Thermodynamic and Kinetic Properties of Shocks in Two-Dimensional Yukawa Systems

Particle-level simulations of shocked plasmas are carried out to examine kinetic properties not captured by hydrodynamic models. In particular, molecular dynamics simulations of 2D Yukawa plasmas with variable couplings and screening lengths are used to examine shock features unique to plasmas, including the presence of dispersive shock structures for weak shocks. A phase-space analysis reveals several kinetic properties, including anisotropic velocity distributions, non-Maxwellian tails, and the presence of fast particles ahead of the shock, even for moderately low Mach numbers. We also examine the thermodynamics (Rankine-Hugoniot relations) of recent experiments [Phys. Rev. Lett. 111, 015002 (2013)] and find no anomalies in their equations of state.

Figure 1

Pressure ratio $p_1/p_0$ versus inverse compression $V_1/V_0$. (a) Fixed ${\kappa }_0=1$, with 12 values of ${\mathrm{\Gamma }}_0$, and varying the shock strength (points in groups, as shown by dashed oval). The solid curves are the theoretical predictions for ideal-gas behavior in 2D (blue) and 3D (green). This result shows that dimensionality plays a larger role than very large variations in coupling. (b) Same as (a), except for fixed ${\mathrm{\Gamma }}_0=1517$. Hugoniots strongly deviate from the 2D-ideal-gas curve as the screening is increased. Error bars, not shown, are smaller than the size of the markers.

Figure 2

(a),(b) Effect of dust-neutral collisions on the shock dynamics. Density profiles are shown in the reference frame of the shock with (red) and without (black) damping for ($\mathrm{\Gamma }=1517$, $\kappa =0.28$) and $M_p=0.5$ [left panel (a)] and $M_p=1.5$ [right panel (b)]. Note the appearance of a strong DSW in the absence of damping in the weak shock case. In panel (c) we see how the wavelength of the first density oscillation varies as a function of the piston Mach number for several plasma states.

Figure 3

Kinetic properties of plasmas in phase space. The one-particle distribution function $f_1(\zeta ,v_z)$ is seen in the reference frame of the shock (velocities are shifted by +$v_s$) for plasma parameters ${\mathrm{\Gamma }}_0=1517$ and ${\kappa }_0=0.5$, at piston Mach numbers (a) $M_p=0.5$, (b) $M_p=0.8$, and (c) $M_p=1$. (d),(e),(f) show the corresponding density profiles (black curve, left axis), normalized second moment ${\sigma }_z$ (red curve, right axis), and ${\sigma }_x$ (blue curve, right axis) of velocity distributions. Right arrows show the existence of a strong non-Maxwellian tail corresponding to velocities higher than the shock speed.

Figure 4

Deviation from the Maxwell velocity distribution. Plots show the relative density profile (value increased by a factor $10^3$; black curve, left axis), the $z$ component of the electric field $⟨E_z⟩$ (blue curve, left axis) and the fourth central moment ($\mathrm{\Delta }v=v-⟨v⟩$) of the local $v_z$-velocity distribution $⟨\mathrm{\Delta }{v}_z^4⟩$ divided by its theoretical Maxwellian value $3⟨\mathrm{\Delta }{v}_z^2{⟩}^2$ (red curve, right axis) for $M_p=0.5$ (a), 0.8 (b), 1 (c), and 2 (d), for plasma parameters $\mathrm{\Gamma }=1517$ and $\kappa =0.5$.