A method is presented for calculating the bound-bound emission from a local thermodynamic equilibrium plasma. The total transition array of a specific single-electron transition, including all possible contributing configurations, is described by only a small number of super-transition-arrays (STA’s). Exact analytic expressions are given for the first few moments of an STA. The method is shown to interpolate smoothly between the average-atom (AA) results and the detailed configuration accounting that underlies the unresolved transition array (UTA) method. Each STA is calculated in its own, optimized potential, and the model achieves rapid convergence in the number of STA’s included. Comparisons of predicted STA spectra with the results of the AA and UTA methods are presented. It is shown that under certain plasma conditions the contributions of low-probability transitions can accumulate into an important component of the emission. In these cases, detailed configuration accounting is impractical. On the other hand, the detailed structure of the spectrum under such conditions is not described by the AA method. The application of the STA method to laser-produced plasma experiments is discussed.

Kα absorption spectroscopy has been used to diagnose the low-temperature, high-density region of layered targets (high-Z on low-Z elements) irradiated by 0.26-μm laser light at irradiances between 2×${10}^{14}$ and 4×${10}^{15}$ W/${\mathrm{cm}}^2$. Time-resolved and time-integrated spectra have been recorded from the front and the rear of the target with high spectral resolution in the 1–3-keV range and low spectral resolution in the 40-eV–4-keV range. Experimental results provide measurements of the electron-temperature gradient shape in the region 50–200 eV. A detailed analysis of the atomic structure of He-like to F-like ions of chlorine and aluminum has been performed to give simulated absorption spectra as a function of plasma parameters. We show here a measurement of the shallow electron-temperature gradient around 100 eV built up by the absorption of x rays emitted by the laser-irradiated high-Z layer. This is in very good agreement with results obtained from a one-dimensional hydrocode including photon transport physics.

The stopping of partially stripped ions by a partially ionized target is investigated for the case of a projectile with an extended electronic core. Long-ranged contributions to energy loss are evaluated within an impact-parameter theoretical framework. Quantities correcting the standard pointlike results are given in analytical form with the aid of a Thomas-Fermi-like effective interaction. They can be substantial for moderate projectile ionicity and for velocities relevant for inertial confinement fusion driven by intense ion beams. As a rule, the stopping quantities pertaining to projectiles with extended core taken into account lie above those computed for their pointlike homologs.

By analysis of data from a specific set of laser-plasma interaction experiments, it is argued that stimulated Raman scattering (SRS) is responsible for the hard (>30-keV) x rays emitted from the targets. The Novette laser [K. R. Manes et al., Laser Part. Beams 3, 173 (1985)] was used to irradiate thick, gold targets with up to 4 kJ of 0.53-μm light in 1-ns, Gaussian pulses at average intensities of (1–200)×${10}^{14}$ W/${\mathrm{cm}}^2$, producing approximately planar plasmas with temperatures of order 3 keV and density-gradient scale lengths of order 250 μm. The spectrum, amplitude, and timing of the hard x rays emitted by the plasma were measured along with various properties of the scattered light. All the data are consistent with the hypothesis that SRS is the source of the hot electrons that emit the x rays, and some data conflict with any other plausible hypothesis.

An amplitude equation in the form of a perturbed nonlinear Schrödinger equation is derived for parametric excitation of surface waves in an extended system. Continuous symmetries of the unperturbed system are used to identify critical modes. Dynamical equations for the latter are derived using singular perturbation theory. The existence of a stable nonpropagating kink solution is predicted. The solution connects two uniform states whose phases of oscillations differ by π, and should be observable in wide enough cells. A stable nonpropagating soliton solution is found for subcritical excitation.

Self-focusing of an intense optical beam in a plasma is studied, including the nonlinear effects of both the relativistic electron mass and the ponderomotive potential due to the electromagnetic wave. An exact steady-state asymptotic solution of beam propagation in a localized solitary waveform is obtained in slab geometry. Amplitude-width scaling relations are obtained, which imply that the width is limited to be less than the square root of three collisionless skin depths. In the weakly relativistic limit our solution reduces to the solution obtained by Schmidt and Horton [Comm. Plasma Phys. Controlled Fusion E 9, 85 (1985)]. Solutions where the beam profile is of oscillatory nature, which correspond to the presence of the steady-state solution of a multiple-beamlet profile, are also presented. Finally, the asymptotic nature of the solitary wave is tested using a recently developed numerical particle simulation code.

