Fluctuations and the ionization potential in dense plasmas

A semi-analytic model is developed to estimate continuum lowering in dense plasmas including fluctuations. The model is applied to aluminum and compared with recent experiments at the Linac Coherent Light Source [O. Ciricosta et al., Phys. Rev. Lett. 109 (2012) 065002] that reported the ionization potential depression of K-shell electrons in solid density aluminum at temperatures up to 180 eV. The analysis suggests fluctuations, which are neglected in most continuum lowering models but are essential to describe energy absorption by a system, are sufficiently large to impact the interpretation of the experimental results.     

Multi-electron-recombination rates estimated within dense plasmas

We investigate the rates for multielectron recombination within a dense plasma with Maxwellian electron energy distribution function. We find that these rates can be high within dense plasmas, and they should be treated in the simulations of the plasmas created by intense radiation, in particular for plasmas created by intense VUV radiation from free-electron-laser (FEL), or for modeling the inertial confinement fusion (ICF) plasmas.     

Collision operator including large-angle scattering for moderately coupled plasma

A new approach has been developed to treat the large-angle as well as the small-angle binary collisions in high temperature and high density plasmas when the test particle distribution function f_α is even function about the test velocity and the relations of the mass and the velocity between the test particles and the field particles are satisfied with m_αm_β (such as electron–ion collision or Lorentz-gas model) and . With the approach, the Boltzmann collision operator is derived to be suitable for the plasma considered as weakly coupled (Coulomb logarithm ) and moderately coupled , i.e., for the electron–ion coupling constant Γ_ei<0.1. The modified collision operator has a direct and practical connection to the Rosenbluth potentials, the new reduced electron–ion collision operator differs from the original Fokker–Planck operator for Coulomb collisions by terms of order . Moreover, some calculations of relaxation rate and transport properties are given for new reduced electron–ion collision operator that shows corrections.     

Dense plasma X-ray scattering: Methods and applications

We have developed accurate x-ray scattering techniques to measure the physical properties of dense plasmas. Temperature and density are inferred from inelastic x-ray scattering data whose interpretation is model-independent for low to moderately coupled systems. Specifically, the spectral shape of the non-collective Compton scattering spectrum directly reflects the electron velocity distribution. In partially Fermi-degenerate systems that have been investigated experimentally in laser shock-compressed beryllium, the Compton scattering spectrum provides the Fermi energy and hence the electron density. We show that forward scattering spectra that observe collective plasmon oscillations yield densities in agreement with non-collective Compton scattering. In addition, electron temperatures inferred from the dispersion of the plasmon feature are consistent with the ion temperature sensitive elastic scattering feature. Hence, theoretical models of the static ion–ion structure factor and consequently the equation of state of dense matter can be directly tested.     

FLYCHK: Generalized population kinetics and spectral model for rapid spectroscopic analysis for all elements

FLYCHK is a straightforward, rapid tool to provide ionization and population distributions of plasmas in zero dimension with accuracy sufficient for most initial estimates and in many cases is applicable for more sophisticated analysis. FLYCHK solves rate equations for level population distributions by considering collisional and radiative atomic processes. The code is designed to be straightforward to use and yet is general enough to apply for most laboratory plasmas. Further, it can be applied for low-to-high Z ions and in either steady-state or time-dependent situations. Plasmas with arbitrary electron energy distributions, single or multiple electron temperatures can be studied as well as radiation-driven plasmas. To achieve this versatility and accuracy in a code that provides rapid response we employ schematic atomic structures, scaled hydrogenic cross-sections and read-in tables. It also employs the jj configuration averaged atomic states and oscillator strengths calculated using the Dirac–Hartree–Slater model for spectrum synthesis. Numerous experimental and calculational comparisons performed in recent years show that FLYCHK provides meaningful estimates of ionization distributions, well within a charge state for most laboratory applications.     

