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.     

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.     

Studying astrophysical collisionless shocks with counterstreaming plasmas from high power lasers

Collisions of high Mach number flows occur frequently in astrophysics, and the resulting shock waves are responsible for the properties of many astrophysical phenomena, such as supernova remnants, Gamma Ray Bursts and jets from Active Galactic Nuclei. Because of the low density of astrophysical plasmas, the mean free path due to Coulomb collisions is typically very large. Therefore, most shock waves in astrophysics are “collisionless”, since they form due to plasma instabilities and self-generated magnetic fields. Laboratory experiments at the laser facilities can achieve the conditions necessary for the formation of collisionless shocks, and will provide a unique avenue for studying the nonlinear physics of collisionless shock waves. We are performing a series of experiments at the Omega and Omega-EP lasers, in Rochester, NY, with the goal of generating collisionless shock conditions by the collision of two high-speed plasma flows resulting from laser ablation of solid targets using ∼10¹⁶ W/cm² laser irradiation. The experiments will aim to answer several questions of relevance to collisionless shock physics: the importance of the electromagnetic filamentation (Weibel) instabilities in shock formation, the self-generation of magnetic fields in shocks, the influence of external magnetic fields on shock formation, and the signatures of particle acceleration in shocks. Our first experiments using Thomson scattering diagnostics studied the plasma state from a single foil and from double foils whose flows collide “head-on”. Our data showed that the flow velocity and electron density were 10⁸ cm/s and 10¹⁹ cm⁻³, respectively, where the Coulomb mean free path is much larger than the size of the interaction region. Simulations of our experimental conditions show that weak Weibel mediated current filamentation and magnetic field generation were likely starting to occur. This paper presents the results from these first Omega experiments.     

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.     

Bow shocks formed by plasma collisions in laser irradiated semi-cylindrical cavities

The formation of shocks in plasmas created by short pulse laser irradiation (λ = 800 nm, I ≈ 1 × 10¹² W cm^?2) of semi-cylindrical cavities of different materials was studied combining visible and soft X-ray laser interferometry with simulations. The plasma rapidly converges near the axis to form a dense bright plasma focus. Later in time a long lasting bow shock is observed to develop outside the cavity, that is shown to arise from the collision of plasmas originating from within the cavity and the surrounding flat walls of the target. The shock is sustained for tens of nanoseconds by the continuous arrival of plasma ablated from the target walls. The plasmas created from the heavier target materials evolve more slowly, resulting in increased shock lifetimes.     

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.     

Shock wave-induced vortex loops emanating from nozzles with singular corners

The focus of the current study is to examine experimentally the diffracted shock wave pattern and the consequent vortex loop formation, propagation, and decay from nozzles having singular corners. Non-intrusive qualitative and quantitative techniques: schlieren, shadowgraphy, and particle image velocimetry (PIV) are employed to analyze the induced flow-fields. Eye-shaped nozzles were used with the corner joints representing singularities. The length of the minor axes are a = 6 and 15 mm, with the major axis b = 30 mm for both cases. The experiments are performed for flow Reynolds numbers in the range 0.8 × 10⁵ and 4.6 × 10⁵. Air is used in both driver and driven sections of the shock tube.     

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.      

High-resolution 22–52 keV backlighter sources and application to X-ray radiography

The requirement for sources of hard X-rays suitable for high resolution radiography through large ρR targets is prominent in many aspects of current laser-driven plasma physics research. In recent work using the OMEGA EP laser facility [L. J. Waxer, M. J. Guardalben, J. H. Kelly et al., CLEO/QELS, Optical Society of America, San Jose, CA, IEEE (2008)] at the Laboratory for Laser Energetics (LLE) in Rochester, NY, experiments have been performed to measure characteristics of 22–52 keV X-ray sources using high intensity short-pulse lasers. High quality point projection, two-dimensional radiography was demonstrated by irradiating microwire targets with laser intensities of 10¹⁶ W cm^?2–10¹⁹ W cm^?2. Microwire targets were manufactured to dimensions of 10 μm × 10 μm × 300 μm and were supported by a 100 μm × 300 μm × 6 μm low-Z substrate. Measurements of the k–α conversion efficiency and X-ray source-size are discussed and, of particular importance for radiography, the spectral purity of the backlighter is characterized to assess the relative importance of the Kα emission to bremsstrahlung background.     