Using time-dependent measurements and calculations of line-intensity ratios, we have determined the electron temperature of a surface flashover anode plasma in an intense ion diode to be 5–8 eV. The electron temperature was determined independently from C iii, Mg ii, and Al iii line intensities. The calculations accounted for the continuous particle flow from the anode surface into the plasma using the measured electron density. Furthermore, the electron-temperature gradient in the plasma was observed and found to be <1 eV/mm. The assumption that the plasma conductivity is classical, resulting in the electron heating being dominated by the currents induced in the plasma by the electron flow in the diode gap, was found to be in clear disagreement with the observed temperature gradient. The use of an anomalous plasma conductivity that is ≃10× lower than the classical conductivity, which was previously suggested based on the magnetic field penetration into the plasma and the plasma expansion against the magnetic field, yields electron heating dominated by the pressure-driven current in the plasma. This can explain the electron heating and the electron-temperature gradient observed.

A mechanical model exhibiting some of the interesting dynamics of rotating systems is introduced and analyzed. Particular attention is focused on the breakdown of stable uniformly rotating states and their evolution to chaotic trajectories as a dimensionless parameter is increased. Three views of this breakdown in the far from integrable regime are given. The first is based on the computation of positive Lyapunov exponents for the system. The second is based on Kolmogorov-Arnold-Moser (KAM) theory and relies on examining Poincaré sections of the phase space. A third view is described in terms of the kinetic energy exchange between the angle variables of the system.

The separation between the ablation surface and the absorption region (called the ‘‘stand-off distance’’) in laser-heated planar target experiments is determined from x-ray spectroscopic measurements of the Kα emission and the resonance lines of highly charged ions. In the intensity range 2×${10}^{12}$–${10}^{13}$ W/${\mathrm{cm}}^2$ of a Nd:glass laser (${\lambda }_L$=1.06 μm) the Kα emission is shown to be produced almost entirely by reabsorption of the x-ray line emission from the hot plasma. By relating the experimentally measured spatial width of the Kα emission region to that of the resonance line emission region through modeling different x-ray source intensity distributions, a stand-off distance of ∼150 μm is determined which is consistent with theoretical estimates.

A numerical implementation of Kraichnan’s [Theoretical Approaches to Turbulence, edited by D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt (Springer, New York 1985), p. 215] constrained decimation scheme (CDS) is formulated and applied to a turbulence model. The full set of dynamical variables in the model is reduced—decimated—to a small sample set. This decimated system is driven by stochastic forces that are subject to statistical constraints. The constraints exploit statistical similarities among dynamical variables to cause the stochastic forces to correctly model the statistical effects of the variables lost in the decimation. The CDS is formulated under two different sets of constraints, one of which is shown to be closely related to the direct-interaction approximation (DIA); numerical results from decimated systems under these constraints approach DIA results as the decimation strength (ratio of full-system size to decimated-system size) becomes large.

Extensive Monte Carlo simulations are reported of a model for tethered membranes that includes bending rigidity and self-avoidance. These simulations are performed over a range of temperature and for embedding dimensions d=3, 4, and 5. The membranes have a stretched configuration that is hexagonal with linear dimension L in the range 5–25. The equilibrium shape of the membranes is analyzed by calculating the eigenvalues of the inertia tensor as well as structure factors S(k) with k in the direction of the eigenvectors of this tensor. The eigenvalues and structure factor show a scaling behavior which indicates that in the thermodynamic limit the membranes are flat rather than crumpled for all temperatures and particle diameters, except possibly in the very weak self-avoidance limit, similar to the ‘‘phantom’’ membrane (one in which particles that are not nearest neighbors on the network do not interact, i.e., they can pass through each other).

A model of an objective function based on polynucleotide folding is used to investigate the dynamics of evolutionary adaptation in finite populations. Binary sequences are optimized with respect to their kinetic properties through a stochastic process involving mutation and selection. The objective function consists in a mapping from the set of all binary strings with given length into a set of two-dimensional structures. These structures then encode the kinetic properties, expressed in terms of parameters of reaction probability distributions. The objective function obtained thereby represents a realistic example of a highly ‘‘rugged landscape.’’ Ensembles of molecular strings adapting to this landscape are studied by tracing their escape path from local optima and by applying multivariate analysis. Effects of small population numbers in the tail of the sequence distribution are discussed quantitatively. Close upper bounds to the number of distinct values produced by our objective function are given. The distribution of values is explored by means of simulated annealing and reveals a random scatter in the locations of optima in the space of all sequences. The genetic optimization protocol is applied to the ‘‘traveling salesman’’ problem.

