Radiative shock solutions with grey nonequilibrium diffusion

This study describes a semi-analytic solution of planar radiative shock waves with a grey nonequilibrium diffusion radiation model. The solution may be used to verify radiation-hydrodynamics codes. Comparisons are made with the equilibrium diffusion solutions of Lowrie and Rauenzahn (Shock Waves 16(6):445–453, 2007). The solution also gives additional insight into the structure of radiative shocks. Previous work has assumed that the material temperature reaches its maximum at the post-shock state of the embedded hydrodynamic shock (Zel’dovich spike). We show that in many cases, the temperature may continue to increase after the hydrodynamic shock and reaches its maximum at the isothermal sonic point. Also, a temperature spike may exist even in the absence of an embedded hydrodynamic shock. We also derive an improved estimate for the maximum temperature.      

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.     

The production and evolution of multiple converging radiative shock waves in gas-filled cylindrical liner z-pinch experiments

A cylindrical liner z-pinch configuration has been used to drive converging radiative shock waves into different gases. On application of a 1.4 MA, 240 ns rise-time current pulse, a series of cylindrical shocks moving at typical velocities of 20 km s^?1 are consecutively launched from the inside liner wall into an initially static gas-fill of density ～10^?5 g cm^?3. The drive current skin depth calculated prior to resistive heating was slightly less than the liner wall thickness and no bulk liner implosion occurred. Axial laser probing images show the shock fronts to be smooth and azimuthally symmetric, with instabilities developing downstream of each shock. Evidence for a radiative precursor ahead of the first shock was seen in laser interferometry imaging and time-gated, spatially resolved optical spectroscopy. The interferometry diagnostic was able to simultaneously resolve the radiative precursor and the density jumps at the shock fronts. Optical streak photography provided information on shock timing and shock trajectories and was used to gain insight into the shock launching mechanisms.     

WADM and radiation MHD simulations of compact multi-planar and cylindrical wire arrays at 1 MA currents

The radiative performance of Z-pinches created by the imploding wire array loads is defined by the ablation and implosion dynamics of these loads. Both these processes can be effectively modeled by the Wire Ablation Dynamics Model (WADM), which extends the formalism exploited earlier for the cylindrical wire arrays to the loads of arbitrary geometries. The WADM calculates the ablation rates for each array wire and provides the important dynamic parameters, such as the specific mass and velocity of the imploding plasma, which can be used to estimate the shapes of the x-ray pre-pulse and, partially, the main x-ray burst. The applications of the WADM also extend to combined material wire array loads. The ablation and implosion dynamics of novel Prism Planar Wire Array (PPWA) and combined material (Mo/Al/Mo) Triple Planar Wire Array (TPWA) loads are discussed in detail. The combined WADM and radiation MHD simulation is applied to model the radiative performance of the precursor plasma column, created by the imploding stainless steel compact cylindrical wire array. As the radiation effects intensify with the mass accumulation at the array center, the simulation reveals the transformation of quasi-uniform precursor column into a heterogeneous plasma structure with strong density and temperature gradients. We find that radiative performance of the precursor plasma is greatly affected by the load geometry as well as by the wire material.     

Simulating radiative shocks in nozzle shock tubes

We use the recently developed Center for Radiative Shock Hydrodynamics (CRASH) code to numerically simulate laser-driven radiative shock experiments. These shocks are launched by an ablated beryllium disk and are driven down xenon-filled plastic tubes. The simulations are initialized by the two-dimensional version of the Lagrangian Hyades code which is used to evaluate the laser energy deposition during the first 1.1 ns. Later times are calculated with the CRASH code. CRASH solves for the multi-material hydrodynamics with separate electron and ion temperatures on an Eulerian block-adaptive-mesh and includes a multi-group flux-limited radiation diffusion and electron thermal heat conduction. The goal of the present paper is to demonstrate the capability to simulate radiative shocks of essentially three-dimensional experimental configurations, such as circular and elliptical nozzles. We show that the compound shock structure of the primary and wall shock is captured and verify that the shock properties are consistent with order-of-magnitude estimates. The synthetic radiographs produced can be used for comparison with future nozzle experiments at high-energy-density laser facilities.     

