Heating of thin foils with a relativistic-intensity short-pulse laser

Spatiotemporal dynamics of fast electron heating in solid-density matter via XFEL

High-intensity, short-pulse lasers are crucial for generating energetic electrons that produce high-energy-density (HED) states in matter, offering potential applications in igniting dense fusion fuels for fast ignition laser fusion. High-density targets heated by these electrons exhibit spatially non-uniform and highly transient conditions, which have been challenging to characterize due to limitations in diagnostics that provide simultaneous high spatial and temporal resolution. Here, we employ an X-ray Free Electron Laser (XFEL) to achieve spatiotemporally resolved measurements at sub-micron and femtosecond scales on a solid-density copper foil heated by laser-driven fast electrons. Our X-ray transmission imaging reveals the formation of a solid-density hot plasma localized to the laser spot size, surrounded by Fermi degenerate, warm dense matter within a picosecond, and the energy relaxation occurring within the hot plasma over tens of picoseconds. These results validate 2D particle-in-cell simulations incorporating atomic processes and provide insights into the energy transfer mechanisms beyond current simulation capabilities. This work significantly advances our understanding of rapid fast electron heating and energy relaxation in solid-density matter, serving as a key stepping stone towards efficient high-density plasma heating and furthering the fields of HED science and inertial fusion energy research using intense, short-pulse lasers.

Assessment of the electron-proton energy relaxation rates extracted from molecular dynamics simulations in weakly-coupled hydrogen plasmas

Electron-proton energy relaxation rates are assessed using molecular dynamics (MD) simulations in weakly-coupled hydrogen plasmas. To this end, we use various approaches to extract the energy relaxation rate from MD-simulated temperatures, and we find that existing extracting approaches may yield results with a sizable discrepancy larger than the variance between analytical models, which is further verified by well-known case studies. Present results show that two of the extracting approaches can produce identical results, which is attributed to a proper treatment of relaxation evolution. To discriminate the use of various methods, an empirical criterion with respect to initial plasma temperatures is proposed, which can self-consistently explain the cases considered. In addition, for a transient electron-proton plasma, we show that it is possible to extrapolate the Coulomb logarithm from that derived by initial plasma parameters in a single MD calculation, which is reasonably consistent with previous MD data. Our results are helpful to obtain accurate MD-based energy relaxation rates.

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.

X-ray Spectroscopies of High Energy Density Matter Created with X-ray Free Electron Lasers

The recent progress in the development of X-ray free electron lasers (XFELs) allows for the delivery of over 1011 high-energy photons to solid-density samples in a femtosecond time scale. The corresponding peak brightness of XFEL induces a nonlinear response of matter in a short-wavelength regime. The absorption of an XFEL pulse in a solid also results in the creation of high energy density (HED) matter. The electronic structure and related fundamental properties of such HED matter can be investigated with the control of XFEL and various X-ray spectroscopic techniques. These experimental data provide unique opportunities to benchmark theories and models for extreme conditions and to guide further advances. In this article, the current progress in spectroscopic studies on intense XFEL–matter interactions and HED matter are reviewed, and future research opportunities are discussed.

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.

Nuclear excitation by electron capture in optical-laser-generated plasmas

The process of nuclear excitation by electron capture in plasma environments generated by the interaction of ultrastrong optical lasers with solid-state samples is investigated theoretically. With the help of a plasma model, we perform a comprehensive study of the optimal parameters for the most efficient nuclear excitation and determine the corresponding laser setup requirements. We discern between the low-density plasma regime, modeled by scaling laws, and the high-density regime, for which we perform particle-in-cell calculations. As a nuclear transition case study we consider the 4.85-keV nuclear excitation starting from the long-lived ^{93m}Mo isomer. Our results show that the optimal plasma and laser parameters are sensitive to the chosen observable and that measurable rates of nuclear excitation and isomer depletion of ^{93m}Mo should be already achievable at laser facilities existing today.

Tailoring Laser-Generated Plasmas for Efficient Nuclear Excitation by Electron Capture

The optimal parameters for nuclear excitation by electron capture in plasma environments generated by the interaction of ultrastrong optical lasers with solid matter are investigated theoretically. As a case study we consider a 4.85 keV nuclear transition starting from the long-lived ^{93m}Mo isomer that can lead to the release of the stored 2.4 MeV excitation energy. We find that due to the complex plasma dynamics, the nuclear excitation rate and the actual number of excited nuclei do not reach their maximum at the same laser parameters. The nuclear excitation achievable with a high-power optical laser is up to twelve and up to six orders of magnitude larger than the values predicted for direct resonant and secondary plasma-mediated excitation at the x-ray free electron laser, respectively. Our results show that the experimental observation of the nuclear excitation of ^{93m}Mo and the subsequent release of stored energy should be possible at laser facilities available today.

