Time evolution of transient plasma states from nanowire arrays irradiated at relativistic intensities

Understanding the response of matter irradiated by high-power lasers at relativistic intensities is a key challenge in high-field physics, relevant to studies of extreme astrophysical objects, particle acceleration mechanisms, and exotic phenomena such as radiation reaction and vacuum polarization. Due to the complexity and ultrafast timescales of these interactions, much fundamental understanding has been driven by particle-in-cell (PIC) simulations. In contrast, there are few studies detailing time-resolved plasma dynamics of solid targets from ultrashort relativistic laser interactions, and the evolution at kilojoule-scale facilities has been largely unexplored experimentally. From an applications perspective, intense laser-matter interactions can create bright X-ray sources for high-energy-density physics and inertial confinement fusion research. These applications motivate the development and careful characterization of brighter, more uniform, and repeatable X-ray sources. Nanowire array targets were proposed for X-ray radiography because their geometry increases laser absorption and enables volumetric heating to reduce strong gradients present in flat targets. Nanowire arrays have demonstrated up to 50-fold increases in X-ray emission compared with flat foils, and improved coupling can yield energy densities of ~2 GJ cm−3 comparable to ICF implosions. Scaling to high-energy facilities is challenging due to stringent laser contrast requirements to avoid pre-damage of highly absorbent targets. Beyond bright sources, nanowire arrays are promising platforms for ultra-HED studies if their complex hydrodynamic evolution can be accurately diagnosed. Here the authors analyze time-resolved X-ray spectra from nanowires driven by relativistic laser intensities, providing insight into dynamics and evolution on picosecond timescales. Time- and spectrally-resolved emission constrains transient plasma conditions, and the observations agree with the interaction picture developed by prior computational studies.

The paper situates its study within several strands of prior work: (1) fundamental high-field and high-energy-density science using ultra-intense lasers, including applications to astrophysical phenomena and strong-field QED effects; (2) extensive reliance on PIC simulations to model ultrafast, complex laser-plasma interactions, with relatively few experimental, time-resolved measurements on solid targets; (3) development of bright short-pulse X-ray sources for HED and ICF diagnostics, emphasizing the need for careful characterization; (4) nanostructured targets (e.g., sub-wavelength gratings, nanolayers, and nanowire arrays) shown to enhance absorption and volumetric heating, leading to stronger, more uniform X-ray emission; (5) reports of up to 50× X-ray enhancements from nanowire arrays, and scaling considerations including stringent laser contrast to prevent pre-pulse damage at high-energy facilities; and (6) recent computational/theoretical insights into nanowire dynamics, including return-current heating, magnetic field generation, Z-pinch effects, and wire recollision dynamics, which motivate experimental validation at kilojoule-scale, relativistic intensities.

Experimental platform: The campaign used the high-contrast Orion petawatt laser (AWE, UK). Arrays of Ni nanowires were irradiated with a frequency-doubled Nd:glass short-pulse laser at 532 nm (100 J, 600 fs, ~10 µm FWHM focal spot), achieving intensities ~1×10^20 W cm−2 (a0 ≈ 6). Laser contrast of ~10^18 at 100 ps was maintained to prevent pre-damage to the nanowires. Targets were Ni nanowire arrays with ~15% fill fraction; wires were 12.5 µm long with diameters of 400 nm or 1000 nm. The laser incidence was 25° from target normal. Time-resolved X-ray spectra were recorded from the target front at 55° off-normal using a curved Ge crystal spectrometer coupled to an ultrafast X-ray streak camera, forming an ultrafast X-ray streaked spectrometer (XRSS). Diagnostics: The XRSS time resolution was ~1 ps, with spectral resolving power E/ΔE ~ 500 over 7.4–8.4 keV. The range captures cold Kα as well as Heα and Lyα emission from highly ionized Ni, including Li-like satellites. Time-resolved satellite emission compared to collisional-radiative modeling constrains the ionization balance and thus temperature and density. Spectral modeling and inversion: Collisional-radiative simulations were performed with FLYCHK, which uses a screened hydrogenic model with relativistic corrections and includes detailed term levels for Li-like satellites up to n=4 derived from HULLAC. Emission from H-, He-, and Li-like ions benefits from accurate line positions important for high charge states. Because the plasma contains a range of conditions, measured spectra were modeled as linear combinations of steady-state emission profiles across a temperature-density grid. A 10×10 grid spanned T = 0–4 keV (10 points) and ρ = 0.1–10 g cm−3 (10 points, exponentially sampled). These limits reflect expected plasma conditions from PIC and radiation-hydrodynamic simulations while ensuring observable emission in the diagnostic energy window. To avoid over-parameterization, a subset of grid points was chosen as free parameters and the remaining spectral weights were interpolated (log-interpolation for density). The fitted weights were obtained by minimizing a weighted least-squares cost function using combined absolute and relative noise estimates from the XRSS. The subset selection was sampled over all possible subsets; for each time step, ensemble fits were averaged, and uncertainty was estimated from the spread of fitted weights. In practice, five points in both temperature and density (retaining endpoints) were used to construct a valid interpolant. Temporal analysis: The plasma distribution was reconstructed at 500 fs steps, though instrumental broadening limits temporal resolution to ~1 ps. The centroid of the ensemble-averaged emitting plasma distribution in the T–ρ plane was tracked over time, with ellipses indicating half the standard deviation in T and ρ at each step. Emission phases were identified by characteristic spectral/temporal signatures. Notes on modeling fidelity: Discrepancies at late times include sharper features in data than in fits, attributed to (a) low-signal Poisson-like noise below XRSS energy resolution, (b) parameter-number-limited resolution of the reconstructed T–ρ profile (a narrower distribution may be present), and/or (c) significant populations of high-lying satellite states not included in FLYCHK.

