K-α emission spectroscopic analysis from a Cu Z-pinch

Advances in diagnostic techniques at the Sandia Z-facility have facilitated the production of very detailed spectral data. In particular, data from the copper nested wire-array shot Z1975 provides a wealth of information about the implosion dynamics and ionization history of the pinch. Besides the dominant valence K- and L-shell lines in Z1975 spectra, K-α lines from various ionization stages were also observed. K-shell vacancies can be created from inner-shell excitation and ionization by hot electrons and from photo-ionization by high-energy photons; these vacancies are subsequently filled by Auger decay or resonance fluorescence. The latter process produces the K-α emission. For plasmas in collisional equilibrium, K-α emission usually occurs from highly charged ions due to the high electron temperatures required for appreciable excitation of the K-α transitions. Our simulation of Z1975 was carried out with the NRL 1-D DZAPP non-LTE radiation-hydrodynamics model, and the resulting K- and L-shell synthetic spectra are compared with measured radiation data. Our investigation will focus on K-α generation by both impacting electrons and photons. Synthetic K-α spectra will be generated either by self-consistently calculating the K-shell vacancy production in a full Z-pinch simulation, or by post-processing data from a simulation. The analysis of these K-α lines as well as K- and L-shell emission from valence electrons should provide quantitative information about the dynamics of the pinch plasma.     

Spectroscopic analysis of Cu wire array implosions on the refurbished Z generator

Experimental investigations of pinches on the refurbished Z (ZR) generator using Cu arrays have been initiated and more are planned for the near future. Significant X-ray emissions in the K-shell from moderately high atomic number plasmas such as Cu generate extreme interest. However, the production of these hard photons from high Z materials comes with a price. There is substantial loss of radiative yield due to stripping through many electrons present in high Z materials to reach to the H- or He-like ionization stages. Production of hard X-rays for materials with atomic number higher than Cu such as Kr is very difficult and theoretical predictions are even more uncertain. Previous experimental efforts using Cu as a plasma pinch load are encouraging and promote further investigations of this element on the refurbished Z machine for achieving photon energies higher than 5 keV and obtaining sufficient radiative yield. We will analyze the ionization dynamics and generate Cu spectrum using the temperature and density conditions obtained from 1-D non-LTE radiation hydrodynamics simulations of Cu wire array implosions on ZR. These results will be compared with K- and L-shell experimental spectrum of shot Z 1975. Theoretical K- and L-shell spectroscopy provides validation of atomic and plasma modeling when compared to available experimental data and also provides useful diagnostics for the plasma parameters. Our self-consistently generated non-LTE collisional-radiative model employs an extensive atomic level structure and data for all dominant atomic processes that are necessary to model accurately the pinch dynamics and the spectroscopic details of the emitted radiation.     

X-ray absorption spectroscopy for wire-array Z-pinches at the non-radiative stage

Absorption spectroscopy was applied to wire-array Z-pinches on the 1 MA pulsed-power Zebra generator at the Nevada Terawatt Facility (NTF). The 50 TW Leopard laser was coupled with the Zebra generator for X-ray backlighting of wire arrays at the ablation stage. Broadband X-ray emission from a laser-produced Sm plasma was used to backlight Al star wire arrays in the range of 7–9 Å. Two time-integrated X-ray conical spectrometers recorded reference and absorption spectra. The spectrometers were shielded from the bright Z-pinch X-ray burst by collimators. The comparison of plasma-transmitted spectra with reference spectra indicates absorption lines in the range of 8.1–8.4 Å. Analysis of Al K-shell absorption spectra with detailed atomic kinetics models shows a distribution of electron temperature in the range of 10–30 eV that was fitted with an effective two-temperature model. Temperature and density distributions in wire-array plasma were simulated with a three-dimension magneto-hydrodynamic code. Post-processing of this code’s output yields synthetic transmission spectrum which is in general agreement with the data.     

Neutralizer with a gas ejector

A neutralizer model with a gas ejector is studied, whose main element (a sonic nozzle) is a gap between two conical surfaces. Static pressure distributions were measured along the axis of the neutralizer at different gas pressures in the receiver. Stagnation pressure, total flow, gas target thickness, flow separation factor, Knudsen number, and gas-dynamic performance of the neutralizer were calculated from the gas pressure values on the axis of the neutralizer at the point with the coordinate z/d = 3, and static pressure distributions in the characteristic cross sections of the neutralizer were obtained.     

Versatile code DLAYZ for investigating population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium

A versatile code DLAYZ based on collisional-radiative model is developed for investigating the population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium. DLAYZ is implemented on the detailed level accounting (DLA) approach and can be extended to detailed configuration accounting (DCA) and hybrid DLA/DCA approaches. The code can treat both steady state and time-dependent problems. The implementation of the main modules of DLAYZ is discussed in detail including atomic data, rates, population distributions and radiative properties modules. The complete set of basic atomic data is obtained using relativistic quantum mechanics. For dense plasmas, the basic atomic data with plasma screening effects can be obtained. The populations are obtained by solving the coupled rate equations, which are used to calculate the radiative properties. A parallelized version is implemented in the code to treat the large-scale rate equations. Two illustrative examples of a steady state case for carbon plasmas and a time-dependent case for the relaxation of a K-shell excited argon are employed to show the main features of the present code.     

