Session BO6: Shock Waves, Plasma Expansion and Equations of State

Plasma expansion dynamics physics: An understanding on ion energy reduction process

This paper studies the expanding plasma dynamics of ions produced from a 5J Z-pinch xenon light source used for EUV lithography. Ion energy reduction is essential for the successful implementation of this technology. To aid this investigation, ion energy from a z-pinch DPP plasma source is measured using an ion energy analyzer and effect of introducing a small percentage of low Z material on the ion energy and flux is investigated. Presence of low mass such as H$_{2}$ or N$_{2}$, shows a considerable reduction in total flux and in average energy. For example, Xe$^{+}$ ion flux at 5 keV are recorded as 425 $\pm $ 42 ions/cm$^{2}$.eV.pulse at 157 cm and reduced to 125 $\pm $ 12 ions/cm$^{2}$.eV.pulse when using the low mass into the system at same energy. It is also noticed that such a combination leads to decrease in sputtering without changing the EUV output. Study of the possible mechanism supporting the experimental results is numerically calculated. This computational work indicates that the observed high energies of ions are probably resulting from coulomb explosion initiated by pinch instability. It is postulated that the electrons leave first setting up an electrostatic potential which accelerates the ions. The addition of small mass actually screens the potential and decorates the ions.   

Explosively Generated Plasmas in Noble Gases

Non-ideal plasmas occur as a result of the stimulation of matter by strong shocks, detonation waves, or concentrated laser irradiation. Since all of these methods of generating non-ideal plasmas are already in use to address other problems, we focus on a detailed understanding of this plasma. In particular, we study the generation of this plasma by strong, ionizing guided shock waves. The shock wave in the gas is generated by an explosive located at one end of a guide tube filled with a noble gas. The detonation produces a shock wave strong enough to ionize the gas. Spectral line emission profiles, recorded with a streak emission spectroscopy system, are used to ascertain neutral and ionized gas properties. The electric and magnetic fields are measured by electrostatic probes and magnetic induction coils which permit the measurement of the temperature, density, and electric potential of the non-ideal plasma; as well as the flow of net electric charges respectively. The results demonstrate there is a mixing of the detonation products and the noble gas and that there is a pulse of electrons that travel ahead of the shock wave as it travels down the guide tube.   

Numerical simulations of relativistic collisionless shocks and their radiation

Using 2.5D and 3D PIC codes, we simulate the collisions of relativistic electron-positron and electron-ion plasmas with and without upstream background magnetic fields. We study the growth and saturation of Weibel and other instabilities, and the diffusive acceleration of high energy particles. Using post-processing codes we also compute the in-situ radiation output of the accelerated particles. We find that in general the radiation output of Weibel mediated shocks without upstream background magnetic fields is small. Shocks mediated by strong background fields tend to radiate more efficiently due to stronger coupling between the accelerated particles and penetrated fields. The structure of e-ion shocks is complicated by electron-ion charge separation, which transfers energy from high energy electrons to ions. Particle acceleration is facililated by both charge separation and Langmuir waves in this case.   

Two-dimensional effects on shock planarity in confined laser ablation

The ablation of solid material when illuminated with focused laser pulses is a common method for driving strong shocks into the target material and is typically treated as one-dimensional. The expansion and blow-off of the low-density, high-temperature coronal plasma has, however, non-axial flow components. In laser shock experiments, the plasma can be confined by a transparent substrate resulting in higher pressures and longer duration shock waves in the solid material for moderate laser energies. In an effort to understand the loading history and shock planarity in these targets to greater accuracy, numerical simulations have been carried out and compared to experimental velocity profiles. Two-dimensional continuum mechanics simulations have been carried out using high-temperature equations-of-state for C and Al. The laser energy is deposited into a thin layer of C or Al at the interface between a sapphire substrate and target material (Be) in a simplified manner without rigorously accounting for realistic laser-matter interactions. Variations in total energy and irradiance history on the loading are included in the study. Simulations are compared to one-dimensional radiation hydrodynamics calculations and possible improvements to the confined ablation target design are given.   

