Thermal conductivity measurements of proton-heated warm dense aluminum

A Platform for Ultra-Fast Proton Probing of Matter in Extreme Conditions

Recent developments in ultrashort and intense laser systems have enabled the generation of short and brilliant proton sources, which are valuable for studying plasmas under extreme conditions in high-energy-density physics. However, developing sensors for the energy selection, focusing, transport, and detection of these sources remains challenging. This work presents a novel and simple design for an isochronous magnetic selector capable of angular and energy selection of proton sources, significantly reducing temporal spread compared to the current state of the art. The isochronous selector separates the beam based on ion energy, making it a potential component in new energy spectrum sensors for ions. Analytical estimations and Monte Carlo simulations validate the proposed configuration. Due to its low temporal spread, this selector is also useful for studying extreme states of matter, such as proton stopping power in warm dense matter, where short plasma stagnation time (<100 ps) is a critical factor. The proposed selector can also be employed at higher proton energies, achieving final time spreads of a few picoseconds. This has important implications for sensing technologies in the study of coherent energy deposition in biology and medical physics.

Dynamic and transient processes in warm dense matter

In this paper, we discuss some of the key challenges in the study of time-dependent processes and non-equilibrium behaviour in warm dense matter. We outline some of the basic physics concepts that have underpinned the definition of warm dense matter as a subject area in its own right and then cover, in a selective, non-comprehensive manner, some of the current challenges, pointing along the way to topics covered by the papers presented in this volume. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Developing a platform for Fresnel diffractive radiography with 1 μm spatial resolution at the National Ignition Facility

An x-ray Fresnel diffractive radiography platform was designed for use at the National Ignition Facility. It will enable measurements of micron-scale changes in the density gradients across an interface between isochorically heated warm dense matter materials, the evolution of which is driven primarily through thermal conductivity and mutual diffusion. We use 4.75 keV Ti K-shell x-ray emission to heat a 1000 μm diameter plastic cylinder, with a central 30 μm diameter channel filled with liquid D₂, up to 8 eV. This leads to a cylindrical implosion of the liquid D₂ column, compressing it to ∼2.3 g/cm³. After pressure equilibration, the location of the D₂/plastic interface remains steady for several nanoseconds, which enables us to track density gradient changes across the material interface with high precision. For radiography, we use Cu He-α x rays at 8.3 keV. Using a slit aperture of only 1 μm width increases the spatial coherence of the source, giving rise to significant diffraction features in the radiography signal, in addition to the refraction enhancement, which further increases its sensitivity to density scale length changes at the D₂/plastic interface.

Temperature evolution of dense gold and diamond heated by energetic laser-driven aluminum ions

Recent studies have shown that energetic laser-driven ions with some energy spread can heat small solid-density samples uniformly. The balance among the energy losses of the ions with different kinetic energies results in uniform heating. Although heating with an energetic laser-driven ion beam is completed within a nanosecond and is often considered sufficiently fast, it is not instantaneous. Here we present a theoretical study of the temporal evolution of the temperature of solid-density gold and diamond samples heated by a quasimonoenergetic aluminum ion beam. We calculate the temporal evolution of the predicted temperatures of the samples using the available stopping power data and the SESAME equation-of-state tables. We find that the temperature distribution is initially very uniform, which becomes less uniform during the heating process. Then, the temperature uniformity gradually improves, and a good temperature uniformity is obtained toward the end of the heating process.

Learning transport processes with machine intelligence

Transport processes ruled by complex micro-physics and impractical to theoretical investigation may exhibit emergent behavior describable by mathematical expressions. Such information, while implicitly contained in the results of microscopic-scale numerical simulations close to first principles or experiments is not in a form suitable for macroscopic modelling. Here we present a machine learning approach that leverages such information to deploy micro-physics informed transport flux representations applicable to a continuum mechanics description. One issue with deep neural networks, arguably providing the most generic of such representations, is their noisiness which is shown to break the performance of numerical schemes. The matter is addressed and a methodology suitable for schemes characterised by second order convergence rate is presented. The capability of the methodology is demonstrated through an idealized study of the long standing problem of heat flux suppression relevant to fusion and cosmic plasmas. Symbolic representations, although potentially less generic, are straightforward to use in numerical schemes and theoretical analysis, and can be even more accurate as shown by the application to the same problem of an advanced symbolic regression tool. These results are a promising initial step to filling the gap between micro and macro in this important area of modeling.

Proton stopping measurements at low velocity in warm dense carbon

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

Charged particle interaction and energy dissipation in plasma is fundamentally interesting. Here the authors study proton stopping in laser-produced plasma for the moderate to strong coupling with electrons.

