Measurements of opacity and temperature of warm dense matter heated by focused soft X-ray laser irradiation

The transmission of plasma-based soft X-ray lasers through thin targets can be used to measure the target opacity. Measurements of warm dense matter transmission obtained using a focused 59 eV photon energy laser irradiation on thin targets of polyimide (C₂₂H₁₀N₂O₅) and aluminum are shown to produce simultaneous heating and probing enabling opacity and temperature measurements of warm dense matter. It is shown that the opacity of the warm dense matter considered in the experiments follows closely tabulated cold ‘room temperature’ opacities at temperatures below ～10 eV. Transmission measurements of thin iron targets which are highly opaque to the X-ray laser radiation are also presented.     

Measurement and simulations of hollow atom X-ray spectra of solid-density relativistic plasma created by high-contrast PW optical laser pulses

K-shell spectra of solid Al excited by petawatt picosecond laser pulses have been investigated at the Vulcan PW facility. Laser pulses of ultrahigh contrast with an energy of 160 J on the target allow studies of interactions between the laser field and solid state matter at 10²⁰ W/cm². Intense X-ray emission of KK hollow atoms (atoms without n = 1 electrons) from thin aluminum foils is observed from optical laser plasma for the first time. Specifically for 1.5 μm thin foil targets the hollow atom yield dominates the resonance line emission. It is suggested that the hollow atoms are predominantly excited by the impact of X-ray photons generated by radiation friction to fast electron currents in solid-density plasma due to Thomson scattering and bremsstrahlung in the transverse plasma fields. Numerical simulations of Al hollow atom spectra using the ATOMIC code confirm that the impact of keV photons dominates the atom ionization. Our estimates demonstrate that solid-density plasma generated by relativistic optical laser pulses provide the source of a polychromatic keV range X-ray field of 10¹⁸ W/cm² intensity, and allows the study of excited matter in the radiation-dominated regime. High-resolution X-ray spectroscopy of hollow atom radiation is found to be a powerful tool to study the properties of high-energy density plasma created by intense X-ray radiation.     

X-ray scattering from warm dense iron

We have carried out X-ray scattering experiments on iron foil samples that have been compressed and heated using laser-driven shocks created with the VULCAN laser system at the Rutherford-Appleton Laboratory. This is the highest Z element studied in such experiments so far and the first time scattering from warm dense iron has been reported. Because of the importance of iron in telluric planets, the work is relevant to studies of warm dense matter in planetary interiors. We report scattering results as well as shock breakout results that, in conjunction with hydrodynamic simulations, suggest the target has been compressed to a molten state at several 100 GPa pressure. Initial comparison with modelling suggests more work is needed to understand the structure factor of warm dense iron.     

Tungsten L transition line shapes and energy shifts resulting from ionization in warm dense matter

Spectra of the W L transitions in the energy range 8–12 keV from warm dense plasmas generated by the Naval Research Laboratory's Gamble II pulsed power machine were recorded by a newly developed high-resolution transmission-crystal X-ray spectrometer with ±2 eV accuracy. The discharges have up to 2 MV voltage, 0.5 MA current, and produce up to 2.4 MJ/cm^?3 energy density. The plasma-filled rod pinch (PFRP) diode produces a plasma with N_e ≈ 10²² cm^?3 and T_e ≈ 50 eV during the time of maximum X-ray emission. By analyzing the line shapes, it was determined that the Lβ₂ inner-shell transition from the 4d_5/2 level was shifted to higher energy by up to 23 eV relative to nearby Lβ transitions from n = 3 levels. In addition, the Lβ₂ transition was significantly broader and asymmetric compared to the n = 3 transitions. The energy shift of the Lβ₂ transition results from the ionization of electrons outside the 4d shell that perturbs the transition energies in the ions to higher values. The increased line width and asymmetry result from unresolved transitions from a range of ionization states up to +28. The ionization distribution was determined by comparison of the measured energy shifts and widths to calculated transition energies in W ions, and the ionization was correlated with Gamble discharge parameters such as the anode type and the high voltage delay time. This work demonstrates a new hard X-ray spectroscopic diagnostic technique for the direct measurement of the ionization distribution in warm dense plasmas of the heavy elements W through U that is independent of the other plasma parameters and does not require interpretation by hydrodynamic, atomic kinetics, and radiative simulation codes.     