The effects of ionization potential depression on the spectra emitted by hot dense aluminium plasmas

Recent experiments at the Linac Coherent Light Source (LCLS) X-ray Free-Electron-Laser (FEL) have demonstrated that the standard model used for simulating ionization potential depression (IPD) in a plasma (the Stewart–Pyatt (SP) model, J.C. Stewart and K.D. Pyatt Jr., Astrophysical Journal 144 (1966) 1203) considerably underestimates the degree of IPD in a solid density aluminium plasma at temperatures up to 200 eV. In contrast, good agreement with the experimental data was found by use of a modified Ecker–Kröll (mEK) model (G. Ecker and W. Kröll, Physics of Fluids 6 (1963) 62–69). We present here detailed simulations, using the FLYCHK code, of the predicted spectra from hot dense, hydrogenic and helium-like aluminium plasmas ranging in densities from 0.1 to 4 times solid density, and at temperatures up to 1000 eV. Importantly, we find that the greater IPDs predicted by the mEK model result in the loss of the n = 3 states for the hydrogenic ions for all densities above ≈0.8 times solid density, and for the helium-like ions above ≈0.65 solid density. Therefore, we posit that if the mEK model holds at these higher temperatures, the temperature of solid density highly-charged aluminium plasmas cannot be determined by using spectral features associated with the n = 3 principal quantum number, and propose a re-evaluation of previous experimental data where high densities have been inferred from the spectra, and the SP model has been used.     

The effect of bound states on X-ray Thomson scattering for partially ionized plasmas

X-ray Thomson scattering is being developed as a method to measure the temperature, electron density, and ionization state of high energy density plasmas such as those used in inertial confinement fusion. X-ray laser sources have always been of interest because of the need to have a bright monochromatic X-ray source to overcome plasma emission and eliminate other lines in the background that complicate the analysis. With the advent of the X-ray free electron laser (X-FEL) at the SNAL Linac Coherent Light Source (LCLS) and other facilities coming online worldwide, we now have such a source available in the keV regime. An important challenge with X-ray Thomson scattering experiments is understanding how to model the scattering for partially ionized plasmas. Most Thomson scattering codes used to model experimental data greatly simplify or neglect the contributions of the bound electrons to the scattered intensity. In this work we take the existing models of Thomson scattering that include elastic ion–ion scattering and inelastic electron–electron scattering and add the contribution of bound electrons in the partially ionized plasmas. Except for hydrogen plasmas, most plasmas studied today have bound electrons and it is important to understand their contribution to the Thomson scattering, especially as new X-ray sources such as an X-FEL will allow us to study much higher Z plasmas. To date, most experiments have studied hydrogen or beryllium plasmas. We first analyze existing experimental data for beryllium to validate the code. We then consider several higher Z materials such as Cr and predict the existence of additional peaks in the scattering spectrum that require new computational tools to understand. For a Sn plasma, we show that bound contributions change the shape of the scattered spectrum in a way that would change the plasma temperature and density inferred from experiment.     

The quantum hypernetted chain model of warm dense matter

Modeling warm dense matter, where a combination of partial ionization, partial electron degeneracy, and strong ion–ion and ion–electron coupling occur, is a frontier of equation of state research. We present the quantum hypernetted chain model which can be applied to studies of liquid metals, warm dense matter, and plasmas. This is an all-electron model that considers a mixture of a classical fluid of ions (with bound electrons) and a quantum electron fluid. The model describes self-consistently the structure of the ion fluid as well as the bound states of the ions and the non-linear response of the electron fluid. We present our initial results and compare them with experimental and ab initio results for liquid metals and low-temperature plasmas.     

Approximate solution of the problem of the bottom zone in a rarefied gas

The problem of the steady-plane monatomic rarefied gas flow around a semiinfinite bar is considered (the plane stationary case of the problem about the bottom zone). The problem is solved numerically at the level of the Krook relaxation model [1, 2]. A depenence of the gas density, velocity, and temperature in the whole flow domain on the space coordinates is obtained for supersonic and subsonic gas streams flowing around a body by using calculations on an M-20 electronic calculator.Khar'kov. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 139–143, January–February, 1972.     

