The study of structure, thermodynamic state, equation of state (EOS) and transport properties of warm dense matter (WDM) has become one of the key aspects of laboratory astrophysics. This field has demonstrated its importance not only concerning the internal structure of planets, but also other astrophysical bodies such as brown dwarfs, crusts of old stars or white dwarf stars. There has been a rapid increase in interest and activity in this field over the last two decades owing to many technological advances including not only the commissioning of high energy optical laser systems, z-pinches and X-ray free electron lasers, but also short-pulse laser facilities capable of generation of novel particle and X-ray sources. Many new diagnostic methods have been developed recently to study WDM in its full complexity. Even ultrafast nonequilibrium dynamics has been accessed for the first time thanks to subpicosecond laser pulses achieved at new facilities. Recent years saw a number of major discoveries with direct implications to astrophysics such as the formation of diamond at pressures relevant to interiors of frozen giant planets like Neptune, metallic hydrogen under conditions such as those found inside Jupiter’s dynamo or formation of lonsdaleite crystals under extreme pressures during asteroid impacts on celestial bodies. This paper provides a broad review of the most recent experimental work carried out in this field with a special focus on the methods used. All typical schemes used to produce WDM are discussed in detail. Most of the diagnostic techniques recently established to probe WDM are also described. This paper also provides an overview of the most prominent examples of these methods used in experiments. Even though the main emphasis of the publication is experimental work focused on laboratory astrophysics primarily at laser facilities, a brief outline of other methods such as dynamic compression with z-pinches and static compression using diamond anvil cells (DAC) is also included. Some relevant theoretical and computational efforts related to WDM and astrophysics are mentioned in this review.

The interaction of femtosecond laser with initially cold solid metallic targets (Al, Au, Cu, Mo, Ni) was investigated in a wide range of laser intensity with focus on the laser energy absorption efficiency. Our developed simulation code (FEMTO-2D) is based on two-temperature model in two-dimensional configuration, where the temperature-dependent optical and thermodynamic properties of the target material were considered. The role of the collisional processes in the ultrashort pulse laser–matter interaction has been carefully analyzed throughout the process of material transition from the cold solid state into the dense plasma state during the pulse. We have compared the simulation predictions of the laser pulse absorption with temperature-dependent reflectivity and optical penetration depth to the case of constant optical parameters. By considering the effect of the temporal and spatial (radial) distribution of the laser intensity on the light absorption efficiency, we obtained a good agreement between the simulated results and available experimental data. The appropriate model for temperature-dependent optical parameters defining the laser absorption efficiency will allow more accurate simulation of the target thermal response in the applications where it is critical, such as prediction of the material damage threshold, laser ablation threshold, and the ablation profile.

The stopping power of warm dense matter (WDM) is estimated by means of the individual contributions of free electrons and bound electrons existing in this special kind of matter, located between classical and degenerate plasmas. For free electrons, the dielectric formalism, well described in our studies, is used to estimate the free electron stopping power. For bound electrons, the mean excitation energy of ions is used. Excitation energies are obtained through atomic calculations of the whole atom or, shell by shell in order to estimate their stopping power. Influence of temperature and density is analyzed in case of an impinging projectile. This influence becomes important for low projectile velocities and is negligible for high ones. Using free and bound electron analysis, the stopping power of an extended WDM is inferred from a dynamical calculation of energy transferred from the projectile to the plasma, where the stopping range is calculated. Finally, this theoretical framework is used to study a typical plasma density profile of a WDM heated by lasers.

The heating of the titanium foil in a recent femtosecond laser plasma experiment is investigated theoretically in two different ways. In the first, the energy content and thus the heating efficiency of the central volume of the foil is derived by integrating the transverse temperature profiles obtained in this experiment, using specific heats based on the average atom model. In the second approach target heating by the fast electrons, both by direct energy deposition and by resistive heating is investigated. The latter approach makes use of a specially devised electron flow model which includes a simplified quantitative treatment of multi-refluxing as a crucial component. In all, the calculated results of electron beam heating are consistent with experiment within the limitations of the modeling. Finally, a prediction for the temporal dependence of the Kα pulse from the central volume of the foil based on our electron flow model is given.

To control an input energy for a load, an impedance control with a gap distance of an electron beam diode was studied using an intense pulsed-power generator. The output current of the pulsed-power generator as a function of the gap distance of electron beam diode was measured. It indicated that the behaviors of the experimentally obtained peak current and the theoretically obtained space-charge limited current were found to decrease with an increase in the gap distance. The input energy for the load was estimated from the output current, which decreased with an increase in the gap distance. It also revealed the space-charge limited current suppresses the input energy for the load with a decade.

