In this paper, we study the thermodynamic properties of dense plasmas considered as high-temperature liquid metals. The problems that have to be solved are the following: (1) calculation of the ‘‘average’’ electron-density profile around an ion in the plasma, (2) determination of a self-consistent average ionization of the plasma, (3) calculation of the pair interaction between two ions, and (4) calculation of the total Helmholtz free energy. The first point is approximately solved in the Mermin-Kohn-Sham (MKS) density-functional theory of thermal ensembles, for a single ion in a spherical cavity in jellium. A prescription is then proposed for calculating the average ionization as a function of density and temperature using the electron densities from the MKS scheme. This prescription is shown to work well when the electron structure of the plasma is simple (i.e., when the overlap of bound states is not too large, and when there is no resonance in the free spectrum). The use of a superposition of single-ion densities for the total charge density of the plasma, together with a cluster expansion of the kinetic and exchange-plus-correlation energy, leads to the definition of the pair interaction that is readily calculable. Finally, the structural (ionic) part of the free energy is obtained from the hypernetted-chain theory of fluids.

An explicit expression is obtained for the pair potential φ(R) in liquid simple metals from low-order density-gradient theory when the superposition of single-center displaced charges is employed. Corrections are thereby explicitly exhibited to the local Thomas-Fermi result ${\mathrm{\phi }}_{\mathrm{TF}}$(R) from second- and fourth-order inhomogeneity corrections Δ${\mathit{T}}_2$(R) and Δ${\mathit{T}}_4$(R) to the Thomas-Fermi electronic kinetic-energy change Δ${\mathit{T}}_{\mathrm{TF}}$(R). The important point to emphasize is that, in each order, the potential V(R/2) and displaced charge Δ(R/2) of a single screened ion at the midpoint of the metallic bond completely determines the pair potential in the density-gradient theory. These approximate results are illustrated by explicit calculations on liquid Na and liquid Be near their respective freezing points. While the pair potentials obtained by including Δ${\mathit{T}}_2$(R)+Δ${\mathit{T}}_4$(R) are major improvements over the linear response result, the remaining nonlocal corrections to the total kinetic-energy change ΔT(R) are substantial, as again demonstrated by explicit results for Na and Be. The importance of further study of a possible functional relation between ΔT(R)-Δ${\mathit{T}}_{\mathrm{TFG}}$(R) and the potential V(R/2) at the midpoint of the metallic bond is finally emphasized.

Exact equations describing nonlinear surface-wave propagation on a cold plasma sphere are derived and solved. It is found that, even for the case of small amplitudes, nonlinear effects can be important.

A new type of a simple ${\mathrm{LaB}}_6$ hollow cathode tube allows us to have very stable discharge even in the regime of the glow-arc transition, which is commonly unstable for widely used cathode materials (Ta,W). Because of the relatively large size of our device (25 mm diameter) and the low-temperature operation (∼1400 K), we were able to investigate various plasma parameters of the internal plasma in detail by using a standard Langmuir probe and an ion sampling technique with a tiny orifice (1 mm diameter) to study the ion behavior near the cathode wall. Our measurements of the electron-energy distribution function F(ɛ), the space potential φ, the mean electron energy ɛ¯, the electron density ${\mathit{n}}_{\mathit{e}}$, and the sampling ion current density ${\mathit{J}}_{\mathit{i}}$ were carried out under various discharge conditions in order to understand the basic characteristics of hollow cathode discharge. We have found that these plasma parameters show anomalous properties in the glow-arc transition: (1) The different discharge regime of hollow cathode discharge, namely the abnormal glow, the arc, and the glow-arc transition, are clearly distinguished, and the discharge voltage ${\mathit{V}}_{\mathit{d}}$ and ${\mathit{J}}_{\mathit{i}}$ are a unique function of the discharge current in our hollow cathode tube. (2) A distinct high-energy component appears in the range ∼1–7 eV, with two types of high-energy tails. (3) The local growth of ɛ¯, the local ionization, and appearance of the space potential hill are observed near the anode and central region of the tube. These anomalous disturbances correspond to nonuniform self-heating: the nonuniform thermionic electron-emission effect along the ${\mathrm{LaB}}_6$ hollow cathode tube in the glow-arc transition.