We present a dynamical system analysis of an experimental study on an axisymmetrical excited air jet. The transition to turbulence—weak turbulence— is investigated by imposing on the laminar flow a controlled excitation which triggers the spatial development of the jet instability. By longitudinal and azimuthal coherence and phase measurements, we find that a helical structure with azimuthal mode m=±1 is being selected, in accordance with spatial linear stability analysis. Further downstream, the transition to turbulence is evidenced, through a decrease in spatial coherence, by destabilization and a breakdown of the helical structure. We analyze the transition to turbulence with the techniques of dynamical systems theory. The presence of an initial helical structure in the flow suggests that the chaotic dynamics has low dimensionality: the correlation dimension computed along the jet axis (18φ≤l≤24φ, where φ is the nozzle diameter) at R=543 shows that the dimension of the chaotic attractor increases continuously from ∼3 to ∼6. Good correlation is found between spatial coherence and attractor dimension, which confirms the validity of the values obtained for the chaotic attractor dimensionality. From local coherence measurements, we infer a power-law dependence between the attractor dimension and the local correlation length (the range of the local turbulent structure). This result clearly indicates that in open systems the attractor dimension (as computed from time series data) is to be connected to the local chaotic dynamics of the flow.

In this work we critically reexamine an approximation method, called the adiabatic approximation (AA), based more on a mathematical foundation than on a phenomenological physical basis. We extend it to many-body systems and investigate the application of AA to simple molecular and nuclear systems in order to extract insights into the criterion of validity of this approximation method. The validity criterion is in part established by introducing a meaningful dimensionless parameter that indicates the ‘‘goodness’’ of AA. We also analyze the Born-Oppenheimer approximation and see if a correlation can be established between the two approximation schemes.

The hyperbolic sine model is obtained by continuing the hierarchy of simple multiplicative stochastic processes beyond the Verhulst model or by transforming some physically important models from different disciplines to their canonical form. The Fokker-Planck equation associated with this Markov process is solved for the stationary first-order probability density function (PDF), and an exact time-dependent solution for the transition PDF is derived in terms of a new type of eigenfunction. As an example, eigenvalues and eigenfunctions are numerically evaluated for the symmetrical case. It is shown that some new models, of possible mathematical or physical importance, can be derived from the hyperbolic sine model.

In this paper we show how the ideas behind extended irreversible thermodynamics are used to generate a systematic treatment of the relaxation and resonance phenomena in the propagation and absorption of electromagnetic energy in dielectric materials in a nonequilibrium state. Two cases are discussed: the first, in which the forced oscillations arising from the correlation between the fluctuations of the polarization vector and the electric field are neglected, and the second, in which this term is taken into account. In both cases we show how the main equations serve to make a connection between the macroscopic approach followed here and a number of results obtained for both, gases and polar liquids using molecular models. The results obtained here are compared with previous work on this problem, and new effects arising from the second case are pointed out.

We present an extensive numerical study of a long rf-biased Josephson junction in the presence of an applied magnetic field. We show the great complexity of the system and clarify some of the diverse spatiotemporal relationships that exist. At low values of the rf amplitude the spatial constraint succeeds in exciting an oscillating and localized pattern of solitonlike character. The dynamical response of this excitation as the forcing amplitude is increased allows us to observe three distinct intermittent phenomena: intermittency induced by interior crises, spatiotemporal intermittency between strange attractors, and tangentlike spatiotemporal intermittency. We also analyze at higher rf-bias amplitude a transition to a regime consisting of traveling waves with the spontaneous development of dc voltage which we interpret as being due to spatiotemporal chaos.

We present and discuss an algorithm for integrating a set of stochastic differential equations driven by colored noise. The algorithm, being fully implicit for the stochastic differential equation governing the noise, is stable upon changing τ (the noise correlation time) to any desired value. In particular, the limit of vanishingly small τ can be safely taken, and the algorithm yields the corresponding white-noise quantities in a natural way.

A quantal-dissipative system described by the Schrödinger equation with an additional nonlinear term is formulated in the Lagrangian stochastic mechanics on the basis of the symmetric stochastic calculus of variations (SSCV). A certain class of stochastic Lagrangian dynamical systems defined through the least-action principle in SSCV is associated with solutions of the nonlinear Schrödinger equations, and thereby the quantal-dissipative system described by the equation is connected with a stochastic Lagrangian dynamical system. The long-time behavior of momentum, angular momentum, and energy, and the virial theorem for the stochastic Lagrangian system corresponding to the quantal-dissipative system, are investigated through the conserved quantities and the first variations of the functional induced by one-parameter transformations. Examples are given for a free particle and for the harmonic oscillator.

Tunneling of initially squeezed wave packets in moderately asymmetric double-well potentials is studied in the presence of dissipation. The time dependence of the mean position is studied in order to investigate the features of the trajectory, which strongly depends on the involved parameters. Some questions related to the evaluation of the dissipative parameters are discussed.