Transverse beam-profile variations are investigated for a system which shows cavityless optical bistability due to increasing absorption. Coupled transport equations for the light field and the excitation density are derived and solved numerically for the case of an optically thin sample, where longitudinal density variations can be neglected and where diffusion of the excitation is the dominant transverse coupling mechanism. Assuming a Gaussian input beam, the increasing absorption is shown to cause substantial profile modifications when the medium undergoes the transition from low to high absorption. The formation of spatial ring structures is predicted and it is shown that transverse carrier diffusion plays an important role in determining both the steady-state and the temporal response of the system.

A nonperturbative semiclassical theory is presented for the treatment of four-wave mixing (FWM) in a four-level system. This treatment is based on a transformation to a generalized rotating frame followed by a numerical diagonalization of the resulting time-independent Hamiltonian. For strong fields, all resonant frequencies are shifted from the atomic (molecular) frequencies. Lines are split up in a way similar to the ac Stark effect for a two-level system, and for even stronger fields, the effect of stirring is observed for the first time in four-wave mixing. In addition, a new extra resonance appears which is induced by the saturating field. This field-induced resonance is the new member in the family of extra resonances (pressure induced, or stochastic fluctuation induced), and it should be observed whenever saturating fields interact with a multilevel atomic or molecular system.

We present measurements of the time evolution of the statistical densities of both amplitude and field intensity obtained from a colored-noise-driven electronic circuit model of a ring laser, as the bifurcation parameter is swept through its critical values. The time-dependent second moments (intensities) were obtained from the densities. In addition, the individual stochastic trajectories were available from which the distribution of bifurcation times was constructed. For short-correlation-time (quasiwhite) noise our results are in quantitative agreement with the recent calculations of Boggi, Colombo, Lugiato, and Mandel [Phys. Rev. A 33, 3635 (1986)]. New results for long noise correlation times are obtained.

We present a new class of radiation field states which exhibit squeezed fluctuations. This new class of states are formed by a simple implementation of the superposition principle and are fundamentally different from the conventional two-photon coherent squeezed states. We demonstrate the importance of these states as the natural product of the resonant interaction of suitably prepared atoms with the radiation field. We establish a general relationship between reduced quantum fluctuations of these field states and the dipole fluctuations of the atoms which produce them.

Microdot spectroscopy of a laser-produced plasma was used to study the x-ray emission from highly ionized europium in the wavelength region between 6.5 and 9.6 Å. New identifications of spectral lines from europium ions isoelectronic with Ni, Co, and Fe were made using ab initio calculations of the wavelengths and gf values. The emission was measured with spatial and temporal resolution and as a function of the laser irradiance. The relative abundances of the different ionization stages, as inferred from the intensities of the 3d-4f transitions, compare favorably with the ionization distribution predicted by a collisional-radiative model and with the results of a two-dimensional lasnex simulation.

We have measured the profiles of plasma-broadened and slightly red- or blue-shifted spectral lines of neutral argon and nitrogen in a wall-stabilized arc and have performed a detailed line-shape analysis with a computerized data acquisition and processing system. According to Stark broadening theory, isolated lines of neutral atoms in dense plasmas are mostly broadened by electron impact resulting in symmetrical Lorentzian profiles, and are also broadened by the plasma ions, which produce a small additional contribution to the width as well as asymmetries in the line profile. As in two earlier experimental studies, we have utilized this difference in symmetries to study the effects of ion broadening. In this paper we have extended our work to some unusual cases where lines exhibit relatively rare ‘‘blue’’ shifts and where we study spectral transitions which are appreciably broadened because they originate from high-lying atomic levels. Our results are again in close agreement with the quasistatic theory of ion broadening which predicts that the asymmetry pattern has a characteristic minimum and maximum near the central part of the lines, but this pattern is reversed for the blue-shifted lines. We have also utilized the asymmetries for a check on plasma homogene- ity. By deliberately including nonhomogeneous areas of emission into the line of sight, we found drastic, readily observable distortions in the asymmetry patterns.

Magnetic dipole (M1) transitions between the levels of the ground configurations in the 3$s^2$3$p^x$ Al-like through Cl-like and the 3s3p Mg-like isoelectronic sequences of Cu, Zn, Ga, As, Kr, and Y have been observed. These elements were introduced into the Texas experimental Tokomak plasma by laser ablation of metallic thin films and gas puffing. The spectral lines were recorded by using three monochromators with photoelectric detection and a spectrometer with a channel electron multiplier array detector. Twenty-eight newly observed M1 lines were measured and classified.