Transport of an intense proton beam from a cone-structured target through plastic foam with unique proton source modeling

Laser-accelerated proton beams are applicable to several research areas within high-energy density science, including warm dense matter generation, proton radiography, and inertial confinement fusion, which all involve transport of the beam through matter. We report on experimental measurements of intense proton beam transport through plastic foam blocks. The intense proton beam was accelerated by the 10ps, 700J OMEGA EP laser irradiating a curved foil target, and focused by an attached hollow cone. The protons then entered the foam block of density 0.38g/cm^{3} and thickness 0.55 or 1.00mm. At the rear of the foam block, a Cu layer revealed the cross section of the intense beam via proton- and hot electron-induced Cu-K_{α} emission. Images of x-ray emission show a bright spot on the rear Cu film indicative of a forward-directed beam without major breakup. 2D fluid-PIC simulations of the transport were conducted using a unique multi-injection source model incorporating energy-dependent beam divergence. Along with postprocessed calculations of the Cu-K_{α} emission profile, simulations showed that protons retain their ballistic transport through the foam and are able to heat the foam up to several keV in temperature. The total experimental emission profile for the 1.0mm foam agrees qualitatively with the simulated profile, suggesting that the protons indeed retain their beamlike qualities.

Isochoric heating of solid-density plasmas beyond keV temperature by fast thermal diffusion with relativistic picosecond laser light

The interaction of relativistic short-pulse lasers with matter produces fast electrons with over megaampere currents, which supposedly heats a solid target isochorically and forms a hot dense plasma. In a picosecond timescale, however, thermal diffusion from hot preformed plasma turns out to be the dominant process of isochoric heating. We describe a heating process, fast thermal diffusion, launched from the preformed plasma heated resistively by the fast electron current. We demonstrate the fast thermal diffusion in the keV range in a solid density plasma by a series of one-dimensional particle-in-cell simulations. A theoretical model of the fast thermal diffusion is developed and we derive the diffusion speed as a function of the laser amplitude and target density. Under continuous laser irradiation, the diffusion front propagates at a constant speed in uniform plasma. Our model can provide a guideline for fast isochoric heating using future kilojoule petawatt lasers.

Toward an integrated platform for characterizing laser-driven, isochorically heated plasmas with 1 µm spatial resolution

Warm dense matter is a region of phase space that is of high interest to multiple scientific communities ranging from astrophysics to inertial confinement fusion. Further understanding of the conditions and properties of this complex state of matter necessitates experimental benchmarking of the current theoretical models. We discuss the development of an x-ray radiography platform designed to measure warm dense matter transport properties at large laser facilities such as the OMEGA Laser Facility. Our platform, Fresnel diffractive radiography, allows for high spatial resolution imaging of isochorically heated targets, resulting in notable diffractive effects at sharp density gradients that are influenced by transport properties such as thermal conductivity. We discuss initial results, highlighting the capabilities of the platform in measuring diffractive features with micrometer-level spatial resolution.

Femtosecond Resolution of the Nonballistic Electron Energy Transport in Warm Dense Copper

The ultrafast electron energy transport is investigated in laser-heated warm dense copper in a high flux regime (2.5±0.7×10^{13}  W/cm^{2} absorbed). The dynamics of the electron temperature is retrieved from femtosecond time-resolved x-ray absorption near-edge spectroscopy near the Cu L3 edge. A characteristic time of ∼1  ps is observed for the increase in the average temperature in a 100 nm thick sample. Data are well reproduced by two-temperature hydrodynamic simulations, which support energy transport dominated by thermal conduction rather than ballistic electrons.

Model of electron transport in dense plasmas spanning temperature regimes

We present a new model of electron transport in warm and hot dense plasmas which combines the quantum Landau-Fokker-Planck equation with the concept of mean-force scattering. We obtain electrical and thermal conductivities across several orders of magnitude in temperature, from warm dense matter conditions to hot, nondegenerate plasma conditions, including the challenging crossover regime between the two. The small-angle approximation characteristic of Fokker-Planck collision theories is mitigated to good effect by the construction of accurate effective Coulomb logarithms based on mean-force scattering, which allows the theory to remain accurate even at low temperatures, as compared with high-fidelity quantum simulation results. Electron-electron collisions are treated on equal footing as electron-ion collisions. Their accurate treatment is found to be essential for hydrogen, and is expected to be important to other low-Z elements. We find that electron-electron scattering remains influential to the value of the thermal conductivity down to temperatures somewhat below the Fermi energy. The accuracy of the theory seems to falter only for the behavior of the thermal conductivity at very low temperatures due to a subtle interplay between the Pauli exclusion principle and the small-angle approximation as they pertain to electron-electron scattering. Even there, the model is in fair agreement with ab initio simulations.