From global dynamical models to the Hénon–Heiles potential

We present a global non-galactic dynamical model reducing to the Hénon–Heiles potential. Expanding the global model in the vicinity of a circular orbit, we find the potential of a two-dimensional perturbed harmonic oscillator which can give the Hénon–Heiles potential for certain values of the parameters of the global model. Our numerical calculations suggest that the properties of motion in the global model are similar of those displayed by the local model for small as well as for large values of energy. Comparison to previous work is also made.     

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.     

Ion distribution function at the boundary with an electrode

The ion distribution function is found in the case in which the Langmuir layer freely passes the ions incident from the plasma while the reverse ion flux is zero. These conditions are realized near the cathode in an arc discharge and at the surface of a probe operating on the ion branch of the characteristic. The electric field outside the Langmuir layer is assumed small. We obtain the connection between ion current and plasma density at the boundary with the electrode, the expressions for the ion mean kinetic energy and for the mean energy removed from the plasma by the ion, which differ markedly from the corresponding expressions in the Maxwellian distribution case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 47–54, May–June, 1969.     

Equation of state calculations for hot,dense matter at arbitrary densities and temperatures

Within the approximations of spherical lattice cell, central-field, and relativistic Fermi statistics, an algorithm with average atom model is presented to calculate the electronic energy levels and equation of state for hot and dense matter at arbitrary densities and temperatures. Choosing Zink's analytical potential as initial potential, we have solved the Dirac-Slater equation which satisfies the Weigner-Seitz boundary condition. The electronic energy bands are not taken into account. Taking energy level degeneracy as a continuous function of density, we have considered the pressure ionization effects for highly dense matter. Results for¹³Al atom are shown.     

Effects of Bubbles on the Hydraulic Conductivity of Porous Materials – Theoretical Results

In a porous material, both the pressure drop across a bubble and its speed are nonlinear functions of the fluid velocity. Nonlinear dynamics of bubbles in turn affect the macroscopic hydraulic conductivity, and thus the fluid velocity. We treat a porous medium as a network of tubes and combine critical path analysis with pore-scale results to predict the effects of bubble dynamics on the macroscopic hydraulic conductivity and bubble density. Critical path analysis uses percolation theory to find the dominant (approximately) one-dimensional flow paths. We find that in steady state, along percolating pathways, bubble density decreases with increasing fluid velocity, and bubble density is thus smallest in the smallest (critical) tubes. We find that the hydraulic conductivity increases monotonically with increasing capillary number up to Ca 10^–2, but may decrease for larger capillary numbers due to the relative decrease of bubble density in the critical pores. We also identify processes that can provide a positive feedback between bubble density and fluid flow along the critical paths. The feedback amplifies statistical fluctuations in the density of bubbles, producing fluctuations in the hydraulic conductivity.     

Effect of cooling rate on fracture behavior of polypropylene

The purpose of this work is to investigate the influence of morphology, induced by cooling rate during molding, on the time–temperature dependence of fracture behavior of polypropylene (PP). Fractures tests were performed over a range of loading rates from 0.2 mm/min to 2.5 m/s, using the single edge notched bending specimen. The results show that the transition temperature from brittle to ductile behavior increases with decreasing cooling rate. However, at very low loading speed (0.2 mm/min), an opposite effect is observed, the brittle–ductile transition temperature diminishes with lower cooling rate. At low test speeds, the fracture performance is reduced with a decreasing cooling rate. Conversely, under impact, the fracture toughness of PP is enhanced with a decrease in cooling rate. This is explained by the mechanism of blunting of the crack tip due to adiabatic heating under high loading rates. The blunting effect results in a more significant plastic deformation of the crystalline region that requires a higher energy. The brittle–ductile transition was characterized by an energy activation process expressed by the Arrhenius equation. Decreasing the cooling rate results in a decrease of both the pre-exponential factor and the energy barrier controlling the time–temperature dependence of fracture behavior. The reduction of the pre-exponential factor corresponds to a more ordered morphology due to a reduction in the entropy and is consistent with a higher crystallinity. The reduction of activation energy with higher crystalline level suggests that the brittle–ductile transition also involves the primary relaxation process that is known to occur mostly in an amorphous structure. A higher crystallinity would restrain the primary relaxation processes and the brittle–ductile transition becomes more dependent on the secondary movements of the chain segments. The results demonstrate that the relationship between deformation rate, temperature, and mechanical performance of PP is not only controlled by molecular relaxation processes, but also strongly dependent on its morphology.     