The line profiles of the Balmer α transitions of hydrogen and deuterium were measured simultaneously in a theta-discharge plasma. The characteristics of the light source were the following: peak electron density of the order of 7×${10}^{14}$ ${\mathrm{cm}}^{\mathrm{-}3}$, electron temperatures between 15 and 20 eV, and neutral and ion temperatures between 2.5 and 3.5 eV. The filling gas was helium with a 1% admixture of equal parts of hydrogen and deuterium. The experimental profiles were compared with a theoretical spectrum that was calculated taking into account the Stark broadening, independent Gaussian widths for each line, a fine-structure correction, and the instrumental broadening. In the data reduction a correction of the experimental data was made to allow for a radial inhomogeneity of the plasma. The measurements confirm the existence of large deviations from calculated profiles that do not account for ion dynamical effects. It has also been found that a model to include ion dynamical effects as a Gaussian broadening partly corrects the discrepancies. Finally, about 10% agreement is obtained when Lorentzian profiles based on relaxation theory calculations are used for the Stark broadening. Similar agreement is obtained with numerically simulated profiles.

The implications on the Brillouin lines of our recently developed theory of the density fluctuations in a fluid exposed to a strong stationary heat flux are discussed. This theory takes into account, for the first time, the combined effects of sound-absorbing and -reflecting walls as well as the spatial inhomogeneities induced by the temperature gradient. The theory is slightly generalized to be applicable to arbitrary bending of sound, in particular when sound rays are totally bent inside the fluid. No restrictions are made concerning the thermal equations of state. This allows a critical reexamination of earlier theories and experiments, the resolution of an existing ambiguity, and the proposal of new experiments.

We describe a simple order-parameter theory for the interfacial tension of body-centered-cubic solids. The principal order parameter is the amplitude of the density wave at the smallest nonzero reciprocal-lattice vector of the solid, but the density difference between solid and liquid is included to second order. The parameters entering the theory are fitted to the measured heat of fusion, melting temperature, and solid-liquid density difference, and to the liquid structure factor and its temperature derivative at freezing as calculated by a variational technique. Agreement with experiment is good for Na and Fe, and the calculated anisotropy of the surface tension among different crystal faces is of order 2%, in agreement with earlier calculations of Oxtoby and Haymet. With certain additional assumptions about universal behavior of bcc crystals at melting, the formalism predicts that the surface tension is proportional to the heat of fusion per surface atom, in agreement with the empirically derived relation of Turnbull [J. Appl. Phys. 24, 1022 (1950)].

Detailed properties of the cyclotron maser and whistler instabilities in a relativistic magnetized plasma are investigated for a particular choice of anisotropic distribution function F($p_{\perp }^2$,$p_z$) that permits an exact analytical reduction of the dispersion relation for arbitrary energy anisotropy. The analysis assumes electromagnetic wave propagation parallel to a uniform applied magnetic field $B_0$e${^}_z$. Moreover, the particular equilibrium distribution function considered in the present analysis assumes that all electrons move on a surface with perpendicular momentum $p_{\perp }$=p${^}_{\perp }$=const and are uniformly distributed in axial momentum from $p_z$=-p${^}_z$=const to $p_z$=+p${^}_z$=const (so-called ‘‘waterbag’’ distribution in $p_z$). This distribution function incorporates the effects of a finite momentum spread in the parallel direction. The resulting dispersion relation is solved numerically, and detailed properties of the cyclotron maser and whistler instabilities are determined over a wide range of energy anisotropy, normalized density ${\omega }_p^2$/${\omega }_c^2$, and electron energy.

In this paper we present an analysis of the theory of the energy deposition of ions in cold materials and hot dense plasmas together with numerical calculations for heavy and light ions of interest to ion-beam fusion. We have used the gorgon computer code of Long, Moritz, and Tahir (which is an extension of the code originally written for protons by Nardi, Peleg, and Zinamon) to carry out these calculations. The energy-deposition data calculated in this manner has been used in the design of heavy-ion-beam-driven fusion targets suitable for a reactor, by its inclusion in the medusa code of Christiansen, Ashby, and Roberts as extended by Tahir and Long. A number of other improvements have been made in this code and these are also discussed. Various aspects of the theoretical analysis of such targets are discussed including the calculation of the hydrodynamic stability, the hydrodynamic efficiency, and the gain. Various different target designs have been used, some of them new. In general these targets are driven by ${\mathrm{Bi}}^{+}$ ions of energy 8–12 GeV, with an input energy of 4–6.5 MJ, with output energies in the range 600–900 MJ, and with gains in the range 120–180. The peak powers are in the range of 500–750 TW. We present detailed calculations of the ablation, compression, ignition, and burn phases. By the application of a new stability analysis which includes ablation and density-gradient effects we show that these targets appear to implode in a stable manner. Thus the targets designed offer working examples suited for use in a future inertial-confinement fusion reactor.

The universality of strange attractors is explored. In order to explain the scaling properties of these attractors, renormalization theory is extended between two-dimensional Hamiltonian and one-dimensional strongly dissipative systems. The theory describes the crossover behavior between Hamiltonian and one-dimensional maps. The universal Hamiltonian map $T^{\mathrm{*}}$ serves as the generator for dissipative maps via repeated iterations of a renormalization operator. These maps exhibit universal scaling for period doubling, strange attractors and their crisis, Liapunov exponents, and dimensions.