Turbulent Energy Analysis Behind Normal Ionizing Shock Waves

Using an Arc-Driven Shock Tube and Laser Induced Fluorescence, we measured the turbulent energy behind an ionizing shock wave in the presence of a weak axial magnetic field. Simultaneous density estimates were made from multiple points behind the flow. Two points measure density along the flow, while two additional points measure density across the flow. With the test gas held at constant pressure, it was determined that the turbulent energy increases linearly with increasing magnetic field strength. In contrast, the turbulent energy decreases with increasing pressure when the magnetic field is held constant. While the turbulent energy at the radial points are about the same, the strength of the turbulent energy at the axial points differ significantly from each other as well as from the radial points. This may be due to higher rates of radial diffusion towards the walls of the tube where recombination is greatest. In addition, the results of other turbulent parameters of interest will be discussed.   

Enhanced Signal to Noise in a Turbulent Laser Enhanced Laser Induced Plasma

A Nd-Yag pulsed laser created a plasma at a focal point in the path of a CW 1kW fiber laser beam. The CW fiber laser power increases in steps of 100W from 0W (CW fiber laser off) up to 1000W. The plasma is created in air. The optical emissions from this turbulent plasma were captured with two fiber optic cables and transmitted first to two monochrometers and ultimately to an ICCD and an oscilloscope. From the emissions of the plasma, the spectra of both the ionized and neutral lines can be captured using the ICCD. Both spectra are influenced as the power of the CW fiber laser increases. More specifically, the signal to noise ratio is systematically enhanced by the presence of the CW fiber laser beam in the path of the plasma.   

Experimental determination of the Plasmon dispersion in warm-dense Beryllium.

The dispersion of electron plasma waves is of fundamental interest as it determines optical properties of matter. We apply x-ray Thomson scattering to measure the Plasmon dispersion in a solid-density radiatively heated beryllium plasma. A 0.6 mm diameter beryllium cylinder was isochorically heated by x-rays produced by irradiation of a silver foil with laser pulses of up to 10 kJ of energy at a wavelength of 355 nm. The plasma is probed by chlorine Lyman-alpha line radiation at 2.96 keV, produced from chlorine containing plastic foils driven by 12 kJ of laser energy. The scattered probe radiation is spectrally resolved with a high efficiency gated crystal spectrometer in forward direction giving access to the collective scattering regime. By varying the probe source location various scattering angles have been accessed. The data are compared to the current high-density statistical plasma models.   

Nonequilibrium Conditions in a Shock Front

Recent measurements\footnote{ J. E. Miller \textit{et al}., ``Equation-of-State Measurements in Ta$_{2}$O$_{5}$ Aerogel,'' submitted to the Proceedings of AIP.} on shock waves propagating in Ta$_{2}$O$_{5}$ foams showed that the shock temperature did not rise with rising pressure. An explanation is that the electrons are not in equilibrium with the ions and their temperature rise lags behind the rapidly moving shock front. Results of hydrodynamic simulations that predict such behavior and provide calculations of optical transport that explain the observations are presented. Experimental methods that could be used to further diagnose this phenomenon will be discussed. This work was supported by U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-92SF19460.   

High pressure melt curve and yield strength of high-density carbon

Single and double shock temperature measurements have been used to map the melt curve of high-density carbon (diamond) from 6 to $\sim $23 Mbars. Combining temperature and Hugoniot measurements of the high-density fluid reveal carbon melts from the diamond phase to a chemically complex, perhaps polymeric carbon phase. Ultra-high density states of carbon well off of the diamond Hugoniot have been explored using ramp wave compression techniques. These ramp wave experiments have compressed carbon to the highest pressure solid ever studied and were used to map the stress strain of carbon to a stress of $\sim $ 10 Mbars. Finally, the yield strength of single, micro, and nano-crystalline carbon have been measured to several Mbars revealing an ultra-high, rate-dependent, and orientation dependent elastic limit ranging between 60 and 200 GPa. These measurements have been used to constrain equation of state and strength models used for designing ICF capsules with high-density carbon ablators.   

Design for LTE EOS and opacity experiments using supersonic radiation waves

Opacity and EOS at 100-200 eV are important physical parameters in ICF experiments. We describe an experiment design that uses the supersonic propagation of hohlraum radiation in foams to isochorically heat samples. Laser and Z-pinch experiments frequently use 150 to 220-eV quasi-blackbody emission from hohlraums to drive physics experiments. A foam target encapsulated in a gold-wall cylinder is placed next to the hohlraum. The low density and opacity foam captures some hohlraum emission and generates a supersonically-propagating radiation wave. The material heated by the wave is cooler towards the high-albedo gold wall. Modeling and past measurements show that core regions of the foam have small thermal gradients. We place a small, thin sample (e.g., Al, Si, or Fe) in the thermally-uniform region. X-ray emission of tracers and the sample as well as quasi-continuum x-ray absorption will be measured using time-resolved x-ray spectroscopy. The foam's EOS can be measured to $\pm $5{\%} by blast waves with a well characterized drive. This experiment could use the OMEGA, Z-Beamlet, and/or ZR facilities to explore temperature-dependent conditions.   

