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.     

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.     

Simulation of laser-driven,ablated plasma flows in collisionless shock experiments on OMEGA and the NIF

Experiments investigating the physics of interpenetrating, collisionless, ablated plasma flows have become an important area of research in the high-energy-density field. In order to evaluate the feasibility of designing experiments that will generate a collisionless shock mediated by the Weibel instability on the National Ignition Facility (NIF) laser, computer simulations using the Center for Radiative Shock Hydrodynamics (CRASH) radiation-hydrodynamics model have been carried out. This paper reports assessment of whether the experiment can reach the required scale size while maintaining the low interflow collisionality necessary for the collisionless shock to form. Comparison of simulation results with data from Omega experiments shows the ability of the CRASH code to model these ablated systems. The combined results indicate that experiments on the NIF are capable of reaching the regimes necessary for the formation of a collisionless shock in a laboratory experiment.     

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.     

Diagnosing laser-driven,shock-heated foam target with Al absorption spectroscopy on OMEGA EP

Results on diagnoses of laser-driven, shock-heated foam plasma with time-resolved Al 1s-2p absorption spectroscopy are reported. Experiments were carried out to produce a platform for the study of relativistic electron transport. In cone-guided Fast Ignition (FI), relativistic electrons generated by a high-intensity, short-pulse igniter beam must be transported through a cone tip to an imploded core. Transport of the energetic electrons could be significantly affected by the temperature-dependent resistivity of background plasmas. The experiment was conducted using four UV beams of the OMEGA EP laser at the Laboratory For Laser Energetics. One UV beam (1.2 kJ, 3.5 ns square) was used to launch a shock wave into a foam package target, consisting of 200 mg/cm³ CH foam with aluminum dopant and a solid plastic container surrounding the foam layer. The other three UV beams with the total energy of 3.2 kJ in 2.5 ns pulse duration were tightly focused onto a Sm dot target to produce a point X-ray source in the energy range of 1.4–1.6 keV. The quasi-continuous X ray signal was transmitted through the shock-heated Al-doped, foam layer and recorded with an X-ray streak camera. The measured 1s-2p Al absorption features were analyzed using an atomic physics code FLYCHK. Electron temperature of 40 eV inferred from the spectral analysis is consistent with 2-D DRACO Radiation-hydrodynamic simulations.     

Comparison between Kelvin–Helmholtz instability experiments on OMEGA and simulation results using the CRASH code

The Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan has developed a Eulerian radiation-hydrodynamics code with dynamic adaptive mesh refinement, CRASH, which can model high-energy-density laser-driven experiments. One of these experiments, performed previously on the OMEGA laser facility, was designed to produce and observe the Kelvin–Helmholtz instability. The target design included low-density carbonized-resorcinol-formaldehyde (CRF) foam layered on top of polyamide–imide plastic, with a sinusoidal perturbation on the interface and with the assembled materials encased in beryllium. The results of a series of CRASH simulations of these Kelvin–Helmholtz instability experiments are presented. These simulation results show good agreement both quantitatively and qualitatively with the experimental data.     

X-ray amplification in intense ultrashort KrF laser–Xe cluster interactions

In earlier work, a time-dependent, ionization dynamic model of a cluster of xenon atoms was constructed [2], [3] in an effort to determine conditions under which the X-ray line amplification data that was observed experimentally at wavelengths between 2.71 and 2.88 Å [1] could be replicated. Model calculations showed that, at laser intensities greater than 10¹⁹ W/cm², the outermost N-shell electrons of xenon would be stripped away by tunnel ionization in less than a femtosecond. They also showed that L-shell electrons within the resulting cluster of Ni-like ions could be photoionized at a sufficient rate as to generate population inversions between these hole states and the states they radiatively decayed into. These inversions only lasted for several femtoseconds, and they were generated early in time when the cluster was being rapidly heated and the cluster's density was rapidly evolving, but was still high. They were seen to depend on the heating and expansion dynamics of the cluster, which had not been modeled in detail in this early work. In this paper, molecular dynamics calculations are described in which the rapidly evolving temperatures and ion densities of an intensely laser-heated cluster are calculated for different peak laser intensities and for two different sized xenon nano-clusters. This data is then used as an input to the ionization dynamic calculations in order to determine the influence of cluster size and of peak laser intensity on the gain coefficient calculations. In these calculations, inner-shell photoionization rates are shaped by the temperature and density dependence of the bremsstrahlung emissions under the assumption that these emissions drive the photoionizations. This shaping produces calculated gain coefficients that agree well with the measured ones.     

