Molecular dynamics simulation of strong shock waves propagating in dense deuterium, taking into consideration effects of excited electrons

We present a molecular dynamics simulation of shock waves propagating in dense deuterium with the electron force field method [J. T. Su and W. A. Goddard, Phys. Rev. Lett. 99, 185003 (2007)], which explicitly takes the excitation of electrons into consideration. Nonequilibrium features associated with the excitation of electrons are systematically investigated. We show that chemical bonds in ${\mathrm{D}}_2$ molecules lead to a more complicated shock wave structure near the shock front, compared with the results of classical molecular dynamics simulation. Charge separation can bring about accumulation of net charges on large scales, instead of the formation of a localized dipole layer, which might cause extra energy for the shock wave to propagate. In addition, the simulations also display that molecular dissociation at the shock front is the major factor that accounts for the “bump” structure in the principal Hugoniot. These results could help to build a more realistic picture of shock wave propagation in fuel materials commonly used in the inertial confinement fusion.

Figure 1

Profiles of temperature components along the $z$ axis for $v_p=30\mathrm{km}/\mathrm{s}$. They represent typical temperature distributions of strong shock waves. The inset is the zoom-in of temperature components in the upstream region.

Figure 2

Ion velocity distributions at selected positions near the shock front, in the simulation with a piston velocity $v_p=30\mathrm{km}/\mathrm{s}$. The color of each curve represents the distance with respect to the center of the shock front, as denoted by the color bar on the right side. (a) Velocity distribution on the perpendicular direction, and (b) the same as (a) but on the parallel direction, with respect to the propagation direction of shock waves. Positive distance in the color bar refers to location where the shock wave has not yet reached.

Figure 3

Profiles of net charge density along the $z$ axis for different piston velocities and electron masses. The black, red, and blue solid lines correspond to $v_p=20$, 30, and 40 km/s and $m_e=0.01\mathrm{amu}$, while the green dashed curve corresponds to $v_p=30\mathrm{km}/\mathrm{s}$ and $m_e=0.1\mathrm{amu}$.

Figure 4

Radial distribution functions at selected positions along the propagating direction of shock waves. The color of each curve corresponds to its distance from the center of the shock front, which is denoted in the color bar on the right side. Two cases are displayed corresponding to different piston velocities. In (a), $v_p=20\mathrm{km}/\mathrm{s}$, and in (b) $v_p=30\mathrm{km}/\mathrm{s}$. Positive distance in the color bar refers to location where the shock wave has not yet reached.

Figure 5

Principal Hugoniot calculated in the eFF “dynamic” simulations of shock propagation, compared with those obtained from other approaches. The two arrows indicate the two states corresponding to $v_p=20\mathrm{km}/\mathrm{s}$ and $v_p=30\mathrm{km}/\mathrm{s}$. Results from the eFF method through the Rankine-Hugoniot relation are taken from [37], experimental results are taken from [45, 50, 51], and the PIMC results are from [29].

Figure 6

Ionization ratio profiles along the propagating direction of shock waves. Profiles of different color correspond to different piston velocities, as indicated in the legend.