Wide-Range Equation of State for Ablation Studies of Titanium

An equation of state (EOS) for Ti was constructed using electronic structure calculations, based on the plane-wave pseudopotential method for condensed phases and the atom-in-jellium method in other states. The EOS was adjusted to match the observed STP state using a pressure correction which extrapolates correctly to zero density. The predicted principal shock Hugoniot was in good agreement with impact-induced shock measurements. The EOS was used to simulate ablative loading experiments on rolled foils of Ti at the TRIDENT. Laser ablation generated states in the warm dense matter regime. The measured free surface velocity histories exhibited multiple wave structures indicative of plastic flow and the alpha-omega phase transition. Estimates of the flow stress and the phase transition pressure on nanosecond time scales were obtained.   

{\sl ab initio} Molecular Dynamics simulations of dense boron plasmas up to the semiclassical Thomas Fermi regime

We have performed {\sl ab initio} simulations of dense boron along the 1 and 4 eV isotherms [1], starting from the regime where quantum mechanical effects are important to the regime where semiclassical simulations based on the Thomas Fermi approach are, by default, the only simulation method currently available. To overcome the limitations of {\sl ab initio} simulations at high density, we have build an ``all electron'' norm conserving pseudopotential for boron which allows simulations up to 50 times the normal density, $\rho_0$. We show that, at high pressure, all electrons {\sl ab initio} simulations are necessary to get a correct pressure, which is in close agreement with the one given by the, much faster, Thomas-Fermi molecular dynamics method [2].We further compare the Kubo-Greenwood and the Ziman formulations for the electrical conductivity. \newline \newline [1] S. Mazevet et al. PRE {\bf 75}, 056404 (2007). \newline [2] F. Lambert et al. PRE {\bf 73}, 016403 (2006).   

On and off Hugoniot measurements of aluminum using laser driven shock wave

We performed absolute Hugoniot measurements on one of the most important metal, aluminum as a standard material. Shock and particle velocities were simultaneously measured with a side-on x-ray backlighting technique. The pressure was reached up to around 2 TPa. To know the off-Hugoniot properties, we also performed reflected shock experiments. Using copper and tantalum anvils, the Al reflected shock states were obtained in TPa pressure regime. The difference between shock reflection curves from some models is discussed.   

The EOSTA model for opacities and EOS calculations

The EOSTA model developed recently combines the STA and INFERNO models to calculate opacities and EOS on the same footing. The quantum treatment of the plasma continuum and the inclusion of the resulted shape resonances yield a smooth behavior of the EOS and opacity global quantities vs density and temperature. We will describe the combined model and focus on its latest improvements. In particular we have extended the use of the special representation of the relativistic virial theorem to obtain an exact differential equation for the free energy. This equation, combined with a boundary condition at the zero pressure point, serves to advance the LDA EOS results significantly. The method focuses on applicability to high temperature and high density plasmas, warm dens matter etc. but applies at low temperatures as well treating fluids and even solids. Excellent agreement is obtained with experiments covering a wide range of density and temperature. The code is now used to create EOS and opacity databases for the use of hydro-dynamical simulations.   

Transient Formation of Super-Explosives under High Pressure for Fast Ignition.

Dense matter, if put under high pressure, can undergo a transformation from an atomic to a molecular configuration, where the electron orbits go into lower energy levels. If the rise in pressure is very sudden, for example by a strong shock wave, the electrons change their orbits rapidly under the emission of photons, which for more than 100 megabar can reach keV energies. With the opacity of dense matter going in proportion to the square of the density, the photons can be efficiently released from the surface of the compressed matter by a rarefaction wave. The thusly produced X-ray photons can be used for the fast ignition of a thermonuclear target. Since as for thermite, the conjectured super-explosives are likely to come from the reaction between two different atoms, they should be made from a mixture of nanoparticles. The proposed mechanism may be also responsible for the large keV X-ray bursts in exploding wire arrays, which can not be explained by a simple kinetic into thermal energy conversion model.