A comparison study of discrete-ordinates and flux-limited diffusion methods for modeling radiation transport

The Center for Radiative Shock Hydrodynamics (CRASH) is investigating methods of improving the predictive capability of numerical simulations for radiative shock waves that are produced in Omega laser experiments. The laser is used to shock, ionize, and accelerate a beryllium foil into a xenon-filled shock tube. These shock waves, when driven above a threshold velocity of about 60 km/s, become strongly radiative and convert much of the incident energy flux into radiation.Radiative shocks have properties that are significantly different from purely hydrodynamic shocks and, in modeling this phenomenon numerically, it is important to compute radiative effects accurately. In this article, we examine approaches to modeling radiation transport by comparing two methods: (i) a computationally efficient, multigroup, flux-limited-diffusion approximation, currently in use in the CRASH radiation-hydrodynamics code, with (ii) a more accurate discrete-ordinates treatment that is offered by the radiation-transport code PDT. We present a selection of results from a growing suite of code-to-code comparison tests, showing both results for idealized problems and for those that are representative of conditions found in the CRASH experiment.     

Simulations of laser experiments of radiative and non-radiative shocks

The Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan was established to study the properties of radiative shocks using both numerical simulation and shock-tube experiments on the Omega Laser at the University of Rochester. The laser accelerates a thin Be disk, which acts like a piston, driving a shock with an initial propagation velocity of 200 km/s into a tube filled with Xe. Analytic estimates indicate that a shock propagating with a velocity greater than about 60 km/s through Xe under these conditions should be strongly radiative. This paper discusses numerical simulations of a proposed modification to this experiment that produces a non-radiative shock. Comparison of the radiative and non-radiative cases provides an excellent opportunity for assessing the effects of radiation on shock structure and flow morphology. For the non-radiative case, the initial shock speed is reduced to 20 km/s by increasing the thickness of the Be disk and by decreasing the energy of the laser. Two-dimensional simulations of targets with cylindrical shock tubes and three-dimensional simulations of more complex targets with elliptical shock tubes are described. In addition, the effect of the shock speed on the cross-sectional area of the tube is discussed.     

The quasi-stationary structure of radiating shock waves. I. The one-temperature fluid

We calculate the quasi-stationary structure of a radiating shock wave propagating through a spherically symmetric shell of cold gas by solving the time-dependent equations of radiation hydrodynamics on an implicit adaptive grid. We show that this code successfully resolves the shock wave in both the subcritical and supercritical cases and, for the first time, we have reproduced all the expected features – including the optically thin temperature spike at a supercritical shock front – without invoking analytic jump conditions at the discontinuity. We solve the full moment equations for the radiation flux and energy density, but the shock wave structure can also be reproduced if the radiation flux is assumed to be proportional to the gradient of the energy density (the diffusion approximation), as long as the radiation energy density is determined by the appropriate radiative transfer moment equation. We find that Zel'dovich and Raizer's (1967) analytic solution for the shock wave structure accurately describes a subcritical shock but it underestimates the gas temperature, pressure, and the radiation flux in the gas ahead of a supercritical shock. We argue that this discrepancy is a consequence of neglecting terms which are second order in the minimum inverse shock compression ratio [, where is the adiabatic index] and the inaccurate treatment of radiative transfer near the discontinuity. In addition, we verify that the maximum temperature of the gas immediately behind the shock is given by , where is the gas temperature far behind the shock. Received 21 September 1998/ Accepted 2 February 1999     

Construction of a collisional radiative model of complex multiple charged ions for mid- to high-Z elements

A method of constructing a compact and complete collisional radiative model of multiple charged ions of mid- to high-Z elements is proposed, for studying radiative properties of the plasmas. The proposed tungsten model, which is based on atomic data calculated by the HULLAC code, incorporates a computer algorithm to identify well-populated atomic states and dielectronic recombination channels that have a significant effect on the ionization balance. The model is validated by investigating the convergence of the mean charge and radiative power loss with respect to the size of the model, and by comparing results with other calculations presented at the nLTE kinetics workshop.     