Atomic physics of relativistic high contrast laser-produced plasmas in experiments on Leopard laser facility at UNR

The results of the recent experiments focused on study of x-ray radiation from multicharged plasmas irradiated by relativistic (I > 10¹⁹ W/cm²) sub-ps laser pulses on Leopard laser facility at NTF/UNR are presented. These shots were done under different experimental conditions related to laser pulse and contrast. In particular, the duration of the laser pulse was 350 fs or 0.8 ns and the contrast was varied from high (10^?7) to moderate (10^?5). The thin laser targets (from 4 to 750 μm) made of a broad range of materials (from Teflon to iron and molybden to tungsten and gold) were utilized. Using the x-ray diagnostics including the high-precision spectrometer with resolution R ～ 3000 and a survey spectrometer, we have observed unique spectral features that are illustrated in this paper. Specifically, the observed L-shell spectra for Fe targets subject to high intensity lasers (～10¹⁹ W/cm²) indicate electron beams, while at lower intensities (～10¹⁶ W/cm²) or for Cu targets there is much less evidence for an electron beam. In addition, K-shell Mg features with dielectronic satellites from high-Rydberg states, and the new K-shell F features with dielectronic satellites including exotic transitions from hollow ions are highlighted.     

Shocks in local supersonic zones

The results of numerical integration of the Euler equations governing two-dimensional and axisymmetric flows of an ideal (inviscid and non-heat-conducting) gas with local supersonic zones are presented. The subject of the study is the formation of shocks closing local supersonic zones. The flow in the vicinity of the initial point of the closing shock is calculated on embedded, successively refined grids with an accuracy much greater than that previously achieved. The calculations performed, together with the analysis of certain controversial issues, leave no doubt that it is the intersection of C ^?-characteristics proceeding from the sonic line inside the supersonic zone that is responsible for the closing shock formation.     

Optimization of Conical Wings in Hypersonic Flow

A method of calculation is presented to determine conical wing shapes that minimize the coefficient of (wave) drag, C _D, for a fixed coefficient of lift, C _L, in steady, hypersonic flow. An optimization problem is considered for the compressive flow underneath wings at a small angle of attack δ and at a high free-stream Mach number M _∞ so that hypersonic small-disturbance (HSD) theory applies. A figure of merit, F=C _D/C _L ^3/2, is computed for each wing using a finite volume discretization of the HSD equations. A set of design variables that determine the shape of the wing is defined and adjusted iteratively to find a shape that minimizes F for a given value of the hypersonic similarity parameter, H= (M _∞δ)⁻², and planform area. Wings with both attached and detached bow shocks are considered. Optimal wings are found for flat delta wings and for a family of caret wings. In the flat-wing case, the optima have detached bow shocks while in the caret-wing case, the optimum has an attached bow shock. An improved drag-to-lift performance is found using the optimization procedure for curved wing shapes. Several optimal designs are found, all with attached bow shocks. Numerical experiments are performed and suggest that these optima are unique. Received 1 May 1998 and accepted 14 October 1998     

Isochoric heating of reduced mass targets by ultra-intense laser produced relativistic electrons

We present measurements of the chlorine K-alpha emission from reduced mass targets, irradiated with ultra-high intensity laser pulses. Chlorinated plastic targets with diameters down to 50 μm and mass of a few 10^?8 g were irradiated with up to 7 J of laser energy focused to intensities of several 10¹⁹ W/cm². The conversion of laser energy to K-alpha radiation is measured, and high-resolution spectra that allow observation of line shifts are observed, indicating isochoric heating of the target up to 18 eV. A zero-dimensional 2-temperature equilibration model, combined with electron impact K-shell ionization and post processed spectra from collisional radiative calculations reproduces the observed K-alpha yields and line shifts, and shows the importance of target expansion due to the hot electron pressure.     