X-ray Thomson scattering on shocked graphite

We present measurements of the changes in the microscopic structure of graphite in a laser-driven shock experiment with X-ray scattering. Laser radiation with intensities of ∼2 × 10¹³ W/cm² compressed the carbon samples by a factor of two reaching pressures of ∼90 GPa. Due to the change of the crystalline structure the scattered signals of the probe radiation were modified significantly in intensity and spectral composition compared to the scattering on cold samples. It is shown that the elastic scattering on tightly bound electrons increases strongly due to the phase transition whereas the inelastic scattering on weakly bound electrons remains nearly unchanged for the chosen geometry.     

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.     

Navier–Stokes Computations in Micro Shock Tubes

Micro shock tube flows were simulated using unsteady 2D Navier–Stokes equations combined with boundary slip velocities and temperature jumps conditions. These simulations were performed using the parallel version of a multi-block finite-volume home code. Different initial low pressures and shock tube diameters allow to have the scaling ratio ReD/4L vary. The numerical results show a strong attenuation of the shock wave strength with a decrease of the hot flow values along the tube. When the scaling ratio decreases the shock waves can transform into compression waves. Comparison to the existing 1D models also shows the limit of these models.     

Design of short pulse laser driven opacity experiments

Hot electrons created by short, intense laser pulses can heat solid density material to temperatures of order 500 eV. Inertial confinement can maintain such hot-dense plasmas for times of order 10 ps. This provides a platform for measurement of basic properties of hot dense matter, such as opacity and equation-of-state. In this paper we describe the role of computational modeling in the design and analysis of such opacity experiments. We describe a method to model the hot electron transport and deposition and the resulting target radiation-hydrodynamics. We present several design concepts to achieve uniform, long-lasting plasmas.     

Atomic modeling of the plasma EUV sources

We present the development of population kinetics models for tin plasmas that can be employed to design an EUV source for microlithography. The atomic kinetic code is constrained for the requirement that the model must be able to calculate spectral emissivity and opacity that can be used in radiation hydrodynamic simulations. Methods to develop compact and reliable atomic model with an appropriate set of atomic states are discussed. Specifically, after investigation of model dependencies and comparison experiment, we improve the effect of configuration interaction and the treatment of satellite lines. Using the present atomic model we discuss the temperature and density dependencies of the emissivity, as well as conditions necessary to obtain high efficiency EUV power at λ = 13.5 nm.     

A plasma wiggler beamline for 100 TW to 10 PW lasers

We introduce the theoretical framework of laser wakefield acceleration and plasma wiggler radiation generation in the matched regime, give scaling laws and apply the scheme to laser systems planned for the near future. We compare the anticipated electron and x-ray beam parameters for a 100 TW, 1 PW and 10 PW short pulse Ti:Sapphire laser with previous experimental results. Depending on the chosen laser configuration, x-rays from a plasma wiggler beamline (PWB) can be several orders of magnitude brighter than current betatron sources, and comparable to or better than 3rd generation synchrotron facilities. Furthermore, increasing the laser power from 0.1 to 10 PW, the spectral peak of the betatron radiation shifts into the hard x-ray and γ-ray regime. We also discuss a basic layout of a PWB and motivate 100 TW, 1 PW and 10 PW beamlines with a wide range of uses, experiments and applications. The ability to couple the PWBs with various optical laser drivers has the potential to facilitate uses across the spectrum of light source applications.     

Experimental investigation of plastic finned-tube heat exchangers,with emphasis on material thermal conductivity

In this paper, two modified types of polypropylene (PP) with high thermal conductivity up to 2.3 W/m K and 16.5 W/m K are used to manufacture the finned-tube heat exchangers, which are prospected to be used in liquid desiccant air conditioning, heat recovery, water source heat pump, sea water desalination, etc. A third plastic heat exchanger is also manufactured with ordinary PP for validation and comparison. Experiments are carried out to determine the thermal performance of the plastic heat exchangers. It is found that the plastic finned-tube heat exchanger with thermal conductivity of 16.5 W/m K can achieve overall heat transfer coefficient of 34 W/m² K. The experimental results are compared with calculation and they agree well with each other. Finally, the effect of material thermal conductivity on heat exchanger thermal performance is studied in detail. The results show that there is a threshold value of material thermal conductivity. Below this value improving thermal conductivity can considerably improve the heat exchanger performance while over this value improving thermal conductivity contributes very little to performance enhancement. For the finned-tube heat exchanger designed in this paper, when the plastic thermal conductivity can reach over 15 W/m K, it can achieve more than 95% of the titanium heat exchanger performance and 84% of the aluminum or copper heat exchanger performance with the same dimension.     

