Radiation and hot electron temperature measurements of short-pulselaser driven hohlraums

We have performed measurements of the radiation and the hot electron temperature in sub-millimetre size hohlraums driven by a high intensity short-pulse laser. The results indicate that radiation temperatures 80 eV can be obtained with 20 J of laser energy delivered on target. Radiation-hydrodynamics simulations indicate an absorption into thermal X-rays of 1–2%, with peak temperatures similar to those measured experimentally.     

Simulations of hot, dense iron plasma opacity at 89 eV and comparison with experiment

Predictions of hot, dense iron plasma opacity at 89 eV photon energy are compared with experimental determinations from the transmission of laser-heated iron to extreme ultra-violet (EUV) laser radiation. The EUV laser was pumped using six beams of an Nd-Yag laser in a refraction compensating geometry, while another beam irradiated a tamped solid iron target with an intensity of 10¹⁴ W cm⁻². The Ehybrid hydrodynamic and atomic physics code was used to predict temperatures, densities and ionisation throughout the evolving iron plasma. The iron opacities were deduced taking into account free–free, bound–free and bound–bound absorption. Bound–bound absorption was considered using atomic data generated by the Opacity Project. Reasonable overall agreement between theory and experiment was obtained for the iron layer transmission. The simulations indicated the dominance of bound–bound absorption throughout most regions of the iron plasma, but also the potential importance of photoionisation from core levels where energetically possible.     

Critical datasets for benchmarking atomic codes: Calibrated line intensities emitted by well-diagnosed solar plasmas

The accuracy of available spectral codes is dependent on the quality of the atomic data and transition rates that they include, and can only be tested by benchmarking predicted line emissivities with observations from plasmas whose physical properties are known with precision. In the present work we describe a few high-resolution spectra emitted by solar flare plasmas under condition of ionization equilibrium, and one quiet Sun off-disk region spectrum, and we propose these datasets as benchmarks for the assessment of the accuracy of existing spectral codes in the 1.84–1.90 Å and 3.17–3.22 Å X-ray ranges and in the 500–1600 Å far ultraviolet range.     

Core temperature and density profile measurements in inertial confinement fusion implosions

We have measured time-integrated and time-gated electron temperature (T_e) and density (N_e) spatial profiles from indirect-drive implosions. In our experiments, we used a multiple-pinhole two-dimensional imaging spectrometer to obtain multispectral X-ray images of the imploded core. Quantitative comparisons between quasi-monochromatic images in different energy bands allowed T_e and N_e spatial profiles to be determined using two independent and validated techniques: a multi-objective search and reconstruction analysis, and an analytical analysis. We then compared the results to a simple one-dimensional (1D) mix-free hydrodynamics simulation in order to evaluate the ability of such a model to predict our experiments. Our data show spatial T_e profiles that are qualitatively consistent with the predictions of our 1D simulations, but we observe central cores that are 10–25% cooler and emit X-rays as late as 200 ps after peak compression. We infer time-gated spatial N_e profiles that are consistent with our 1D simulations near the times of peak compression, but we find significant disagreement between time-integrated data and 1D simulation predictions at large radii. Careful analysis of the time-gated and time-integrated T_e and N_e spatial profiles, together with streaked X-ray emission spectra from core and shell dopants, suggests mixing of shell material into the core is an important process that our 1D hydrodynamics simulations fail to capture, and comparison between image data and a simple analytical model suggests that 2–5 μm of the initial inner shell thickness mixes into the core during the time period of significant X-ray emission. This mix width is consistent with the predictions of a growth-factor analysis that treats instability growth seeded by capsule surface roughness, and points to the need to consider time-dependent mixing effects when interpreting T_e and N_e spatial profiles derived from multispectral X-ray image data, particularly at large radii where mixing effects will be most significant.     

