Measurements of Laser-Driven Plasma Expansion into Hohlraum-Relevant Background Gas

Technical Summary: Measurements of Laser-Driven Plasma Expansion into Hohlraum-Relevant Background Gas

Problem Statement
In indirect-drive inertial confinement fusion (ICF), high-power lasers irradiate the interior of a high-Z hohlraum to generate x-rays for capsule implosion. This process creates high-temperature plasmas that expand from the hohlraum walls into a low-Z gas fill (typically helium). These expanding plasma bubbles influence laser propagation, energy deposition, and x-ray conversion efficiency. While the macroscopic dynamics of this expansion are critical, the detailed physics governing the structure of the compressed gas layer, the role of self-generated magnetic fields, and the impact of filamentary instabilities remain incompletely understood. Previous experimental platforms have struggled to isolate the expansion of a single plasma bubble into a hohlraum-relevant gas fill due to geometric complexity. Furthermore, existing magnetohydrodynamic (MHD) and radiation-hydrodynamics codes (such as Gorgon and HYDRA) often fail to fully reproduce the temporal expansion rates or the fine-scale structures observed in hohlraum-relevant plasmas.

Methodology
The authors designed and executed experiments at the OMEGA EP laser facility to create a surrogate platform for studying hohlraum wall blow-off. The experimental setup involved:

• Target Configuration: 2–5 µm thick copper (Cu) foils supported by aluminum backings, positioned at the exit of a bent gas jet nozzle.
• Gas Conditions: A background helium gas fill was generated with densities of 0.3 mg/cc and 0.6 mg/cc, corresponding to nominal backing pressures of 350 psi and 700 psi, respectively.
• Drive: Frequency-tripled (351 nm) drive beams delivered approximately 4200–4300 J in a 4 ns pulse, creating a spot diameter of ~750 µm with peak intensities of ~2.5 × 10¹⁴ W/cm².
• Diagnostics:
  • Shadowgraphy: A frequency-quadrupled (263 nm) probe beam was used to visualize steep density gradients and shock boundaries.
  • Wollaston Interferometry: Used for relative density measurements, though quantitative phase retrieval was limited at later times due to perturbations in the reference leg.
  • Proton Radiography: Dual-axis proton radiography (using protons up to 30 MeV generated via TNSA) provided sensitivity to path-integrated electromagnetic fields and density modulations.
• Simulations: The experimental data were compared against simulations performed using the HYDRA (quasi-2D cartesian) and Gorgon (2D cylindrical) radiation-hydrodynamics codes. These simulations included various physics models, such as flux-limited diffusion, Biermann battery magnetic field generation, and Nernst advection.

Key Results

• Plasma Morphology: Shadowgraphy revealed well-defined density features and filamentary structures as the Cu plasma expanded into the He gas. In the 0.6 mg/cc case, three distinct expansion features were resolved: an outer shock propagating into the background gas, a turbulent intermediate region (likely the Cu-He interface), and an inner compressed Cu front. Fine-scale filamentation with transverse scales of 10–100 µm was observed near the foil surface.
• Expansion Dynamics: The expansion positions were tracked from 1 to 4 ns. In the 0.3 mg/cc case, the outer shock expanded at an average velocity of 0.611 mm/ns between 1 and 2 ns. In the denser 0.6 mg/cc case, the expansion was slower (~0.514 mm/ns), consistent with increased inertia.
• Discrepancies with Simulation: Both HYDRA and Gorgon successfully reproduced the large-scale shape of the plasma bubble but systematically over-predicted the expansion rate. Between 1 and 3 ns, the codes predicted expansion velocities 20–50% faster than observed. Consequently, the simulated bubble sizes diverged significantly from experimental measurements at later times.
• Missing Physics: Neither code reproduced the observed 10–100 µm scale filamentation or the complex turbulent structures in the compressed helium layer. Proton radiography indicated the presence of electromagnetic structures (magnetic fields and electric fields) throughout the bubble volume, which the standard hydrodynamic models did not capture.
• Kinetic Estimates: Calculations of ion-ion slowing mean-free-paths and diffusion lengths suggested that simple kinetic ion diffusion or interpenetration could not account for the observed large-scale turbulent features, implying that other mechanisms (such as kinetic instabilities or magnetic field effects) are dominant.

Significance and Claims
The paper presents a new experimental platform that isolates laser-driven plasma expansion into hohlraum-relevant gas fills, providing a benchmark for simulation codes. The primary significance lies in the identification of specific deficiencies in current radiation-hydrodynamics models:

1. Expansion Rate: The consistent over-prediction of expansion rates suggests that current models may overestimate thermal transport or underestimate the inhibiting effects of self-generated magnetic fields (e.g., via the Biermann battery mechanism) on cross-field conduction.
2. Fine-Scale Structures: The absence of filamentation and turbulence in the simulations indicates a lack of kinetic physics (such as Weibel-like modes or anisotropic heat flux) and nonlocal transport effects in standard flux-limited diffusion models.
3. Model Validation: The dataset serves as a critical validation tool for extended-MHD and kinetic models, highlighting the need to incorporate magnetized thermal conduction, nonlocal transport, and instability growth mechanisms to accurately predict the behavior of gas-filled hohlraums.

The authors conclude that while the large-scale morphology is captured, the temporal evolution and fine-scale structure require additional physical constraints in simulations to ensure accurate, predictive modeling for future indirect-drive ICF experiments.