Ab Initio Studies on the Stopping Power of Warm Dense Matter with Time-Dependent Orbital-Free Density Functional Theory

Electronic transport properties of warm dense matter, such as electrical or thermal conductivities and nonadiabatic stopping power, are of particular interest to geophysics, planetary science, astrophysics, and inertial confinement fusion (ICF). One example is the $\alpha$-particle stopping power of dense deuterium-tritium (DT) plasmas, which must be precisely known for current small-margin ICF target designs to ignite. We have developed a time-dependent orbital-free density functional theory (TD-OF-DFT) method for ab initio investigations of the charged-particle stopping power of warm dense matter. Our current dependent TD-OF-DFT calculations have reproduced the recently well-characterized stopping power experiment in warm dense beryllium. For $\alpha$-particle stopping in warm and solid-density DT plasmas, the ab initio TD-OF-DFT simulations show a lower stopping power up to $\sim 25\%$ in comparison with three stopping-power models often used in the high-energy-density physics community.

Figure 1

Snapshots of electron densities in an enlarged window on the $x-y$ plane from TD-OF-DFT simulations (with CD) of a 1-MeV proton traveling through a warm dense Be plasma of $k_{B}T=32\mathrm{eV}$ and $\rho =1.78\mathrm{g}/{\mathrm{cm}}^3$.

Figure 2

(a) A comparison of TD-OF-DFT calculated proton stopping power by a $k_{B}T=32\mathrm{eV}$ and ambient-density Be plasma, with (CD) and without (TFW) current dependent dynamic potential, from a single MD snapshot and averaged over initial projectile positions. (b) The TD-OF-DFT calculated proton stopping power in high velocities (away from the Bragg peak) in comparison with three stopping-power models of LP [11], BPS [14, 15], and DF [16]. (c) Comparisons of the downshifted proton spectra among the experimental measurements [46], predictions of LP and BPS models, and the TD-OF-DFT calculations.

Figure 3

(a) The $\alpha$-particle stopping power of warm dense DT plasmas ($\rho =0.25\mathrm{g}/{\mathrm{cm}}^3$ and $k_{B}T=10\mathrm{eV}$) predicted by TD-OF-DFT calculations (green circles) compared to the LP, BPS, and DF models. (b) The calculated downshifted spectra of $\alpha$ particles passing through the $50\text{−}\mu \mathrm{m}$ DT slab at the same warm dense condition from both TD-OF-DFT simulations (green) and the two stopping-power models (red and blue).