Accurate heat transfer measurements using thermochromic liquid crystal. Part 1: Calibration and characteristics of crystals

Encapsulated thermochromic liquid crystal (TLC) can accurately measure surface temperature in a variety of heat transfer and fluid flow experiments. Narrow-band TLC, where the colour changes over a temperature range of 1 °C, can be used to determine surface temperature within an uncertainty of 0.1 °C. Wide-band TLC, typically active over 5–20 °C, allow the possibility of mapping surface temperature distributions. In part 1 of this two-part paper, an extensive set of calibrations for narrow-band and wide-band TLC is reported. This generic study provides insight into the importance and influence of the various factors governing the colour–temperature relationship. These governing effects include the variation in optical path, the spectrum of the illumination source, the lighting and viewing angles, the differences between cooling or heating cycles (hysteresis), the variation with the number of heating or cooling cycles (aging) and how this varies with TLC film thickness. Two narrow-band crystals are also specifically calibrated for application to experiments on a transparent disc rotating at high speed (5000 rpm). Part 2 of this paper describes how these accurately-calibrated crystals were used to measure the transient surface temperature on, and heat transfer to, a rotating disc.     

Measurements of niobium absorption spectra in plasmas with nearly full M-shell configurations

A systematic study has been carried out on the changes in the L-shell absorption structure of niobium as a result of changing the population of the n = 3 shell from full to having vacancies in the 3d level. The niobium spectra were measured in the 2–3 keV frequency range, which spanned the 2p-nd transitions where 3 ≤ n ≤ 11. In addition to the detailed structure in these arrays the data also show 2s-4p and 2p-4s transitions and the bound-free L edge. The frequencies and widths of transition arrays, transmission between arrays, and the absorption due to the bound-free edge, can be seen in the data. The sample conditions were found from a combination of two-dimensional radiation-hydrodynamics calculations using the AWE NYM code and flux measurements using X-ray diodes, measurements of 1s-2p absorption spectra in aluminium and mixed aluminium/niobium samples. The electron temperature error, inferred from the modelling, is ±2 eV, with a density error of 30%. The data were recorded over the temperature range from 28 to 45 eV and show marked changes in the spectra over this range.The data were compared to spectra predicted by the AWE CASSANDRA [B.J.B. Crowley, J.W.O. Harris, J. Quant. Spectrosc. Radiat. Transfer 71 (2000) p. 257] opacity code. The calculated spectra were able to reproduce the measurements reasonably well. However, there are some differences in line positions that cannot be accounted for by gradients and there are differences in the array structure in the prediction and the measurements, with additional structure predicted but not seen in the measurements. There is also lower transmission on the blue side of the 2p-3d transition arrays compared to prediction.     

Absorption spectroscopy of mid and neighboring Z plasmas: Iron, nickel,copper and germanium

Opacities of four medium Z element plasmas (iron, nickel, copper and germanium) have been measured at the LULI-2000 facility in similar conditions: temperatures between 15 and 25 eV and densities between 2 and 10 mg/cm³, in a wavelength range (8–18 Å) including the strong 2p–3d structures.Two laser beams from the LULI facility were used in the nanosecond-picosecond configuration. The NANO-2000 beam (at λ = 0.53 μm) heated a gold hohlraum with an energy between 30 and 150 J with a duration of 0.6 ns. Samples covering half a hohlraum hole were thus radiatively heated. The picosecond pulse PICO-2000 beam (at λ = 1.053 μm) has been used to produce a short (about 10 ps) X-ray backlighter in order to reduce time variations of temperatures and densities during the measurement. A crystal high-resolution spectrometer was used as the main diagnostic to record at the same time the non-absorbed and the absorbed backlighter spectra. Radiation temperatures were measured using a broadband spectrometer. 1D and 2D simulations have been performed in order to estimate hydrodynamic plasmas parameters.The measured spectra have been compared with theoretical ones obtained using either the superconfiguration code SCO or the detailed term accounting code HULLAC. These comparisons allow us to check the modeling of the statistical broadening and of the spin-orbit splitting of the 2p–3d transitions and related effects such as the interaction between relativistic subconfigurations belonging to the same non-relativistic configuration.     

K-shell spectroscopy of plasmas created by intense laser irradiation of micron-scale pyramid and sphere targets

K-shell spectra of targets with microstructured features irradiated by an intense femtosecond laser have been studied. Examination of K_α emission from laser irradiated Si targets coated with micron-scale polystyrene spheres indicates that the emission is enhanced by a factor of 3 over emission from planar solids. Sphere-coated targets also emit K-shell He-like Si radiation indicating the presence of a hot dense plasma beneath the microspheres. Furthermore, K_α from Ti foils coupled to micro-tipped reentrant pyramid and wedge shaped targets has been studied, however, no significant enhancement of the K_α yield is observed for these kinds of targets. These studies illustrate that, with correct tailoring of the target surface, field enhancements can be used to increase X-ray emission from intensely irradiated targets.     