The short review on the possible applications of the hollow ion spectra for the diagnostics of the high-temperature plasma created by intensive laser and particle beams is presented. Because of the hollow ion spectra features are defined mainly by the mechanisms of their excitation, we consider the various types of the high-temperature plasma where different excitation processes are important. It is shown that like ordinary spectral lines, spectra of the hollow ions offer considerable diagnostic opportunities. At the present time, hollow ion spectra are used mainly to investigate plasma heated by X-ray radiation, but the hollow ions must be generated when plasma is heated by fast heavy ion beams too. In this case, the resultant substance state will be also characterized by solid-state density, and some spatial regions of targets will have relatively low temperatures, i.e., will be a nonideal plasma. It is emphasized that hollow ion spectra are promising diagnostic tool for both nonideal plasma and warm dense matter.

This paper examines the reliability of a widely used method for temperature determination by multi-wavelength pyrometry. In recent warm dense matter experiments with ion-beam heated metal foils, we found that the statistical quality of the fit to the measured data is not necessarily a measure of the accuracy of the inferred temperature. We found a specific example where a second-best fit leads to a more realistic temperature value. The physics issue is the wavelength-dependent emissivity of the hot surface. We discuss improvements of the multi-frequency pyrometry technique, which will give a more reliable determination of the temperature from emission data.

This paper presents numerical simulations to study the heating of a solid target under a proton beam pulse interaction. The target is heated by the proton beam pulse with particle energy Eb, intensity N and focal radius rb of transverse Gaussian distribution, with a fixed pulse time 10 ps. The dynamics of target and beam ions are described by a classical hydrodynamic model and the target electrons are described by the quantum hydrodynamic model. Numerical simulations are carried out by employing the two dimensional flux-corrected transport methods. The target is heated to 0.5−5 eV, therefore, warm dense matter is created in the heated target region on a picosecond time scale.

In this work, we review current trends in China to investigate beam plasma interaction phenomena. Recent progresses in China on low energy heavy ions and plasma interaction, ion beam-plasma interactions under the influences of magnetic fields, high energy heavy ion radiography through marginal range method, energy deposition of highly charged ions on surfaces and Raman spectroscopy of surfaces after irradiation of highly charged ions are presented.

This paper presents numerical simulations to study the heating of a two-dimensional (2D) solid target under an ion cluster interaction. 2D quantum hydrodynamic (QHD) model is employed for the heating of solid target to warm dense matter on a picosecond time scale. A Gaussian cluster is used to uniformly heat the solid target to a temperature of several eV. The density and temperature of the target are calculated by a full self-consistent treatment of the QHD formalisms and the Poisson's equation. The technique described in this paper provides a method for creating uniformly heated strongly coupled plasma states.

Quantum molecular dynamic simulations have been employed to study the equation of state (EOS) of fluid helium under shock compressions. The principal Hugoniot is determined from EOS, where corrections from atomic ionization are added onto the calculated data. Our simulation results indicate that principal Hugoniot shows good agreement with gas gun and laser driven experiments, and maximum compression ratio of 5.16 is reached at 106 GPa.

We report on experiments aimed at the generation and characterization of solid density plasmas at the free-electron laser FLASH in Hamburg. Aluminum samples were irradiated with XUV pulses at 13.5 nm wavelength (92 eV photon energy). The pulses with duration of a few tens of femtoseconds and pulse energy up to 100 µJ are focused to intensities ranging between 1013 and 1017 W/cm2. We investigate the absorption and temporal evolution of the sample under irradiation by use of XUV and optical spectroscopy. We discuss the origin of saturable absorption, radiative decay, bremsstrahlung and atomic and ionic line emission. Our experimental results are in good agreement with simulations.

The aim of the present work is the further development of the thermodynamics of hydrogen-like plasmas with densities on the order of 1027–1029 m−3 at temperatures of 106−108 K. Therefore, the Jacobi-Padé approximation for the so-called relative energy level shifts is applied to a quasineutral plasma consisting of six-fold and five-fold ionized carbon atoms and electrons. The relative energy level shift of the five-fold ionized carbon is determined by the difference between Coulomb and Debye potential, and by the kinetic energy of the particles. The shift caused by the kinetic energy (KES) has to be found considering the momentum space of the particles, so that nine-fold integrals in phase space have to be calculated. Quantum-physically, former numerical calculations of KES were only performed for particle states with zero angular quantum numbers. In the present work, a detailed, to a large extent analytical analysis of the KES is given for any angular quantum number, enabling also an improved analysis of future further-developed Jacobi-Padé formulae. Relative energy shifts of the bound-states of the fivefold ionized carbon are numerically obtained as function of the Mott parameter of the plasma. Dependencies of the shifts on main quantum numbers and orbital quantum numbers are discussed.

