High-intensity laser-solid interactions have significant applications in various fields, including inertial confinement fusion, laser-driven ion acceleration, warm dense matter investigation, and secondary-source development. Numerical modeling, primarily using particle-in-cell (PIC) simulations, is essential for understanding these interactions. However, current PIC simulations often focus on ultrarelativistic laser intensities (a₀ > 1), while the subrelativistic regime (a₀ ≤ 1) presents unique challenges due to correlated and collisional plasma physics. This necessitates the development of standardized experimental testbeds to benchmark existing modeling capabilities and guide future improvements in simulation tools. The accurate prediction of laser-target interaction conditions and the ability to capture all relevant physical processes during the target's transition from solid to plasma state are key challenges in translational research areas such as radiation oncology. Existing simulation approaches for ultrarelativistic laser-solid interactions often involve pre-expansion modeling using either single-stage PIC simulations (for short leading edges) or staged approaches combining radiation-hydrodynamics and PIC simulations (for longer leading edges). The transition between relativistic and subrelativistic intensities (a₀ ≤ 1), however, requires further advancements in both hydrodynamics and PIC simulations to incorporate correlated and collisional effects adequately, highlighting the need for standardized benchmarks for both theoretical and experimental validation. This work introduces a novel testbed to experimentally benchmark PIC simulations of laser-solid interactions using a micron-sized cryogenic hydrogen-jet target. The choice of cryogenic hydrogen offers several advantages: low density, single-species composition, negligible Bremsstrahlung radiation (Z=1), and simple ionization dynamics. This simplicity enhances comparability with analytic calculations, facilitating a more robust validation of simulation results.

The literature extensively covers high-intensity laser-plasma interactions, with significant advancements in both experimental techniques and numerical simulations. Studies focusing on fast ignition in inertial confinement fusion highlight the complexities of energy transfer and hydrodynamic expansion. Research on laser-driven ion acceleration underscores the need for precise modeling of the interaction processes to optimize ion beam parameters. Investigations into warm dense matter utilize high-intensity lasers to create extreme conditions for studying material properties under pressure and temperature extremes. Existing PIC codes have been extensively used but often lack a robust experimental benchmark at subrelativistic intensities where collisional effects become more pronounced. The need for standardized experimental benchmarks and detailed comparisons between simulation and experimental results has been emphasized by several recent reviews, calling for more controlled and well-defined test cases to improve the predictive power of these simulations.

This study establishes a testbed using a laser-irradiated micron-sized cryogenic hydrogen jet. The experiment was performed at the Draco-150 TW laser. The pump laser energy was adjusted from 160 mJ down to 26.6 µJ, with pulse durations between 37 fs and 12.6 ps. A cryogenic hydrogen jet with a diameter of 4.4 µm (standard deviation 0.2 µm) served as the target. The interaction was investigated via time-resolved off-harmonic optical shadowgraphy using two copropagating backlighter pulses (515 nm and 258 nm). The shadow diameter was measured as a function of pump-probe delay. Hydrodynamics simulations (using FLASH) and ray-tracing simulations (using Zemax) were used to fit the experimental data, allowing the extraction of the bulk electron temperature evolution. This HD-RT fit involved varying the initial electron temperature (T_eo) and plasma diameter (D₀) in the hydrodynamics simulation and then comparing the resulting simulated shadow diameters with the experimental data using a χ² fitting procedure. Particle-in-cell (PIC) simulations (using PIConGPU), including relativistic binary collisions, were performed to model the laser-solid interaction. The PIC simulation uses a density profile that takes into account the experimentally determined target diameter and surface-density gradient. The simulations were compared with the experimental data and HD-RT fit results, focusing on the temporal evolution of the bulk electron temperature. The PIC simulations incorporated several critical elements such as relativistic binary collisions, and were systematically varied (surface scalelength, Coulomb logarithm, etc.) to investigate factors affecting the accuracy of the simulations.

The experimental results using two-color optical shadowgraphy showed that the shadow diameter increased with the pump-probe delay, eventually exhibiting volumetric transparency at longer delays. The hydrodynamics and ray-tracing simulations (HD-RT fit) yielded an initial bulk-electron temperature (T_eo) between 250 and 300 eV at 0 ps delay. The PIC simulations revealed a two-stage heating process: initially isochoric heating and subsequent thermalization of the bulk electrons, followed by adiabatic plasma expansion. The initial surface-density gradient of the target proved to be a decisive factor for achieving quantitative agreement between the PIC simulations and the experimental results at 1 ps post-interaction. Systematic scans of PIC simulations with varying initial surface-density scalelength (L₀) showed a strong dependence of the bulk electron temperature on L₀, ranging from 1087 eV (L₀ = 0 nm) to 353 eV (L₀ = 500 nm). This variation highlights the importance of precisely modeling the target's initial density profile in PIC simulations, especially regarding the transition between vacuum heating and resonance absorption. Additional simulations examining the impact of the Coulomb logarithm and the dimensionality of the simulation showed these factors had a much smaller effect on the bulk electron temperature (less than 20%). The comparison between the PIC simulation and the HD-RT fit revealed that the PIC simulation overestimated the bulk electron temperature at early times, but the trend of adiabatic cooling was consistent with experimental observations.

The results demonstrate the effectiveness of the proposed testbed for quantitatively benchmarking PIC simulations. The agreement between the experimental shadowgraphy data, the HD-RT fit, and the PIC simulations, particularly after the thermalization of the bulk electrons, validates the testbed’s ability to provide a reliable macroscopic observable (bulk electron temperature) for comparing experimental results with numerical simulations. The significant impact of the initial surface density gradient highlights the importance of accurately representing the target's initial state in PIC simulations. The observed dependence on surface-density scalelength confirms previous studies on the transition between vacuum heating and resonance absorption at subrelativistic intensities. This underlines the need for precise experimental characterization of target parameters and sophisticated models for the initial state in simulations. The observed discrepancies between the PIC simulation and experimental data at early times are attributed to non-thermal electron effects not fully captured by the HD-RT fit or even the PIC simulation. Future studies could focus on improving the models to better account for such non-thermal effects.

This work introduces a robust testbed for benchmarking PIC simulations of laser-solid interactions at subrelativistic intensities. The testbed, based on time-resolved optical shadowgraphy of laser-irradiated cryogenic hydrogen jets, allows for the accurate determination of the bulk electron temperature evolution. The showcase experiment on isochoric heating demonstrates the testbed's capabilities. Future work could extend this testbed to other materials and explore the transition to higher intensities, incorporating advanced diagnostics for investigating non-thermal effects. The insights gained from this study provide valuable guidance for improving the accuracy and predictive power of PIC simulations for laser-solid interactions.

The study focuses on a specific target material (cryogenic hydrogen) and laser parameters. The HD-RT fit relies on several assumptions, including homogenous initial bulk electron temperature and two-dimensional radial symmetry. While systematic scans of the PIC simulations were performed, there might be other factors influencing the results that were not fully explored. Future studies could investigate the effect of uncertainties in other experimental parameters and enhance the model to better capture the early-time dynamics. The use of two specific wavelengths for the shadowgraphy may also limit the ability to fully capture the entire range of plasma densities.