Localized Non-diffusive Asymptotic Patterns for Nonlinear Parabolic Equations with Gradient Absorption

We study the large-time behaviour of the solutions u of the evolution equation involving nonlinear diffusion and gradient absorption

Intense ultrashort laser–Xe cluster interaction

The last several years have witnessed a surge of activity involving the interaction of clusters with intense ultrashort pulse lasers. The interest in laser–cluster interaction has not been only of academic interest, but also because of the wide variety of potential applications. Clusters can be used as a compact source of X-rays, incoherent as well as coherent, and of fast ions capable of driving a fusion reaction in deuterium plasmas. In one set of xenon cluster experiments, in particular, amplification of ～2.8 Å X-rays has been observed [28]. X-ray amplification in cluster media is a phenomenon of critical importance and may lead to applications such as EUV lithography, EUV and X-ray microscopy, X-ray tomography, and variety of applications in biology and material sciences. However, while amplification of ～2.8 Å X-rays has been documented in experiments, the mechanism for producing it remains to be fully understood. In this talk, a xenon model of laser–cluster interaction dynamics is presented to shed light on the processes responsible for amplification. The focus of this research is on the feasibility of creating population inversions and gain in some of the inner-shell hole state transitions within the M-shell of highly ionized xenon. The model couples a molecular dynamics (MD) treatment of the explosively-driven, non-Maxwellian cluster expansion to a comprehensive multiphoton-radiative ionization dynamic (ID) model including single- and double-hole state production within the Co- and Fe-like ionization stages of xenon. The hole-state dynamics is self-consistently coupled to a detailed valence-state collisional-radiative dynamics of the Ni-, Co-, and Fe-like ionization stages of xenon. In addition, the model includes tunneling ionization rates that confirm an initial condition assumption that Ni-like ground states can be created almost instantaneously, on the order of a femtosecond or less, i.e., at laser intensities larger than 10¹⁹ W/cm², all of the N-shell, n = 4 electrons are striped from a xenon atom in less than a femtosecond. Because of the abundance of these ground states, large numbers of n = 2, inner-shell hole states and large population inversions can be created when the Ni-like ground states are photo- or collisionally ionized. Once the M-shell is entered, tunneling ionization slows down as does collisional ionization due to the fall in ion density as the cluster expands. Moreover, as the cluster density goes down, our combined MD and ID calculations show that so do the calculated population inversions. Thus, our calculations do not support the initial experimental data interpretations in which the measured gains have been associated with double holes in more highly ionized stages of xenon (Xe³²⁺, Xe³⁴⁺, Xe³⁵⁺, and Xe³⁷⁺), which our calculations suggest would require laser intensities in excess of 1.5 × 10²⁰ W/cm², for a 248 nm, ～250 fs laser pulse focused in a gas of xenon clusters. At laser intensities used in the experiment, such ionization stages would be reached, but only later in time when cluster densities have fallen by several orders of magnitude from their initial values to values where pumping rates are too low and gains cannot be generated.     

Dynamic interaction of various beams with the underlying soil – finite and infinite, half-space and Winkler models

Various beams lying on the elastic half-space and subjected to a harmonic load are analyzed by a double numerical integration in wavenumber domain. The compliances of the beam–soil systems are presented for a wide frequency range and for a number of realistic parameter sets. Generally, the soil stiffness G has a strong influence on the low-frequency beam compliance whereas the beam parameters EI and m^′ are more important for the high-frequency compliance. An important parameter is the elastic length l=(EI/G)^1/4 of the beam–soil system. Around the corresponding frequency ω_l=v_S/l, the wave velocity of the combined beam–soil system changes from the Rayleigh wave v_R≈v_S to the bending wave velocity v_B and the combined beam–soil wave has typically a strong damping. The interaction frequency ω_l is found not far from the characteristic frequency ω₀=(G/m^′)^1/2 where an amplification compared to the static compliance is observed for special parameter constellations. In contrast, real foundation beams show no resonance effects as they are highly damped by the radiation into the soil. At medium and high frequencies, asymptotes for the compliance of the beam–soil system are found, u/P(ρv_Paiω)^−3/4 in case of the dominating damping and u/P(−m^′ω²)^−3/4 for high frequencies. The low-frequency compliance of the coupled beam–soil system can be approximated by u/P1/Gl, but it also depends weakly on the width a of the foundation. All numerical results of different beam–soil systems are evaluated to yield a unique relation u/P₀=f(a/l). The integral transform method is also applied to ballasted and slab tracks of railway lines, showing the influence of train speed on the deformation of the track beam. The presented results of infinite beams on half-space are compared with results of finite beams and with infinite beams on a Winkler support. Approximating Winkler parameters are given for realistic foundation-soil systems which are useful when vehicle-track interaction is analyzed for the prediction of railway induced vibration.     

