Energy Flow in Thin Shell Implosions and Explosions

Energy flow and balance in convergent systems beyond petapascal energy densities controls the fate of late-stage stars and the potential for controlling thermonuclear inertial fusion ignition. Time-resolved x-ray self-emission imaging combined with a Bayesian inference analysis is used to describe the energy flow and the potential information stored in the rebounding spherical shock at 0.22 PPa (2.2 Gbar or billions of atmospheres pressure). This analysis, together with a simple mechanical model, describes the trajectory of the shell and the time history of the pressure at the fuel-shell interface, ablation pressure, and energy partitioning including kinetic energy of the shell and internal energy of the fuel. The techniques used here provide a fully self-consistent uncertainty analysis of integrated implosion data, a thermodynamic-path independent measurement of pressure in the petapascal range, and can be used to deduce the energy flow in a wide variety of implosion systems to petapascal energy densities.

Figure 1

(a) Schematic of the experimental setup, showing a $3\text{−}\mu \mathrm{m}$ ${\mathrm{SiO}}_2$ shell filled with 18.9 atm of ${\mathrm{D}}_2$ gas. Symmetric laser illumination drives a shock wave (dashed gold curve) through the shell into the gas and the shell continues to converge. The shock wave reaches the center of the target and then returns moving outward and eventually interacts with the shell a second time. (b) The time history of the laser drive and measurements along with the time that the shock reaches the center of the target given by the nuclear bang time (vertical green line), a measurement of thermonuclear fusion products due to the extreme temperatures and densities created by the converging shock wave. When the rebounding shock wave interacts with the shell, the conditions generate the x rays (e) measured in the roughly 30-ps snapshots. (d) The peak of the radially averaged lineouts corresponds to the ring of emission in the (c) individual snapshot and the red data points shown in (b).

Figure 2

The inferred (a) shell trajectory, (b) pressure at fuel shell interface, and (c) ablation pressure resulting from Bayesian parameter estimation based on the experimentally measured data. Color bar shows highest posterior density intervals for each quantity with the 68.3% credible interval given by the dashed line in each.

Figure 3

(a) 68.3% credible intervals for the different energy components within the model. The energy components include shell kinetic energy (dark blue shading), total fuel energy (red shading), shell kinetic energy that does not to work on the fuel (gold shading), and ablated kinetic energy (green shading). Also shown is the total mechanical energy in the model (gray shading), the laser energy deposited (light blue shading), and the difference (magenta shading) being a measure of nonmechanical energy in the system including internal energy of the corona and shell, radiation losses, and uncoupled laser energy. The mechanical energy of the system accounts for approximately half of the total incident laser energy, but of that only about 10% contributes to doing work on the fuel. (b) Mass credible intervals from the model including the shell mass (dark blue shading), ablated mass (green shading), the released mass (gold shading), and the fuel mass (red shading) as a function of time.

Figure 4

A temperature-density diagram showing four isobars (black curves), predicted states found in the solar interior as a function of solar radius (orange color scale) and the states found in the fuel during the experiment presented here assuming an ideal equation of state. The gray shaded region is where most HED experimental measurements are historically made, generally below 50 Mbar.