Effect of the surface thermal radiation on turbulent natural convection in tall cavities of façade elements

The effect of the surface thermal radiation in tall cavities with turbulent natural convection regime was analyzed and quantified numerically. The parameters considered were: the Rayleigh number 10⁹–10¹², the aspect ratio 20, 40 and 80 and the emmisivity 0.0–1.0. The percentage contribution of the radiative surface to the total heat transfer has a maximum value of  15.19% (Ra = 10⁹, A = 20) with emissivity equal to 1.0 and a minimum of 0.5% (Ra = 10¹², A = 80) with ε* = 0.2. The average radiative Nusselt number for a fixed emissivity is independent of the Rayleigh number, but for a fixed Rayleigh number diminishes with the increase of the aspect ratio. The results indicate that the surface thermal radiation does not modify significantly the flow pattern in the cavity, just negligible effects in the bottom and top of the cavity were observed. Two different temperature patterns were observed a conductive regime Ra = 10⁹ and a boundary layer regime Ra = 10¹².     

An experimental and theoretical study of converging polygonal shock waves

An experimental investigation was carried out to explore the possibility of producing converging polygonal shocks in an essentially two-dimensional cavity. Previous calculations by Apazidis and Lesser (1996) suggested that such configurations could be produced by reflecting a cylindrical outgoing shock from a smoothly altered circular boundary, the alteration having n-gonal symmetry. In the experiments the outgoing shock was produced by a spark discharge which yielded shocks in the Mach number range from 1.1 to 1.7 at a radius just prior to the reflection. Polygonal shocks were observed as predicted by using a modified form of geometrical shock dynamics, derived in the above paper. In addition, the modified theory was used to calculate the results of an experiment carried out by Sturtevant and Kulkarny (1976). The results of the numerical calculations were found to be in substantial agreement with both experiments, suggesting that the modifications in geometrical shock dynamics for non-uniform flow ahead of an advancing shock are useful in the case of shock focusing. The experiment also showed that the polygonal shapes were stable in the examined range of shock Mach numbers, a result that may be of importance for a number of practical situations in which shock focusing is present. Received 9 October 2001 / Accepted 7 January 2002 – Published online 11 June 2002     

Kinetic simulations of the heating of solid density plasma by femtosecond laser pulses

Experiments have been performed in which fs-timescale laser pulses, focused to an intensity ～10¹⁶ W cm^?2, are able to directly create and interact with solid density plasma (1). We have performed one-dimensional simulations of the experiments with a kinetic model which solves Maxwell's equations coupled to the Fokker–Planck equation enabling us to self-consistently model the non-local heat flow and absorption process. We find that the heat-flux is magnetized by the laser field and is inhibited relative to the Spitzer value.     

Measurements of turbulent mixing due to Kelvin–Helmholtz instability in high-energy-density plasmas

Kelvin–Helmholtz (KH) turbulent mixing measurements were performed in experiments on the OMEGA Laser Facility [T.R. Boehly et al., Opt. Commun. 133 (1997) 495]. In these experiments, laser-driven shock waves propagated through low-density plastic foam placed on top of a higher-density plastic foil. Behind the shock front, lower-density foam plasma flowed over the higher-density plastic plasma. The interface between the foam and plastic was KH unstable. The experiments were performed with pre-imposed, sinusoidal 2D perturbations, and broadband 3D perturbations due to surface roughness at the interface between the plastic and foam. KH instability growth was measured using X-ray, point-projection radiography. The mixing layer caused by the KH instability with layer width up to ～100 μm was observed at a location ～1 mm behind the shock front. The measured mixing layer width was in good agreement with simulations using a K–L turbulent mixing model in the two-dimensional ARES hydrodynamics code. In the definition of the K–L model K stands for the specific turbulent kinetic (K) energy, and L for the scale length (L) of the turbulence.     

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.     

Plasma jets produced by low energy laser pulse interaction with planar and cratered targets

Laser experiments of the plasma jet formation using nanosecond laser pulses with low energy, i.e., <20 J, are presented. Planar and cratered gadolinium and aluminum targets are irradiated with laser intensities of several 10¹⁴ W/cm². Spatially-resolved time-integrated X-ray spectra were recorded in the spectral range from 7 to 10 Å. A jet-like structure is obtained from aluminum targets with a preformed crater, which is not seen in planar target irradiation. For gadolinium, a jet is observed from both planar and preformed cratered targets, suggesting that the collimation is dominated by radiative cooling. A radiation-hydrodynamics code coupled to a non-LTE ionization code was used to model the plasma. The calculated plasma emission was found to be consistent with the experimental results.     

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.