Towards laboratory produced relativistic electron–positron pair plasmas

We review recent experimental results on the path to producing electron–positron pair plasmas using lasers. Relativistic pair-plasmas and jets are believed to exist in many astrophysical objects and are often invoked to explain energetic phenomena related to Gamma Ray Bursts and Black Holes. On earth, positrons from radioactive isotopes or accelerators are used extensively at low energies (sub-MeV) in areas related to surface science positron emission tomography and basic antimatter science. Experimental platforms capable of producing the high-temperature pair-plasma and high-flux jets required to simulate astrophysical positron conditions have so far been absent. In the past few years, we performed extensive experiments generating positrons with intense lasers where we found that relativistic electron and positron jets are produced by irradiating a solid gold target with an intense picosecond laser pulse. The positron temperatures in directions parallel and transverse to the beam both exceeded 0.5 MeV, and the density of electrons and positrons in these jets are of order 10¹⁶ cm⁻³ and 10¹³ cm⁻³, respectively. With the increasing performance of high-energy ultra-short laser pulses, we expect that a high-density, up to 10¹⁸ cm⁻³, relativistic pair-plasma is achievable, a novel regime of laboratory-produced hot dense matter.     

Modeling of the oscillating field effects on the Heβ line emission in short pulse laser-produced plasmas

Strong oscillating fields may induce strong modifications of the emission spectra of ions. We discuss here the possibility of observing such effects in actual laser experiments where space- and time-integration effects can easily mask their existence. Focusing on the Al He_β transition, we first discuss the calculation of its spectral broadening in the presence of a strong laser field. Then, starting from 1D hydro-simulations of short, intense, laser pulse-produced plasmas that provide the density, temperature and laser intensity profiles as a function of time, full integrated collisional-radiative calculations of the laser field-dependent emissivity of the Al He_β line, are presented.     

Equation of state studies of warm dense matter samples heated by laser produced proton beams

Heating of matter by proton beams produced by short pulse, laser-solid target interaction has been demonstrated over the last ten years by a number of workers. In the work described in this paper heating by a pulse of laser produced protons has been combined with high-resolution soft x-ray radiography to record the expansion of thin wire targets. Analysis of the radiographs yields material properties in the warm dense matter regime. These measurements imply initial temperatures in the experimental samples over a range from 14 eV up to 40 eV; the sample densities varied from solid to a tenth solid density. Assuming an adiabatic expansion after the initial proton heating phase isentropes of the aluminium sample material were inferred and compared to tabulated data from the SESAME equation of state library. The proton spectrum was also measured using calibrated magnetic spectrometers and radiochromic film. The accuracy of the technique used to infer material data is discussed along with possible future development.     

Effect of Schmidt number on the structure and propagation of density currents

The results of a numerical study of two- and three-dimensional Boussinesq density currents are described. They are aimed at exploring the role of the Schmidt number on the structure and dynamics of density driven currents. Two complementary approaches are used, namely a spectral method and a finite-volume interface capturing method. They allow for the first time to describe density currents in the whole range of Schmidt number 1 ≤ Sc ≤ ∞ and Reynolds number 10² ≤ Re ≤ 10⁴. The present results confirm that the Schmidt number only weakly influences the structure and dynamics of density currents provided the Reynolds number of the flow is large, say of O(10⁴) or more. On the contrary low- to moderate-Re density currents are dependant on Sc as the structure of the mixing region and the front velocities are modified by diffusion effects. The scaling of the characteristic density thickness of the interface has been confirmed to behave as (ScRe)^−1/2. Three-dimensional simulations suggest that the patterns of lobes and clefts are independent of Sc. In contrast the Schmidt number is found to affect dramatically (1) the shape of the current head as a depression is observed at high-Sc, (2) the formation of vortex structures generated by Kelvin–Helmholtz instabilities. A criterion is proposed for the stability of the interface along the body of the current based on the estimate of a bulk Richardson number. This criterion, derived for currents of arbitrary density ratio, is in agreement with present computed results as well as available experimental and numerical data.      

Equation of state calculations for hot,dense matter at arbitrary densities and temperatures

Within the approximations of spherical lattice cell, central-field, and relativistic Fermi statistics, an algorithm with average atom model is presented to calculate the electronic energy levels and equation of state for hot and dense matter at arbitrary densities and temperatures. Choosing Zink's analytical potential as initial potential, we have solved the Dirac-Slater equation which satisfies the Weigner-Seitz boundary condition. The electronic energy bands are not taken into account. Taking energy level degeneracy as a continuous function of density, we have considered the pressure ionization effects for highly dense matter. Results for¹³Al atom are shown.     