Bubbly jets in stagnant water

Air–water bubbly jets are studied experimentally in a relatively large water tank with a gas volume fraction, C_o, of up to 80% and nozzle Reynolds number, Re, ranging from 3500 to 17,700. Measurements of bubble properties and mean axial water velocity are obtained and two groups of experiments are identified, one with relatively uniform bubble sizes and another with large and irregular bubbles. For the first group, dimensionless relationships are obtained to describe bubble properties and mean liquid flow structure as functions of C_o and Re. Measurements of bubble slip velocity and estimates of the drag coefficient are also provided and compared to those for isolated bubbles from the literature. The study confirms the importance of bubble interactions to the dynamics of bubbly flows. Bubble breakup processes are also investigated for bubbly jets. It was found that a nozzle Reynolds number larger than 8000 is needed to cause breakup of larger bubbles into smaller bubbles and to produce a more uniform bubble size distribution. Moreover, the Weber number based on the mean water velocity appears to be a better criteria than the Weber number based on the bubble slip velocity to describe the onset of bubble breakup away from the nozzle, which occurs at a Weber number larger than 25.     

Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle

In this paper, we study the transonic shock problem for the full compressible Euler system in a general two-dimensional de Laval nozzle as proposed in Courant and Friedrichs (Supersonic flow and shock waves, Interscience, New York, 1948): given the appropriately large exit pressure p _e(x), if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle, a shock front intervenes and the gas is compressed and slowed down to subsonic speed so that the position and the strength of the shock front are automatically adjusted such that the end pressure at the exit becomes p _e(x). We solve this problem completely for a general class of de Laval nozzles whose divergent parts are small and arbitrary perturbations of divergent angular domains for the full steady compressible Euler system. The problem can be reduced to solve a nonlinear free boundary value problem for a mixed hyperbolic–elliptic system. One of the key ingredients in the analysis is to solve a nonlinear free boundary value problem in a weighted Hölder space with low regularities for a second order quasilinear elliptic equation with a free parameter (the position of the shock curve at one wall of the nozzle) and non-local terms involving the trace on the shock of the first order derivatives of the unknown function.     

An experimental platform for creating white dwarf photospheres in the laboratory

We present an experimental platform for measuring hydrogen Balmer emission and absorption line profiles for plasmas with white dwarf (WD) photospheric conditions (T_e ～1 eV, n_e ～10¹⁷ cm^?3). These profiles will be used to benchmark WD atmosphere models, which, used with the spectroscopic method, are responsible for determining fundamental parameters (e.g., effective temperature, mass) for tens of thousands of WDs. Our experiment, performed at the Z Pulsed Power Facility at Sandia National Laboratories, uses the large amount of X-rays generated from a z-pinch dynamic hohlraum to drive plasma formation in a gas cell. The platform is unique compared to past hydrogen line profile experiments in that the plasma is radiation-driven. This decouples the heating source from the plasma to be studied in the sense that the radiation temperature causing the photoionization is independent of the initial conditions of the gas. For the first time we measure hydrogen Balmer lines in absorption at these conditions in the laboratory for the purpose of benchmarking Stark-broadened line shapes. The platform can be used to study other plasma species and to explore non-LTE, time-dependent collisional-radiative atomic kinetics.     

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.     

Searching for efficient X-ray radiators for wire array Z-pinch plasmas using mid-atomic-number single planar wire arrays on Zebra at UNR

We continue to search for more efficient X-ray radiators from wire array Z-pinch plasmas. The results of recent experiments with single planar wire array (SPWA) loads made from mid-atomic-number material wires such as Alumel, Cu, Mo, and Ag are presented and compared. In particular, two new efficient X-ray radiators, Alumel (95% Ni, 2% Al, and 2% Si) and Ag, are introduced, and their radiative properties are discussed in detail. The experiments were performed on the 1 MA Zebra generator at UNR. The X-ray yields from such mid-atomic-number SPWAs exceed twice those from low-atomic-number SPWAs, such as Al, and increase with the atomic number to reach more than 27–29 kJ for Ag. To consider the main contributions to the total radiation, we divided the time interval of the Z-pinch dynamic where wire ablation and implosion, stagnation, and plasma expansion occur in corresponding phases and studied the radiative and implosion characteristics within them. Theoretical tools such as non-LTE kinetics and wire ablation dynamic models were applied in the data analysis. These results and the models developed have much broader applications, not only for SPWAs on Zebra, but for other HED plasmas with mid-atomic-number ions.     