Modelling of transient Ni-like silver X-ray lasers

We have modelled an experiment performed at the LULI facility (Ecole Polytechnique, Palaiseau, France). This experiment was devoted to the measurement of the temporal coherence of the transient Ni-like silver X-ray laser at the wavelength of 13.9 nm.In population kinetics studies of saturated lasers, it is necessary to account for the interaction between the X-ray laser electric field and the lasing ions. To this end, we have used the Maxwell–Bloch formalism in the paraxial approximation. The Zeeman sublevels (JM) associated with the lower lasing level (J = 1) are not identically affected by the X-ray laser field. As a result, their populations are different. However, elastic collisions between free electrons and lasing ions have the opposite effect: they tend to restore equilibrium between the sublevel populations. Therefore, elastic collision rates obtained in the distorted wave approximation have been included in the rate equations. Refraction of the X-ray beam, due to electron density gradients, is taken into account by using a ray-trace code which works as a post-processor of the hydro-code EHYBRID.We have checked that the Voigt profile is a good approximation for lasing lines in Ni-like ions. This allowed us to implement a subroutine calculating the Voigt profile in the Maxwell–Bloch code.Whilst the FWHM of the spontaneous emission profile is 12 mÅ, the amplified X-ray line shows a smaller width of 3 mÅ. This is known as the gain narrowing effect. We notice the saturation of the line-width for a propagation length of 2–3 mm. Comparison with experiment is discussed.     

Shock tube studies of thermal radiation of diesel-spray combustion under a range of spray conditions

A tailored interface shock tube and an over-tailored interface shock tube were used to measure the thermal energy radiated during diesel-spray combustion of light oil, α-methylnaphthalene and cetane by changing the injection pressure. The ignition delay of methanol and the thermal radiation were also measured. Experiments were performed in a steel shock tube with a 7 m low-pressure section filled with air and a 6 m high-pressure section. Pre-compressed fuel was injected through a throttle nozzle into air behind a reflected shock wave. Monochromatic emissive power and the power emitted across all infrared wavelengths were measured with IR-detectors set along the central axis of the tube. Time-dependent radii where soot particles radiated were also determined, and the results were as follows. For diesel spray combustion with high injection pressures (from 10 to 80 MPa), the thermal radiation energy of light oil per injection increased with injection pressure from 10 to 30 MPa. The energy was about 2% of the heat of combustion of light oil at P _inj = about 30 MPa. At injection pressure above 30 MPa the thermal radiation decreased with increasing injection pressure. This profile agreed well with the combustion duration, the flame length, the maximum amount of soot in the flame, the time-integrated soot volume and the time-integrated flame volume. The ignition delay of light oil was observed to decrease monotonically with increasing fuel injection pressure. For diesel spray combustion of methanol, the thermal radiation including that due to the gas phase was 1% of the combustion heat at maximum, and usually lower than 1%. The thermal radiation due to soot was lower than 0.05% of the combustion heat. The ignition delays were larger (about 50%) than those of light oil. However, these differences were within experimental error.

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An abridged version of this paper was presented at the 18th Int. Symposium on Shock Waves at Sendai, Japan during July 21 to 26, 1991 and at the 19th Int. Symposium on Shock Waves at Marseille, France during July 26 to 30, 1993.     

A computational study of shock speeds in high-performance shock tubes

This paper describes U2DE, a finite-volume code that numerically solves the Euler equations. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm in a shock tube. From the simulations, the speed of the developing shock wave was recorded and compared with other estimates. The ability of U2DE to compute shock speed was confirmed by comparing numerical results with the analytic solution for an ideal shock tube. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one-dimensional models. The shock speeds computed with the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and, thus, were closer to the experimental measurements. This indicates that multi-dimensional flow effects were partly responsible for the relatively high shock speeds measured in the experiments. Received 15 November 1996 / Accepted 3 February 1997