The stochastic properties of negative, point-to-plane, Trichel-pulse corona discharges are completely characterized in terms of a set of measured conditional and unconditional discharge pulse-amplitude and pulse-time-separation distributions. The Trichel-pulse phenomenon is shown to be a clear example of a non-Markovian, marked random point process in which memory effects play an important role. Strong correlations are shown to exist among the amplitudes and time separations of successive discharge pulses that indicate how initiation and growth of a discharge pulse are affected by the presence of residual ion space charge and metastable species from previous pulses. The analysis required to assess consistency among the various measured probability distributions is discussed and used to interpret observed variations in distribution profiles. Because of the observed dependence of discharge pulse amplitude on both the amplitude of and time separation from the previous pulse, memory can propagate indefinitely back in time. The experimental limitations to verifying the extent of memory propagation are analyzed.

The mechanism of excitation of a microwave in a circular waveguide, partially or completely filled with a dense magnetized plasma, by a weak thin annular relativistic electron beam is investigated. In view of the plasma as a weakly dispersive medium, a self-consistent set of coupled nonlinear and relativistic wave-particle equations is derived. The expressions of energy components are presented, and the conservation character of the total energy is proved. Under the linear approximation, the dispersion equation of interaction in the case of a waveguide completely filled with a plasma is obtained both by using a Green’s function and by linearizing the derived coupled wave-particle equations. The frequency of the most unstable wave, as well as the frequency shift and the growth rate, is solved. By using the single-wave model, especially in the approach of one-component simulation, the evolution of the wave in both configurations is studied in some detail. The beam energy to microwave conversion efficiency is obtained when the field is saturated. The effects of the beam energy, position, and quality on the efficiency are discussed. For the configuration of plasma completely filling a waveguide, the distribution of the beam electrons is dotted in the phase space at various times. The saturation of instability is shown to be due to the formation of vortices in the phase space as a result of phase trapping and the bunching of beam electrons.

We present the results of two-dimensional lasnex simulations of the classical and laser-driven Rayleigh-Taylor instability. Our growth rates and eigenmodes for classical two- and three-fluid problems agree closely with the exact analytic expressions. We illustrate in several examples how perturbations feed through from one interface to another. For targets driven by a 1/4-μm laser at I=2×${10}^{14}$ W/${\mathrm{cm}}^2$ our growth rates are 40–80 % of the classical case rates for wavelengths between 5 and 100 μm. We find that radiation transport has a stabilizing effect on the Rayleigh-Taylor instability, particularly at high intensities. A brief comparison with a laser-driven experiment is also presented.

The collapse of wave packets governed by the Zakharov equations is investigated at critical dimension. Their classical self-similar solutions are described by a linear time-dependent contraction scale ξ(t)=V(${\mathit{t}}_{\mathrm{*}}$-t) where ${\mathit{t}}_{\mathrm{*}}$ denotes the collapse time. We study two spherically symmetric versions of self-similar collapses, namely one corresponding to a vectorial electric field and another one relative to a scalar modelization of the Langmuir field. Each of these solutions can be regarded as a function of the collapse velocity V=-ξ̇. In the case of a vectorial electric field, the solutions are analytically shown to exist in the subsonic regime only, provided that the velocity V is lower than a critical velocity ${\mathit{V}}_{\mathrm{crit}}$, in agreement with previous numerical results. By contrast, the solutions of the scalar model are found to exist for every value of the collapse velocity; they exhibit two localized modes that evolve continuously as a function of V from the subsonic to the supersonic regime. These two modes are analytically and numerically shown to merge together in the limit V→∞.

The anisotropic collapse of Langmuir waves is investigated within the Zakharov equations and the nonlinear Schrödinger equation descriptions. By means of a transformation group we exhibit self-similar anisotropic solutions characterized by two different contraction rates. We show the existence of two infinite sets of anisotropic collapsing solutions, corresponding to oblate- or oblong-shaped collapsing structures. The usual isotropic collapsing solution is found to be a natural limit of these two sets. The two classes of anisotropic solutions are furthermore shown to be bounded by two particular solutions whose validity extends from the subsonic to the supersonic regime; the spatial profiles of these so-called trans-sonic solutions are analytically and numerically derived.

The free energy of the classical one-component plasma is calculated analytically in the crystalline phase for both fcc and bcc lattices to O(${\mathit{T}}^2$), where T is the temperature. By application of thermodynamic perturbation theory, we explicitly evaluate the effect of three- and four-phonon interactions on the partition function. Periodic boundary conditions are applied to make contact with previous numerical work, in which the O(${\mathit{T}}^2$) term was assumed to be negligible. We find that it is much larger than previously thought. This increases the thermodynamic stability of the crystal phase over previous estimates.

