-atom local-density approximation; this work is the first test of these theories in WDM plasma.

Figure 1

Experimental geometry. A thin-glass exploding-pusher proton source (left) imploded by 20 laser beams creates energetic $\mathrm{D}{}^3\mathrm{He}$ protons used to probe a subject plasma, which is created by isochorically heating a solid Be plug with x rays (right). These x rays are created by the 30 laser beams irradiating the Ag-coated CH tube.

Figure 2

Parameter space, showing contours of constant degeneracy ($\theta$, black) and coupling (${\mathrm{\Gamma }}_e$, magenta) as functions of electron density and temperature. Previous experiments [26, 27, 28, 29, 30, 31] are shown by blue points (blue shaded region for Ref. [31]), and this work is shown by the red points. A typical range for WDM ($n_e={10}^{22}–{10}^{24}1/{\mathrm{cm}}^3$, $T_e=1–100\mathrm{eV}$) is shown by the green shaded box, while typical parameters for the ICF hot spot (HS) and dense fuel (DF) are shown by green points.

Figure 3

Proton spectral data for a heated (warm) Be target (shot 72018, red) and an undriven (cold) Be target (shot 72026, blue). For each shot, the proton source spectrum (black) is measured directly by three detectors.

Figure 4

Downshift ($\mathrm{\Delta }E$) for cold (a) and warm (b) shots compared to theory. The solid points are data (denoted by shot number), and theories are hollow points. The uncertainties in theoretical calculations are due to uncertainties in $\rho L$ and plasma conditions.

Figure 5

Mean ionization potential ($\overline{I}$) inferred from the stopping-power data in the cold (a) and warm (b) cases compared to the Andersen-Ziegler empirical fits (${\overline{I}}_{\mathrm{AZ}}$), the ideal plasma case ($\hslash {\omega }_{pe}$), and electronic structure theory.