Production of relativistic electrons at subrelativistic laser intensities

Relativistic electron temperatures were measured from kilojoule, subrelativistic laser-plasma interactions. Experiments show an order of magnitude higher temperatures than expected from a ponderomotive scaling, where temperatures of up to 2.2 MeV were generated using an intensity of 1×10^{18}W/cm^{2}. Two-dimensional particle-in-cell simulations suggest that electrons gain superponderomotive energies by stochastic acceleration as they sample a large area of rapidly changing laser phase. We demonstrate that such high temperatures are possible from subrelativistic intensities by using lasers with long pulse durations and large spatial scales.

Testing thermal conductivity models with equilibrium molecular dynamics simulations of the one-component plasma

Equilibrium molecular dynamics simulations are used to calculate the thermal conductivity of the one-component plasma via the Green-Kubo formalism over a broad range of Coulomb coupling strength, 0.1≤Γ≤180. These simulations address previous discrepancies between computations using equilibrium versus nonequilibrium methods. Analysis of heat flux autocorrelation functions show that very long (6×10^{5}ω_{p}^{-1}) time series are needed to reduce the noise level to allow ≲2% accuracy. The simulations provide accurate data for Γ≲1. This enables a test of the traditional Landau-Spitzer theory, which is found to agree with the simulations for Γ≲0.3. It also enables tests of theories to address moderate and strong Coulomb coupling. Two are found to provide accurate extensions to the moderate coupling regime of Γ≲10, but none are accurate in the Γ≳10 regime where potential energy transport and coupling between mass flow and stress dominate thermal conduction.

Heat-release equation of state and thermal conductivity of warm dense carbon by proton differential heating

Warm dense carbon is generated at 0.3-2.0 g/cc and 1-7 eV by proton heating. The release equation of state (EOS) after heating and thermal conductivity of warm dense carbon are studied experimentally in this regime using a Au/C dual-layer target to initiate a temperature gradient and two picosecond time-resolved diagnostics to probe the surface expansion and heat flow. Comparison between the data and simulations using various EOSs and thermal conductivity models is quantified with a statistical χ^{2} analysis. Out of seven EOS tables and five thermal conductivity models, only L9061 with the Lee-More model provides a probability above 50% to match all data.

Enhancing laser beam performance by interfering intense laser beamlets

Increasing the laser energy absorption into energetic particle beams represents a longstanding quest in intense laser-plasma physics. During the interaction with matter, part of the laser energy is converted into relativistic electron beams, which are the origin of secondary sources of energetic ions, γ-rays and neutrons. Here we experimentally demonstrate that using multiple coherent laser beamlets spatially and temporally overlapped, thus producing an interference pattern in the laser focus, significantly improves the laser energy conversion efficiency into hot electrons, compared to one beam with the same energy and nominal intensity as the four beamlets combined. Two-dimensional particle-in-cell simulations support the experimental results, suggesting that beamlet interference pattern induces a periodical shaping of the critical density, ultimately playing a key-role in enhancing the laser-to-electron energy conversion efficiency. This method is rather insensitive to laser pulse contrast and duration, making this approach robust and suitable to many existing facilities.

Enhanced coupling of laser energy to the target particles is a fundamental issue in laser-plasma interactions. Here the authors demonstrate increased photon absorption leading into higher laser to electron and proton energy transfer through the interference of multiple coherent beamlets.

Monochromatic 2D Kα Emission Images Revealing Short-Pulse Laser Isochoric Heating Mechanism

The rapid heating of a thin titanium foil by a high intensity, subpicosecond laser is studied by using a 2D narrow-band x-ray imaging and x-ray spectroscopy. A novel monochromatic imaging diagnostic tuned to 4.51 keV Ti Kα was used to successfully visualize a significantly ionized area (⟨Z⟩>17±1) of the solid density plasma to be within a ∼35  μm diameter spot in the transverse direction and 2  μm in depth. The measurements and a 2D collisional particle-in-cell simulation reveal that, in the fast isochoric heating of solid foil by an intense laser light, such a high ionization state in solid titanium is achieved by thermal diffusion from the hot preplasma in a few picoseconds after the pulse ends. The shift of Kα and formation of a missing Kα cannot be explained with the present atomic physics model. The measured Kα image is reproduced only when a phenomenological model for the Kα shift with a threshold ionization of ⟨Z⟩=17 is included. This work reveals how the ionization state and electron temperature of the isochorically heated nonequilibrium plasma are independently increased.

Experimental observation of the stratified electrothermal instability on aluminum with thickness greater than a skin depth

A direct observation of the stratified electrothermal instability on the surface of thick metal is reported. Aluminum rods coated with 70μm Parylene-N were driven to 1 MA in 100ns, with the metal thicker than the skin depth. The dielectric coating suppressed plasma formation, enabling persistent observation of discrete azimuthally correlated stratified thermal perturbations perpendicular to the current whose wave numbers, k, grew exponentially with rate γ(k)=0.06ns^{-1}-(0.4ns^{-1}μm^{2}rad^{-2})k^{2} in ∼1g/cm^{3}, ∼7000K aluminum.