Radiation in particle simulations

Hot dense radiative (HDR) plasmas common to Inertial Confinement Fusion (ICF) and stellar interiors have high temperature (a few hundred eV to tens of keV), high density (tens to hundreds of g/cc) and high pressure (hundreds of megabars to thousands of gigabars). Typically, such plasmas undergo collisional, radiative, atomic and possibly thermonuclear processes. In order to describe HDR plasmas, computational physicists in ICF and astrophysics use atomic-scale microphysical models implemented in various simulation codes. Experimental validation of the models used to describe HDR plasmas are difficult to perform. Direct Numerical Simulation (DNS) of the many-body interactions of plasmas is a promising approach to model validation but, previous work either relies on the collisionless approximation or ignores radiation. We present four methods that attempt a new numerical simulation technique to address a currently unsolved problem: the extension of molecular dynamics to collisional plasmas including emission and absorption of radiation. The first method applies the Lienard–Weichert solution of Maxwell's equations for a classical particle whose motion is assumed to be known. The second method expands the electromagnetic field in normal modes (plane-waves in a box with periodic boundary conditions) and solves the equation for wave amplitudes coupled to the particle motion. The third method is a hybrid molecular dynamics/Monte Carlo (MD/MC) method which calculates radiation emitted or absorbed by electron–ion pairs during close collisions. The fourth method is a generalization of the third method to include small clusters of particles emitting radiation during close encounters: one electron simultaneously hitting two ions, two electrons simultaneously hitting one ion, etc. This approach is inspired by the virial expansion method of equilibrium statistical mechanics. Using a combination of these methods we believe it is possible to do atomic-scale particle simulations of fusion ignition plasmas including the important effects of radiation emission and absorption.     

A linear viscoelastic model for solid polyethylene

Stress relaxation tests have been carried out on a blue, pipe grade PE 80 medium density polyethylene (BP Chemicals), to provide thermo-viscoelastic rheology for use in calculating thermal stresses in pipe production. Stresses up to 4 MPa were used, with strains up to about 2%, in tests at temperatures from 23° to 90°C. Within this range a linear viscoelastic model was applicable, provided the initial ramp strain rate was less than 7×10^–5 s^–1. The stress relaxation data was fitted directly by a model incorporating an elastic response to volumetric strains, and a generalised linear solid model, consisting of two Maxwell elements and a purely elastic element in parallel, for deviatoric strains. Arrhenius type temperature dependence of relaxation times and shear moduli is found, and within experimental accuracy the temperature dependence of all these model parameters is the same. As a consequence, and provided that the duration of the strain ramp is sufficiently short relative to relaxation times, the model leads to time-temperature superposition of the relaxation moduli, using the same shift factor on both the response magnitude and time axes.     

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.     

A thermodynamical model of conductivity dispersion in plasmas and semiconductors

Summary In this paper, we first introduce a relation between the kinetic energy and the relaxation time, given by the Arrhenius equation, into the electrical conductivity equation of plasmas and semiconductors. Second, we investigate mathematically the change of the conductivity in the frequency and the time domains, and the nature of the distribution of relaxation times, of this new model of conductivity dispersion.