Deciphering the kinetic structure of multi-ion plasma shocks

Strong collisional shocks in multi-ion plasmas are featured in many high-energy-density environments, including inertial confinement fusion implosions. However, their basic structure and its dependence on key parameters (e.g., the Mach number and the plasma ion composition) are poorly understood, and inconsistencies in that regard remain in the literature. In particular, the shock width's dependence on the Mach number has been hotly debated for decades. Using a high-fidelity Vlasov-Fokker-Planck code, iFP, and direct comparisons to multi-ion hydrodynamic simulations and semianalytic predictions, we resolve the structure of steady-state planar shocks in D-${}^3\mathrm{He}$ plasmas. Additionally, we derive and confirm with kinetic simulations a quantitative description of the dependence of the shock width on the Mach number and initial ion concentration.

Figure 1

Electron and ion temperature profiles for an $M=1.5$ shock.

Figure 2

Change in deuterium concentration, $c-c_0$, for an $M=1.5$ shock.

Figure 3

Normalized temperature profiles for a hydro plasma shock with $M\gg 1$. $T_0$ is the upstream temperature.

Figure 4

Temperature profiles for an $M=5$ shock.

Figure 5

Deuterium enrichment for an $M=5$ shock.

Figure 6

Knudsen numbers for electrons, deuterons, and helium ions in an $M=5$ planar shock in a $50:50\%$ D-${}^3\mathrm{He}$ plasma mixture. The $x$ axis is normalized to the total deuteron mean free path.

Figure 7

Semianalytic multi-ion hydro shock width (for $M=5$) vs $c_0$. Included are results from full multi-ion hydro simulations.

Figure 8

The ion shock width vs Mach number for $M=5$ and $c_0=0.40$.

Figure 9

$S_W^{\text{iFP}}-S_W^{\text{hydro}}$ normalized to the length of the electron preheat layer vs $c_0$ with two proposed theoretical models.