Probing atomic physics at ultrahigh pressure using laser-driven implosions

Abstract

Spectroscopic measurements of dense plasmas at billions of atmospheres provide tests to our fundamental understanding of how matter behaves at extreme conditions. Developing reliable atomic physics models at these conditions, benchmarked by experimental data, is crucial to an improved understanding of radiation transport in both stars and inertial fusion targets. However, detailed spectroscopic measurements at these conditions are rare, and traditional collisional-radiative equilibrium models, based on isolated-atom calculations and ad hoc continuum lowering models, have proved questionable at and beyond solid density. Here we report time-integrated and time-resolved x-ray spectroscopy measurements at several billion atmospheres using laser-driven implosions of Cu-doped targets. We use the imploding shell and its hot core at stagnation to probe the spectral changes of Cu-doped witness layer. These measurements indicate the necessity and viability of modeling dense plasmas with self-consistent methods like density-functional theory, which impact the accuracy of radiation transport simulations used to describe stellar evolution and the design of inertial fusion targets.

Fig. 1. Illustration of predicted spectroscopic differences for warm-/hot-dense plasmas by different atomic physics models.

a Schematic of a surrogate dense-plasma object consisting of a Cu-doped CH plasma layer for spectroscopy. b The predicted Kα emission signal from the doped Cu layer of mass density of ρ = 20 g cm⁻³ and kT = 200 eV, by three different models: VERITAS (blue solid), collision radiative equilibrium (CRE) models with continuum lowering of Stewart–Pyatt (green long dash) and Ecker–Kroll (black dash-dotted). c The predicted 1s—2p absorption feature from the doped Cu layer at mass density of ρ = 20 g cm⁻³ and temperature kT = 300 eV.

Fig. 2. Time-resolved x-ray spectroscopy experiment of warm-/hot-dense plasmas at white-dwarf’s envelope conditions of Gbar pressures.

a Schematic targets for implosion spectroscopy on OMEGA. b Example of streaked spectra measured in experiments. c The pressure-density region probed by various HED experiments: GEKKO, OMEGA, Nova, NIF by Doeppner et al., NIF by Kritcher et al.^,, NIF by Fletcher et al., as well as non-Hugoniot work by Doeppner et al. on NIF. d The density-temperature conditions of a typical white dwarf of 0.6M_ʘ (0.6 solar mass) as it’s cooling down from hot and young state (right) to older and colder structures (left). Convective regions in the stars are shown in red. The regime probed by the experiments is shown by the green dashed circle. Inferred from DRACO simulations, the plasma temperature and density conditions of the imploding Cu-doped layer vary from kT ≈ 10‒50 eV and ρ ≈ 2‒10 g cm⁻³ (in-flight stage) to kT ≈ 200‒500 eV and ρ ≈ 10‒25 g cm⁻³ during the stagnation.

Fig. 3. Comparison of time-integrated K_α-emission and 1s-2p absorption signals between experiment and models.

a The DFT-based VERITAS calculations. b The experimental measurement. c The CRE model calculations with atomic database (ATBASE) in combination with Stewart–Pyatt and Ecker–Kroll continuum lowering models. d The CRE model calculations using flexible atomic physics (FAC) code calculation with the two continuum lowering models. The time integration in calculations has been done from t = 1.7 ns to t = 2.4 ns during the hot-spot flash, with snapshots for each 20-ps time interval.

Fig. 4. Comparison of time-resolved x-ray signals between experiment and models during the core flash.

a The streaked spectra predicted by traditional CRE model (Spect3D) with isolated atomic database plus continuum-lowering (Stewart–Pyatt). b The experimental measurement. c The streaked spectra predicted by VERITAS (a DFT-based kinetic model). d–f The spectral comparisons among the three cases at three distinct time line-outs: t = 1.95-ns, 2.05-ns, and t = 2.15-ns. The experimental error bar of ±40% is mainly from x-ray photon statistics of the streaked signal.

Fig. 5. The rad-hydro-predicted warm-/hot-dense plasma conditions during core flash of Cu-doped CH target implosions on OMEGA.

a The density (upper) and temperature (down) contour plots of dense plasma conditions at stagnation (t = 2.05 ns) from 2D DRACO radiation-hydrodynamic simulation. The inner and outer circles of dotted lines indicate the inner and outer boundary of the Cu-doped layer whose region is marked by the black arrow. b The time evolution of plasma ρ/T conditions as well as the population of Cu’s 2p state in the Cu-doping region (inferred by VERITAS) during the core flash, in which red symbols represent the situation at the inner interface and blue symbols are for the outer interface. The stagnation time (t = 2.05 ns) is marked by the vertical dashed line.