We describe a funnel cone for concentrating an ion beam on a target. The cone utilizes the reflection characteristic of ion beams on solid walls to focus the incident beam and increase beam intensity on target. The cone has been modeled with the TRIM code. A prototype has been tested and installed for use in the 350-keV K+ NDCX target chamber.

The Large Hadron Collider (LHC) will operate with 7 TeV/c protons with a luminosity of 1034 cm−2 s−1. This requires two beams, each with 2808 bunches. The nominal intensity per bunch is 1.15 × 1011 protons and the total energy stored in each beam is 362 MJ. In previous papers, the mechanisms causing equipment damage in case of a failure of the machine protection system was discussed, assuming that the entire beam is deflected onto a copper target. Another failure scenario is the deflection of beam, or part of it, into carbon material. Carbon collimators and beam absorbers are installed in many locations around the LHC close to the beam, since carbon is the material that is most suitable to absorb the beam energy without being damaged. In case of a failure, it is very likely that such absorbers are hit first, for example, when the beam is accidentally deflected. Some type of failures needs to be anticipated, such as accidental firing of injection and extraction kicker magnets leading to a wrong deflection of a few bunches. Protection of LHC equipment relies on the capture of wrongly deflected bunches with beam absorbers that are positioned close to the beam. For maximum robustness, the absorbers jaws are made out of carbon materials. It has been demonstrated experimentally and theoretically that carbon survives the impact of a few bunches expected for such failures. However, beam absorbers are not designed for major failures in the protection system, such as the beam dump kicker deflecting the entire beam by a wrong angle. Since beam absorbers are closest to the beam, it is likely that they are hit first in any case of accidental beam loss. In the present paper we present numerical simulations using carbon as target material in order to estimate the damage caused to carbon absorbers in case of major beam impact.

Cylindrical cryogenic targets are required to carry out the Laboratory Planetary Science scheme of the experiments of the High Energy Density matter Generated by Heavy Ion Beams collaboration at FAIR. In this paper, for the first time a thorough analysis of the problem of such targets' fabrication, delivery and positioning in the center of the experimental chamber has been made. Particular attention is paid to the issue of a specialized cryogenic system creation intended for rep-rate supply of the High Energy Density matter Generated by Heavy Ion Beams experiments with the cylindrical cryogenic targets.

This paper describes a fast multi-channel radiation pyrometer that was developed for warm dense-matter experiments with intense heavy ion beams at the Gesellschaft für Schwerionenforschung mbH (GSI). The pyrometer is capable of measuring brightness temperatures from 2000 K to 50,000 K, at six wavelengths in the visible and near-infrared parts of the spectrum, with 5 ns temporal resolution, and several micrometers spatial resolution. The pyrometer's spectral discrimination technique is based on interference filters, which also act as mirrors to allow for simultaneous spectral discrimination of the same ray at multiple wavelengths.

Laser plasma interaction experiments have been performed using an fs Titanium Sapphire laser. Plasmas have been generated from planar PMMA targets using single laser pulses with 3.3 mJ pulse energy, 50 fs pulse duration at 800 nm wavelength. The electron density distributions of the plasmas in different delay times have been characterized by means of Nomarski Interferometry. Experimental data were compared with hydrodynamic simulation. First results to characterize the plasma density and temperature as a function of space and time are obtained. This work aims to generate plasmas in the warm dense matter (WDM) regime at near solid-density in an ultra-fast laser target interaction process. Plasmas under these conditions can serve as targets to develop X-ray Thomson scattering as a plasma diagnostic tool, e.g., using the Vacuum ultraviolet (VUV) free-electron laser (FLASH) at Dentsches Elektronen-Synchrotron (DESY) Hamburg.

Dense plasmas are produced using exploding wire discharges in water. Evolutions of radius, electrical conductivity, temperature of plasma and a shock wave in water accompanied with the explosion, are measured. Conductivities of aluminum, copper, and tungsten are compared with theoretical ones. To evaluate the equation of state, trajectories of the shock wave and the plasma boundary are compared with numerical calculations. Results show that the hydrodynamic behaviors are sensitive to the models of equation of state. Controllability of warm dense state in density-temperature diagram is discussed from the voltage-current characteristics of the wire discharges.

Recently, warm dense matter has emerged as an interdisciplinary field that draws increasing interest in plasma physics, condensed matter physics, high pressure science, astrophysics, inertial confinement fusion, as well as material science under extreme conditions. To allow the study of well-defined warm dense matter states, we introduced the concept of idealized slab plasma (ISP) that can be realized in the laboratory via (1) the isochoric heating of a solid and (2) the propagation of a shock wave in a solid. The application of this concept provides new means for probing AC conductivity, equation of state, ionization, and opacity. These approaches are presented here using results derived from numerical simulations.