• Nanowire arrays exhibit brighter and longer-lasting X-ray emission than flat foils. The enhancement is strongest for high-lying charge states, with a ~2× increase in He-like emission brightness and ~3× increase in time-integrated emission across 7.4–8.4 keV.
• Time-resolved spectral fitting (FLYCHK-based) yields the full plasma T–ρ evolution on picosecond scales, consistent with prior computational pictures of nanowire dynamics at relativistic intensities.
• Identified dynamical phases (I–VI): (I) ultrafast initial heating to keV temperatures; (II) plasma mirror formation and reflection with hot-electron energy redistribution; (III) heating of dense wire cores by megaampere-scale return currents and Z-pinch compression; (IV) nanowire explosion and recollision, producing secondary heating; (V) high-temperature inertial confinement and stagnation of a large near-uniform plasma volume; (VI) expansion and cooling to the XRSS noise floor.
• The emitting plasma density plateaus near ~1 g cm−3 (~11% of solid Ni), commensurate with the initial ~15% nanowire fill fraction, and the distribution narrows in density as the system homogenizes.
• Time-resolved ion population analysis reveals a late-time increase in highly charged ions (e.g., Ni28+) for nanowire targets due to collisional heating during wire recollision, not evident in raw spectrally integrated emission.
• Flat foil targets demonstrate simpler dynamics dominated by phases I, II, and VI, with rapid attainment of peak ionization followed by fast cooling and expansion, lacking the prolonged high-temperature stagnation seen in nanowire arrays.
• 1000 nm nanowire arrays display features of both bulk and nanowire interactions, including early- and late-time heating; irregular wire spacing yields multiple ionization peaks and bimodal T–ρ distributions that are challenging to represent with the chosen generalized functional form.
• Overall, nanowire arrays produce a larger volume of slightly lower-temperature plasma than foils, sustained at high temperature and near-solid density for longer durations, enhancing utility as bright short-pulse X-ray sources and ultra-HED platforms.

Time-resolved XRSS spectra, analyzed via a generalized linear combination of FLYCHK emission profiles, enable reconstruction of the complete T–ρ evolution of transient, near-solid-density plasmas from a single shot. This experimental benchmark is critical for validating PIC and radiation-hydrodynamic models that must make approximations across wide spatio-temporal scales. The observed sequence of phases, including return-current/Z-pinch heating and nanowire recollision, corroborates prior computational predictions for nanostructured targets at relativistic intensities. The volumetric absorption in nanowire arrays creates a large emitting volume with sustained high temperature and near-solid density, bridging regimes traditionally associated with PIC and rad-hydro simulations. The method also yields time-resolved ion populations, including non-observable states (e.g., fully stripped Ni28+), providing additional constraints on collisional heating dynamics. Comparisons with flat foils highlight the advantages of nanowire geometries in achieving prolonged high-energy-density conditions and brighter emission, while 1000 nm arrays reveal sensitivity to array regularity and spacing. These results underscore the need to understand and optimize nanostructure-driven dynamics for source development and HED experiments, and they demonstrate that spectral inversion with appropriate regularization/interpolation can extract meaningful plasma evolution despite diagnostic limitations.

The study presents a robust method to determine the time-dependent temperature and density distributions of rapidly evolving, high-energy-density plasmas using time-resolved XRSS and collisional-radiative modeling. Applied to petawatt-driven Ni nanowire arrays, the approach reconstructs a complete picosecond-scale evolution consistent with prior simulations, revealing characteristic stages of heating, return-current/Z-pinch compression, wire recollision, inertial stagnation, and expansion. Nanowire arrays deliver brighter, longer-duration X-ray emission and sustained near-solid-density, high-temperature conditions relative to flat foils, supporting their use as bright short-pulse probes and platforms for ultra-HED studies. Future work includes optimizing nanostructure design (e.g., regular wire spacing, fill fraction, diameter, and length) and enhancing analysis techniques (e.g., improved spectral resolution, absolute calibration, expanded atomic models) to further refine plasma reconstructions and maximize source performance.

• Diagnostic limitations: time resolution limited to ~1 ps by XRSS streak camera broadening; low-signal Poisson-like noise can introduce sub-resolution spectral features; finite energy resolution (E/ΔE ~ 500) restricts spectral detail.
• Inversion/model limitations: parameter-number-limited resolution of the generalized T–ρ distribution; potential under-representation of narrow distributions or conditions beyond the 10×10 grid; FLYCHK model omissions (e.g., significant high-lying satellite state populations) may cause late-time discrepancies; zero-dimensional modeling with slab spectral assumptions; lack of absolute calibration implies ion populations are relative.
• Temporal ambiguity during the laser pulse: earliest dynamics (e.g., plasma mirror formation, void closure ~100 fs–1 ps) are not temporally resolved and are broadened in the reconstruction.
• Target variability: irregular wire spacing (not perfectly periodic arrays) leads to bimodal or multi-peaked distributions that are not fully captured by centroid tracking.