Investigation of fast-electron-induced Kα x rays in laser-produced blow-off plasma

Refluxing of fast electrons generated by high-intensity, short-pulse lasers was investigated by measuring electron-induced Kα x rays from a buried tracer layer. Using planar foils of Au/Cu/CH, the 150-J, 0.7-ps TITAN short-pulse laser was focused on the gold foil to generate fast electrons and the 3-ns, 300-J long pulse beam irradiated on the CH side to create expanding plasma as a conducting medium. By delaying the short-pulse beam timing from the long pulse laser irradiation, the plasma size was varied to change electron refluxing in the target rear. The total yields and two-dimensional images of 8.05-keV Cu-Kα x ray were recorded with an x-ray spectrometer and two monochromatic crystal imagers. The measurements show that the integrated yields decrease by a factor of 10 from refluxing to the nonrefluxing limit. Similar radial profiles of the Kα images in the rear were observed at all delays. Hybrid-particle-in-cell simulations using plasma profiles calculated by a radiation-hydrodynamic code HYDRA agree well with the measured Kα yields. The simulations suggest that conducting plasma with the size of ∼300 μm in the laser direction and ∼600 μm in the lateral direction at the density of 2 × 1020 1/cm3 is sufficiently large to prevent electrons from refluxing in the target. The parameters found in this study can be useful in designing experiments utilizing a Kα x-ray source in refluxing regime or a tracer layer in nonrefluxing regime.

Simultaneous high-resolution two-dimensional spatial and one-dimensional picosecond streaked x-ray pinhole imaging

A Kentech x-ray streak camera was run at the LLNL compact multipulse terawatt (COMET) laser to record simultaneous space- and time-resolved measurements of picosecond laser-produced plasmas. Four different x-ray energy channels were monitored using broadband filters to record the time history of Cu targets heated at irradiances of 10(16)-10(19) W∕cm(2). Through the Cu filter channel, a time-resolution below 3 ps was obtained. Additionally, an array of 10 μm diameter pinholes was placed in front of the camera to produce multiple time-resolved x-ray images on the photocathode and time-integrated images on the phosphor with 10 and 15 times magnification, respectively, with spatial resolution of < 13 μm.

Time-resolved measurements of hot-electron equilibration dynamics in high-intensity laser interactions with thin-foil solid targets

Time-resolved K(α) spectroscopy has been used to infer the hot-electron equilibration dynamics in high-intensity laser interactions with picosecond pulses and thin-foil solid targets. The measured K(α)-emission pulse width increases from ~3 to 6 ps for laser intensities from ~10(18) to 10(19) W/cm(2). Collisional energy-transfer model calculations suggest that hot electrons with mean energies from ~0.8 to 2 MeV are contained inside the target. The inferred mean hot-electron energies are broadly consistent with ponderomotive scaling over the relevant intensity range.

Temperature and Kalpha-yield radial distributions in laser-produced solid-density plasmas imaged with ultrahigh-resolution x-ray spectroscopy

We study warm dense matter formed by subpicosecond laser irradiation at several 10(19) W/cm(2) of thin Ti foils using x-ray spectroscopy with high spectral (E/DeltaE approximately 15,000) and one-dimensional spatial (Deltax=13.5 microm) resolutions. Ti Kalpha doublets modeled by line-shape calculations are compared with Abel-inverted single-pulse experimental spectra and provide radial distributions of the bulk-electron temperature and the absolute-photon number Kalpha yield in the target interiors. A core with approximately 40 eV extends homogeneously up to ten times the laser-focus size. The spatial distributions of the bulk-electron temperature and Kalpha yield are strongly correlated.

Floquet-Liouville approach for calculating Stark profiles in plasmas in the presence of a strong oscillating field

The formalism for the calculation of Stark line profiles in hot dense plasmas submitted to a strong oscillating field is extensively developed. The Liouville space, usually used to deal with the calculation of Stark profiles in dense plasmas, and the Floquet theory, developed to solve time-periodic problems, have been joined together to solve the time-dependent Liouville equation in the so-called Floquet-Liouville formalism. The strong-oscillating-field spectroscopic signatures and their error estimations are discussed for hydrogen- and heliumlike aluminum lines.

Equation of state for partially ionized carbon at high temperatures

Equation of state for partially ionized carbon at temperatures T approximately > or = 10(5) K is calculated in a wide range of densities, using the method of free energy minimization in the framework of the chemical picture of plasmas. The free energy model includes the internal partition functions of bound species. The latter are calculated by a self-consistent treatment of each ionization stage in the plasma environment taking into account pressure ionization. The long-range Coulomb interactions between ions and screening of the ions by free electrons are included using our previously published analytical model.

Model for computing superconfiguration temperatures in nonlocal-thermodynamic-equilibrium hot plasmas

A model is presented where the level-population densities in quasi-steady-state hot dense plasmas are described by means of large nonrelativistic superconfigurations (SC's), whose configuration populations follow a decreasing-exponential law versus energy (Boltzmann like) for a temperature depending on the SC. Two systems of linear equations are obtained. The first one yields the average-state population densities of the SC's. Using these results, the second system yields the SC temperatures. In this model, a very large number of atomic levels is accounted for in a simple way, thus yielding the configuration populations and, hence, the ionic distribution and average charge. It also yields accurate simulations of the spectra, which are of the essence for emissivity and absorption calculations. It opens a way to time-dependent calculations.

Isochoric heating of solid-density matter with an ultrafast proton beam

A new technique is described for the isochoric heating (i.e., heating at constant volume) of matter to high energy-density plasma states (>10(5) J/g) on a picosecond time scale (10(-12)sec). An intense, collimated, ultrashort-pulse beam of protons--generated by a high-intensity laser pulse--is used to isochorically heat a solid density material to a temperature of several eV. The duration of heating is shorter than the time scale for significant hydrodynamic expansion to occur; hence the material is heated to a solid density warm dense plasma state. Using spherically shaped laser targets, a focused proton beam is produced and used to heat a smaller volume to over 20 eV. The technique described of ultrafast proton heating provides a unique method for creating isochorically heated high-energy density plasma states.