Study of vibrational deactivation of molecules of carbon dioxide gas during cooling of stream in a supersonic nozzle

The vibrational temperature of the antisymmetrical type of vibrations (v ₃) of the CO₂ molecule at the exit of a supersonic nozzle is measured in the present work using the method of recording the infrared emission. Freezing in of thev ₃-type vibrations was observed during the flow of undiluted carbon dioxide in a nozzle. In this case the vibrational temperature T₃ considerably exceeded the translational temperature. On the basis of a comparison of the experimental results with calculation it can be concluded that vibrational deactivation of CO₂ molecules occurs three to five times faster than the excitation of the vibrations during heating in a shock wave. All the experiments were conducted under the following conditions: maximum expansion of gas in nozzle A/A* = 115, temperature range 1900–2400 °K, pressure range 1–17.5 atm.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 32–40, November–December, 1973.The authors are grateful to U. G. Pirumov and É. A. Ashratov for the calculation of the nozzle profile and the distribution of streamlines as well as for a discussion of the results.     

Advances in NLTE modeling for integrated simulations

The last few years have seen significant progress in constructing the atomic models required for non-local thermodynamic equilibrium (NLTE) simulations. Along with this has come an increased understanding of the requirements for accurately modeling the ionization balance, energy content and radiative properties of different atomic species for a wide range of densities and temperatures. Much of this progress is the result of a series of workshops dedicated to comparing the results from different codes and computational approaches applied to a series of test problems. The results of these workshops emphasized the importance of atomic model completeness, especially in doubly-excited states and autoionization transitions, to calculating ionization balance, and the importance of accurate, detailed atomic data to producing reliable spectra.We describe a simple screened-hydrogenic model that calculates NLTE ionization balance with sufficient accuracy, at a low enough computational cost for routine use in radiation-hydrodynamics codes. The model incorporates term splitting, Δn = 0 transitions, and approximate UTA widths for spectral calculations, with results comparable to those of much more detailed codes. Simulations done with this model have been increasingly successful at matching experimental data for laser-driven systems and hohlraums.Accurate and efficient atomic models are just one requirement for integrated NLTE simulations. Coupling the atomic kinetics to hydrodynamics and radiation transport constrains both discretizations and algorithms to retain energy conservation, accuracy and stability. In particular, the strong coupling between radiation and populations can require either very short time steps or significantly modified radiation transport algorithms to account for NLTE material response. Considerations such as these continue to provide challenges for NLTE simulations.     

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.     

Effect of third- and fourth-order moments on the modeling of unresolved transition arrays

The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram–Charlier, Normal Inverse Gaussian and Generalized Gaussian distributions. It is shown that the modeling of unresolved transition arrays with non-Gaussian distributions may reveal more detailed structures, due essentially to the large value of the kurtosis. In the present work, focus is put essentially on the Generalized Gaussian, the power of the argument in the exponential being constrained by the kurtosis value. The relevance of the new statistical line distribution is checked by comparisons with smoothed detailed line-by-line calculations and through the analysis of 2p → 3d transitions of recent laser or Z-pinch absorption measurements. The issue of calculating high-order moments is also discussed (Racah algebra, Jucys graphical method, semi-empirical approach…).     

Numerical investigation of a model of nonequilibrium radiation behind a shock front in the martian atmosphere

A model of nonequilibrium radiation behind the shock front in the CO₂-N₂ gas mixture is investigated. The kinetic mechanisms of the physical and chemical processes occurring in the relaxation zone are described. On the basis of the model presented the spectral emission rate of the shock-heated gas is calculated under the conditions of the experiments carried out on the setups of the Institute of Mechanics of Moscow State University and NASA Ames. The calculated results are compared with the measured data.     

Flow in a viscous jet escaping through a supersonic nozzle into a semi-infinite ambient space

The problem of an axisymmetric gas flow in a supersonic nozzle and in the jet escaping from the nozzle to a quiescent gas is solved within the framework of Navier-Stokes equations. The calculated pressure distribution is compared with that measured in the jet by a Pitot tube. The influence of the jet pressure ratio, Reynolds number, and half-angle of the supersonic part of the nozzle on nozzle flow and jet flow parameters is studied. It is shown that the distributions of gas-dynamic parameters at the nozzle exit are nonuniform, which affects the jet flow. The flow pattern for an overexpanded jet shows that jet formation begins inside the nozzle because of boundary-layer displacement from the nozzle walls. This result cannot be obtained with the inviscid formulation of the problem.     

Experimental and numerical analysis of the structure of pseudo-shock systems in laval nozzles with parallel side walls

Detailed numerical and experimental investigations of pseudo-shock systems in a Laval nozzle with parallel side walls are carried out. The location of the pseudo-shock system is defined in this system of two choked Laval nozzles by the ratio of the critical cross sections A₂^*/A₁^*{{A}_{2}^*/{A}_{1}^*} , the stagnation pressure loss across the shock system and viscous losses. The wall pressure distributions and high-speed schlieren videos recorded in the experiments are compared to the results of a steady and an unsteady numerical simulation. For the steady case, good agreement is found between the calculated and measured shock structure and pressure distribution along the primary nozzle wall, except for a remaining slight deviation in the shock position. For the unsteady case, in which asymmetric shock configurations are observed, deviations of the results with respect to the stochastic wall attachment of the shock system are given which indicate the necessity of further investigations on that topic.