Shock wave structure for a fully ionized plasma

We study planar shock wave structure in a two-temperature model of a fully ionized plasma that includes electron heat conduction and energy exchange between electrons and ions. For steady flow in a reference frame moving with the shock, the model reduces to an autonomous system of ordinary differential equations which can be numerically integrated. A phase space analysis of the differential equations provides an additional insight into the structure of the solutions. For example, below a threshold Mach number, the model produces continuous solutions, while above another threshold Mach number, the solutions contain embedded hydrodynamic shocks. Between the threshold values, the appearance of embedded shocks depends on the electron diffusivity and the electron–ion coupling term. We also find that the ion temperature may achieve a maximum value between the upstream and downstream states and away from the embedded shock. We summarize the methodology for solving for two-temperature shocks and show results for several values of shock strength and plasma parameters in order to quantify the shock structure and explore the range of possible solutions. Such solutions may be used to verify hydrodynamic codes that use similar plasma physics models.     

POLAR project: Numerical modeling of the accretion column

In this paper we study the formation and evolution of radiative accretion shocks in the context of accretion columns in magnetic cataclysmic variables. The phenomenon induces extreme regimes of matter and the radiation emitted by those region dominates the observed emission from polars. A 2D hydrodynamical code, HYDRO-COOL, has been developed in order to deal with high-Mach number flows and is currently improved to produce a numerical model of the accretion column. This code is the hydrodynamical part of the HADES code which aims at modeling radiative hydrodynamical systems. The final goal of this model is to improve our understanding of observational results. First numerical results are reported here, as well as a discussion about the time-dependent evolution of the column.     

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.     

On the existence of intermediate magnetohydrodynamic shock waves

We consider the questions related to the structure of shock waves for a system of magnetohydrodynamic equations. Using Conley's connection matrix, we recover and extend earlier results due to C. Conley and J. Smoller. In particular, we give a simpler proof of the existence of fast and slow shocks with structure. We also demonstrate that for some viscosity parameters intermediate shocks occur. Furthermore, under an assumption of transversality, we show that there exist multi-parameter families of these intermediate shocks.This research was done while both authors were visiting the Lefschetz Center for Dynamical Systems at Brown University.Supported in part by the NSF under Grant DMS-8507056.Supported in part by AFOSR 87-0347.     

Interaction between shocks and clumps with self-contained magnetic fields

Problems involving magnetized clouds and clumps, especially their interaction with shocks are common in astrophysical environments and have been a topic of research in the past decade. Many previous numerical studies have focused on the problem of clumps immersed in a globally uniform magnetic field subject to an oncoming shock. However, realistic clumps may have tangled magnetic field self-contained within them. This magnetic field will be compressed by the shock and its energy spectrum and spatial structure may affect the evolution of the clump during the shock encounter. Using our parallel MHD code AstroBEAR, we set up an initial state with magnetized clumps of different contained magnetic field configurations. We then drive strong shocks through these clumps (including the effects of radiative cooling) and compare our results to previous studies of global uniform field scenarios.     

Radiative transfer effects of an axisymmetric particulate jet into a cylindrical pipe

This paper discusses the radiative transfer effects of an axisymmetric gas-particles jet into a cylindrical pipe. The medium is gray and it participates to radiation by emission, absorption and scattering. The two-phase flow problem is solved numerically by the finite volume method. We investigate the radiative transfer through a sensitivity analysis which considers the effects of the particle radiative properties and the particle number density on the temperature field and on the radiative heat fluxes of the two-phase flow domain. Analysis of the temperature profile in the cylinder, without and then with particle radiation effects, shows a decrease in the medium temperatures and thus an important role of the radiative transfer. These results also show that the presence of scattering makes the medium temperature more uniform. Finally, analysis of the particle number density, through the variation of the injection velocity, shows that a decrease in the injection velocity decreases the temperatures of the gas and particles and rapidly equilibrates the gas and particle temperatures.     