Aluminium Lyman-beta satellite emission in non-Maxwellian dense laser produced plasmas

High-energy decay channels of the Al Lyman-β satellite have been observed in X-ray emission from highly ionized plasma jets created by intense laser irradiation of aluminium foil targets. Atomic structure calculations show that the Lyman β satellite emission consists from six emission groups close to the He-like Al 1s²-1s4p (He_γ) and 1s²-1s5p (He_δ) resonance lines. This provides new possibilities for space resolved analysis of high density plasmas. Non-Maxwellian simulations of the plasma emission carried out with the MARIA code demonstrate that the intensity ratios of the Lyman-β satellites and the He_γ and He_δ resonance lines are very sensitive to the bulk electron temperature. In contrast to standard diagnostic methods, parameter studies show that this bulk electron diagnostics is practically unaffected by suprathermal electrons having less than 10% of the bulk electron density.     

A torsional creep instrument and a torsional pendulum,both with accurate temperature control

Summary This paper describes a torsional pendulum and a torsional creep instrument. With the pendulum shear moduli between 10⁶ and 10¹⁰ N/m² can be measured at frequencies from 0.1 to 20 Hz. The creep instrument is suitable for measurement of shear compliances lower than 10^–7 m²/N in the time range from 1 to 10⁵ seconds. In both instruments, specimens are kept at the right temperature by blowing heated nitrogen gas through a surrounding thermostatic chamber. The signal of a platinum resistance thermometer, provided in each chamber, automatically controls the heating of the gas. Temperatures from –180 to +300 °C can be maintained with an absolute accuracy of ±1 °C and a long term stability of ±0.05 °C. It is shown that one cannot directly compare one and the same shear property, calculated from the shear modulus as measured with the pendulum as well as from the shear compliance as measured with the creep instrument. This is due to differences in the temperature of one thermostatic chamber over against the other. Finally, the paper presents a method to reduce these differences to ±0.1 °C, although the absolute accuracy of temperature control remains ±1 °C.

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Zusammenfassung Die Arbeit beschreibt ein Torsionspendel und eine Torsions-Kriechapparatur. Mit dem Pendel können Schermoduli zwischen 10⁶ und 10¹⁰ N/m² bei Frequenzen zwischen 0,1 und 20 °C gemessen werden. Die Kriechapparatur ist geeignet für die Messung von Scherkomplianzen kleiner als 10^–7 m²/N in Zeiten zwischen 1 bis 10⁵ sec. In beiden Geräten werden die Proben durch das Einblasen von erhitztem Stickstoff durch eine umgebende thermostatische Kammer bei der richtigen Temperatur gehalten. Die Anzeige eines Platin-Widerstandsthermometers, das in jeder Kammer angebracht ist, kontrolliert automatisch die Erwärmung des Gases. Es können Temperaturen zwischen –180 und +300 °C mit einer absoluten Genauigkeit von ±1 °C und einer Langzeitstabilität von ±0,05 °C eingestellt werden. Es wird gezeigt, daß ein direkter Vergleich der gleichen Schereigenschaft, die zum einen aus dem mit dem Pendel gemessenen Schermodul und zum anderen aus der mit der Kriechapparatur ermittelten Kriechkomplianz errechnet wird, nicht möglich ist. Das beruht auf Temperaturdifferenzen zwischen den thermostatisierten Kammern.Abschließend stellt die Arbeit eine Methode vor, um diese Differenzen auf ±0,1 °C zu senken. Die absolute Genauigkeit der Temperaturkontrolle bleibt bei ±1 °C.

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Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968.     

Viscosity estimates of liquid metals and warm dense matter using the Yukawa reference system

A practical method of computing the viscosity of liquid metals and warm dense matter over wide ranges in parameters is proposed. The method is based on mapping the system of interest onto the Yukawa model, for which the viscosity is well known and can be written in a quasiuniversal form. Comparisons are made with quantum molecular dynamics results for compressed iron relevant to the Earth's core, experimental data for many liquid metals, and simulation results for dense deuterium relevant to inertial confinement fusion experiments. Finally, the dispersion and damping of ion-acoustic waves in warm dense matter are considered in this context.     

Absolute diode laser-based in situ detection of HCl in gasification processes

The release of HCl is an important parameter for industrial combustion and gasification processes, which must be determined in the ppm range for active process control and optimization. Based on a low power vertical-cavity surface-emitting laser (VCSEL) at 1.74 μm, we developed a new tuneable diode laser absorption spectrometer for calibration-free, absolute in situ HCl detection using the H³⁵Cl (2 ← 0) R(3) absorption line with minimized cross-sensitivity to CO₂ and H₂O. The spectrometer was applied to in situ measurements in a gasification process (T = 1,130°C, P = 1 atm, L = 28 cm) and yielded an optical resolution of 2.3·10⁻⁴, i.e. a HCl sensitivity of 45 ppm (13 ppm·m).     