Excitation coefficients for the ${\mathit{C}}^3$${\mathrm{\Pi }}_{\mathit{u}}$ state of ${\mathrm{N}}_2$ and ${\mathit{B}}^2$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ state of ${\mathrm{N}}_2^{+}$ were measured in a steady-state self-sustained discharge in nitrogen for a wide range of E/N values from a moderately high 300 Td to 10 kTd (1 Td=1 townsend=${10}^{\mathrm{-}21}$ V ${\mathrm{m}}^2$). The absolute values of the coefficients were obtained by calibrating the apparatus using the standard tungsten-ribbon and hydrogen lamps. The present results are in general agreement with the available experimental and theoretical data in the range of overlap, and cover a range of high values of electric-field to gas-density ratio, for which absolute measurements are not available.

The dielectric response of DNA polymers dissolved in a water solution plays an important role in the determination of the effect of long-range nonbonded interactions on the vibrational dynamics of DNA. All existing calculations for DNA vibrational modes assume the water dielectric function to be constant, independent of the oscillation frequency. However, in real DNA solutions, modes depend on the dielectric constant and the dielectric constant is strongly dependent on frequency, particularly in the frequency range 0–100 ${\mathrm{cm}}^{\mathrm{-}1}$. We have extended our earlier effective-field approach for dissolved DNA polymers to include the important frequency dependence of the dielectric response function. Using the most recent experimental values for the system parameters, particularly dielectric relaxation time, we have calculated the phonon spectrum of the B-form poly(dA)-poly(dT) DNA polymer. [The notation poly(dA)-poly(dT) means that one strand contains adenine (A) bases, and the other only thiamine (T) bases.] Within a single model and with a single set of parameters our results agree with experimental data on speed of sound and inelastic neutron scattering. Besides this, our calculations also present some lines to be observed in poly(dA)-poly(dT) samples. We have analyzed the eigenvectors of all the modes in the range 0–120 ${\mathrm{cm}}^{\mathrm{-}1}$ and have characterized them in terms of various types of motions such as propeller twist, base-roll, breathing mode, etc. As a result of the frequency-dependent behavior of the long-range forces some new and interesting features are predicted at low frequencies in the millimeter range.

The basins of attraction of extremely diluted neural-network models in the presence of external neural stimuli parallel to the starting configuration are calculated analytically. For moderate values of the storage capacity α, the basins of attraction can be enlarged significantly. For larger values of α, the patterns are still locally stable but become dynamically blocked by the external stimuli so that the effective storage capacity decreases. The performance can be improved further by allowing for time-dependent stimuli.

A neural network with three-spin interactions is studied numerically. The number of patterns stored in the memory of the network is varied from 1 to 1400 for a 100-spin system. The storage capacity of the network is found to be approximately 700 patterns. Various factors affecting the quality of retrieval are examined.

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from ${\mathit{D}}_{\mathbf{X}}$=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.

We consider the time scales for the observation of diffusion in small cluster systems. Molecular-dynamics calculations are performed to investigate the long-time behavior of the velocity autocorrelation function for the finite system. It is found that the resulting power spectrum exhibits liquidlike behavior over frequencies larger than those corresponding to large-amplitude motion across the boundaries of the cluster. The results are consistent with an interpretation of the cluster as a finite mixing system exhibiting decay of correlations and zero diffusion constant. The decay to zero diffusion constant as ω approaches zero occurs in a nearly singular fashion.

Total-energy calculations have been performed for hydrogen atoms embedded in a small Be cluster. The effect of Li impurities has also been studied, and it was found that the presence of Li favors the nucleation of protons inside the cluster.

We consider the one-dimensional trapping problem A+S→S when the traps S as well as the reactants A are immobile. The trapping rate k(r) depends on the distance r between the reactant and the trap, and is characterized by an ‘‘effective reaction radius’’ ${\mathit{r}}_0$, which is a measure of the first moment of k(r). We find that the decay of an initial density of A particles is exponential in time at short times and an inverse power law at long times. In the presence of sources, we find that a steady state exists only if the effective reaction radius is larger than half of the average distance between sinks, and we find an inverse-power-law approach to the steady state. If this condition is not met, then there is an unbounded accumulation of A particles in regions that can not be effectively depleted by the reaction. The growth of the density in this case is of power-law form.

The nonlinear Schrödinger equation i${\mathrm{\psi }}_{\mathit{t}}$+Δψ=cψ‖ψ${\mathrm{\Vert }}^{2\mathrm{\sigma }}$ with boundary conditions imposed on a cylinder or on a sphere is reduced to an ordinary differential equation, namely, the Abel equation. This can be used to investigate particular singular solutions in self-trapping and self-focusing theories.