Review of the NLTE-5 kinetics workshop

We review the 5th non-LTE kinetics code comparison workshop, held in November 2007. Both steady-state and time-dependent cases for elements ranging from carbon to gold were examined in detail. Calculations of radiative power losses and specific spectra were requested in addition to typical plasma quantities such as the ionization balance. Non-Maxwellian electrons, external Planckian radiation and opacity effects in spectra were also included in the comparisons. We discuss the organization of the workshop and present a set of representative results. The particular case of a tungsten plasma at tokamak operating densities was considered for the first time. Due to its importance to the ITER project, more detailed results of these comparisons will be published elsewhere.     

Progress of passive daytime radiative cooling technologies towards commercial applications

Global warming has become one of the major environmental problems facing mankind in the 21st century. The existing refrigeration technology of buildings, like air conditioning, consumes a lot of energy. Passive daytime radiative cooling technology works without consuming energy, nor emitting carbon dioxide and other greenhouse gases. This review summarizes the development of daytime passive radiative cooling technology from the basic principles, structure and materials of radiative coolers; analyses and evaluates the various existing radiative coolers. The core of radiative cooling lies in the combination of multi-scale micro/nano structures. The cooler reflects sunlight thus preventing the building from being heated up; while allows the building to radiate its own heat out thus being cooled down; meanwhile maintains the temperature difference by the heat insulation effect of the porous structure in the film. The common challenges and potential solutions for the commercialization of radiative cooling technologies are analyzed, which may promote the applications of the technology in the near future.     

A study of ambient upstream material properties using perpendicular laser driven radiative blast waves in atomic cluster gases

We report on the characterisation of the upstream medium ahead of a radiative cylindrical blast wave launched in an argon cluster gas with a 1 J, 1 ps, 1054 nm Nd:Glass laser system. By launching two perpendicular blast waves and introducing a time delay between the heating beams it is possible to determine the extent of the cluster medium by observing the high energy absorption region associated with clusters, as apposed to the low energy deposition in monatomic gas. It was found that argon ions launched from the initial laser driven cluster ionisation created a ballistic ion wave which sweeps out ahead of the hydrodynamic blast wave at an initial velocity of 1000 kms⁻¹. This ballistic wave disassembles the clusters ahead of the blast wave into a neutral gas medium before the arrival of a radiative precursor. This observation gives us confidence that the dynamics of a radiative blast wave in cluster based experiments is determined primarily by the properties of an upstream atomic gas, and is not significantly influenced by cluster affects on energy transport or other material properties.     

Dynamic measurement of temperature, velocity, and density in hot jets using Rayleigh scattering

A molecular Rayleigh scattering technique is utilized to measure gas temperature, velocity, and density in unseeded gas flows at sampling rates up to 10 kHz, providing fluctuation information up to 5 kHz based on the Nyquist theorem. A high-power continuous-wave laser beam is focused at a point in an air flow field and Rayleigh scattered light is collected and fiber-optically transmitted to a Fabry–Perot interferometer for spectral analysis. Photomultiplier tubes operated in the photon counting mode allow high-frequency sampling of the total signal level and the circular interference pattern to provide dynamic density, temperature, and velocity measurements. Mean and root mean square velocity, temperature, and density, as well as power spectral density calculations, are presented for measurements in a hydrogen-combustor heated jet facility with a 50.8-mm diameter nozzle at NASA John H. Glenn Research Center at Lewis Field. The Rayleigh measurements are compared with particle image velocimetry data and computational fluid dynamics predictions. This technique is aimed at aeronautics research related to identifying noise sources in free jets, as well as applications in supersonic and hypersonic flows where measurement of flow properties, including mass flux, is required in the presence of shocks and ionization occurrence.