Plasma emission spectroscopy of solids irradiated by intense XUV pulses from a free electron laser

The FLASH XUV-free electron laser has been used to irradiate solid samples at intensities of the order 10¹⁶ W cm^?2 at a wavelength of 13.5 nm. The subsequent time integrated XUV emission was observed with a grating spectrometer. The electron temperature inferred from plasma line ratios was in the range 5–8 eV with electron density in the range 10²¹–10²² cm^?3. These results are consistent with the saturation of absorption through bleaching of the L-edge by intense photo-absorption reported in an earlier publication.     

Early-time evolution of a radiative shock

We have performed high-energy-density physics experiments with large radiative fluxes, relevant to radiative shocks in our universe. These experiments were performed at the Omega Laser facility and used a laser irradiance of 7.2 × 10¹⁴ W cm^?2 to launch a Be disk into low-density Xe gas. The radiative shocks were observed early in time as the dense shocked Xe layer began to form. The average shock position indicates that the shock is moving over 130 km s^?1. Data are compared to simulation output from the CRASH code, which was developed at the Center for Radiative Shock Hydrodynamics at the University of Michigan.     

Dynamical deformation of a flat liquid–liquid interface

The passage of solid spheres through a liquid–liquid interface was experimentally investigated using a high-speed video and PIV (particle image velocimetry) system. Experiments were conducted in a square Plexiglas column of 0.1 m. The Newtonian Emkarox (HV45 50 and 65% wt) aqueous solutions were employed for the dense phase, while different silicone oils of different viscosity ranging from 10 to 100 mPa s were used as light phase. Experimental results quantitatively reveal the effect of the sphere’s size, interfacial tension and viscosity of both phases on the retaining time and the height of the liquid entrained behind the sphere. These data were combined with our previous results concerning the passage of a rising bubble through a liquid–liquid interface in order to propose a general relationship for the interface breakthrough for the wide range of Mo ₁/Mo ₂ ∈ [2 × 10⁻⁵–5 × 10⁴] and Re ₁/Re ₂ ∈ [2 × 10⁻³–5 × 10²].     

Numerical study of mixed convection and conduction in a 2-D square ventilated cavity with an inlet at the vertical glazing wall and outlet at the top surface

A steady state numerical study of combined laminar mixed convection and conduction heat transfer in a ventilated square cavity is presented. The air inlet gap is located at the bottom of a vertical glazing wall and air exits the cavity via a gap located at the top surface. Three locations for the opening at the top surface: left (case a), center (case b) and right side (case c) are considered. All the remaining surfaces are considered adiabatic. The mass, momentum and energy conservation equations were solved using the finite volume method for different Rayleigh numbers in the interval of 10⁴ < Ra < 10⁶ and Reynolds number in the interval of 100 < Re < 700. Temperature, flow field, and heat transfer rates are analyzed. The effect of the interaction between ambient conditions outside the glazing and the air inlet gap at the bottom for different air outlet gap positions at the top surface modifies the flow structure and temperature distribution of the air inside the cavity. The Nusselt number as a function of the Reynolds number was determined for the three cases. It was found that configuration for case (a) removes a higher amount of heat entering the cavity compared to cases (b) and (c). This is due to the short distance between the main stream and the glass wall surface. Thus, the forced airflow entering the cavity is assisted by the buoyancy forces, and most of the cavity remains at the inlet flow temperature, which should be appropriate for warm climates. These results may provide useful information about the heat transfer and fluid flow for future studies.     

MeV proton generation and efficiency from an intense laser irradiated foil

The proton energy distribution generated from the interaction of an intense (Iλ² ≈ 10²⁰ W/cm² μm²) short-pulse (100 fs) laser with a thin foil is investigated using energy resolved measurements and 2D collisional PIC-hybrid simulations. The measured absolute proton spectrum is well matched by a 1.7 MeV exponential function for energies <11 MeV. The proton conversion efficiency from hot electrons ≈6%. Simulations predict a strong radial dependence on the maximum proton energy and on the radial extent of 12 Å hydrocarbon depletion region. C and O ions in the hydrocarbon layer gain significant energies, limiting the efficiency to the protons. The efficiency scaling for ion mixtures is derived using a simple model, and is shown to strongly depend on the cooling rate of the hot electrons. Simulations using hydrogen-rich, layered targets predict much higher efficiencies.