Homogenization of Periodic Systems with Large Potentials

We consider the homogenization of a system of second-order equations with a large potential in a periodic medium. Denoting by the period, the potential is scaled as ^–2. Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of a scalar second-order equation. This result applies to various types of equations such as parabolic, hyperbolic or eigenvalue problems, as well as fourth-order plate equation. We also prove that, for well-prepared initial data concentrating at the bottom of a Bloch band, the resulting homogenized tensor depends on the chosen Bloch band. Our method is based on a combination of classical homogenization techniques (two-scale convergence and suitable oscillating test functions) and of Bloch waves decomposition.     

The Logarithmic Tail of Néel Walls

  We study the multiscale problem of a parametrized planar 180° rotation of magnetization states in a thin ferromagnetic film. In an appropriate scaling and when the film thickness is comparable to the Bloch line width, the underlying variational principle has the form

Diagnostics of dielectronic processes in laser produced samarium plasma

Spatially-resolved time-integrated X-ray spectra of laser produced samarium plasma were recorded, in the spectral range from 7 to 10 Å. The spectrum of samarium is characterized by the prominent pattern of transitions 3d – nf (n = 4–7) belonging to Co-like (Sm³⁵⁺), Ni-like (Sm³⁴⁺) and Cu-like (Sm³³⁺) ions. Spectral lines of Mn-like (Sm³⁷⁺) to Zn-like (Sm³²⁺) were identified. The appearance of these ionization stages as a function of distance from the target was measured. Transfer of the dominant ion stages to lower stages with increasing distance from the original target surface was demonstrated, probably indicating dielectronic recombination. The Hebrew University Lawrence Livermore Atomic Code was used to generate emission spectra for comparison with the experimental ones.A radiation-hydrodynamics code coupled to three non-Local Thermal Equilibrium ionization and equation of state models with different approaches for dielectronic processes was used to model the plasma. The simulated plasma ionization and electron densities and temperatures were found to be consistent with the experimental results.     

Minimum-drag cascade design for supersonic flow with subsonic normal velocity component

The variational problem of designing the slender profile of a plane cascade in a supersonic ideal (inviscid and nonheat-conducting) gas flow with a subsonic normal velocity component is solved in the linear approximation. The optimum profiles constructed differ fundamentally from the closest analog — the supersonic single profile creating minimum wave drag for given lift. Following [1], it is easy to show that in this case the optimum profile is a plate at an angle of attack determined by the given lift.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 137–146, January–February, 1995.     

On the Strong Ellipticity of the Anisotropic Linearly Elastic Materials

In this paper we derive necessary and sufficient conditions for strong ellipticity in several classes of anisotropic linearly elastic materials. Our results cover all classes in the rhombic system (nine elasticities), four classes of the tetragonal system (six elasticities) and all classes in the cubic system (three elasticities). As a special case we recover necessary and sufficient conditions for strong ellipticity in transversely isotropic materials. The central result shows that for the rhombic system strong ellipticity restricts some appropriate combinations of elasticities to take values inside a domain whose boundary is the third order algebraic surface defined by x ²+y ²+z ²−2xyz−1=0 situated in the cube , , . For more symmetric situations, the general analysis restricts combinations of elasticities to range inside either a plane domain (for four classes in the tetragonal system) or in an one-dimensional interval (for the hexagonal systems, transverse isotropy and cubic system). The proof involves only the basic statement of the strong ellipticity condition.      

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.