A prototype model of driven nonlinear oscillators with a stable limit cycle is studied. In the fast-relaxation limit, dynamics can be reduced to a one-dimensional mapping parametrized by the amplitude α and the phase β of the driving force. For a weak force, mode locking with rational winding numbers occurs. For a strong force, the parameter space may be divided into two subregions: In the unimodal region, the order of occurrence of the orbits is governed by the Metropolis-Stein-Stein U sequence of unimodal mappings; in the intermediate region, a transition between mode-locking behavior and that of the unimodal mapping takes place, and new sequences of periodic orbits occur. The systematics of the periodic orbits is investigated.

A molecular system is stochastically coupled to a phonon thermal reservoir. The equation for its averaged density matrix describes the approach to thermal equilibrium.

Transient responses and stationary processes with alternating fields are treated in the nonlinear regime in order to clarify their relations in the time and frequency domains. It is shown that a frequency-domain experiment in which a weak ac field is superimposed on a strong biasing dc field corresponds to the transient process of a strong constant biasing field with the sudden application of weak constant field. Furthermore, it is found that the Fourier-Laplace transform of the second-order nonlinear transient rise process corresponds to the amplitude for the ω component of the stationary experiment with coupled dc and ac fields with the angular frequency ω. For a simple ac input, we demonstrated how the stationary nonlinear response may conveniently be calculated with the help of the theory of random walk. Also, interrelations among the rise, decay, and rapidly re- versing transients are clarified.

Nonequilibrium critical phenomena in one-component reaction-diffusion systems are investigated on the basis of a mean-field theory and/or a field-theoretic renormalization-group technique. A superposition of three reactions of type mX→m’X (m>m’), mX→m’’X (m’’), and nX→n’X (n>n’, n>m>0), which represents all universality classes of second-order phase transitions in one-component reaction-diffusion systems, is considered. The upper critical dimension is given by $d_c$=2(n-m+1)/(n-1). Mean-field values of critical exponents are determined as a function of the order of reactions, m, and n. In addition, critical exponents for the process m=1 and n=3 are calculated to first order in ɛ=$d_c$-d ($d_c$=3) by an ɛ-expansion method. Critical exponents depend on m and n and phase transitions in different order reaction systems belong to different universality classes. It should be emphasized that the autocatalytic nature of the process causes the breakdown of the fluctuation-dissipation theorem and associated two different (probably independent in higher-order systems) susceptibility exponents: the static susceptibility exponent describing spatial fluctuations at steady states and the dynamic susceptibility exponent characterizing time evolution of the process.

We have developed a formalism for extending mean-field theories of isotropic fluids to systems containing anisotropic interactions. Our approach is a generalization of a method previously used by Flapper and Vertogen [Phys. Rev A 24, 2089 (1981) and J. Chem. Phys. 75, 3599 (1981)]. We illustrate our formalism by extending the van der Waals theory for isotropic fluids to anisotropic fluids with a nematic phase, and obtain results which are similar to those of Gelbart and Baron [J. Chem. Phys. 66, 207 (1976)] and Cotter [in The Molecular Physics of — Liquid Crystals, edited by G. R. Luckhurst and G. W. Gray (Academic, London, 1979), p. 181]. The theory contains two dimensionless parameters which give measures of the anisotropy of attractive and repulsive parts of the intermolecular interactions. In the present paper we examine the temperature dependence of the order parameter and density in the low-pressure limit. An advantage of the present approach is that it offers a way of generalizing a wide class of equations of state to anisotropic fluids, and we therefore expect the method to be useful in systematically providing empirical equations of state for mesophase systems. Requirements of thermodynamic consistency are automatically satisfied.

Equations describing small-amplitude motion in the proximity of bifurcation at the triple-zero eigenvalue, after being reduced to a normal form by nonlinear transformations, display a double-scale structure that combines relatively fast conservative orbital motion with slow dissipative evolution of two integrals of motion. The homoclinic explosion occurs when the attractor of the averaged dissipative equations comes close to a homoclinic trajectory of the fast conservative subsystem. Applying the method of matched asymptotic expansions allows one to reduce the dynamical system near this point to a simple next return map possessing an infinite family of invariant manifolds that can turn into attractors of different character under small parametric perturbation. After the attractor of the averaged system has been expelled from the region of closed orbits, one observes large-amplitude dynamics with rare events of anomalous intermittency superimposed upon a quasiperiodic or chaotic attractor of nonuniversal character.

Detailed properties of the Weibel instability in a relativistic unmagnetized plasma are investigated for a particular choice of anisotropic distribution function F($p_{\perp }^2$,$p_z$) that permits an exact analytical solution to the dispersion relation for arbitrary energy anisotropy. The particular equilibrium-distribution function considered in the present analysis assumes that all particles move on a surface with perpendicular momentum $p_{\perp }$=p${^}_{\perp }$=const and are uniformly distributed in parallel momentum from $p_z$=-p${^}_z$=const to $p_z$=+p${^}_z$=const. (Here, the propagation direction is the z direction.) The resulting dispersion relation is solved analytically, and detailed stability properties are determined for a wide range of energy anisotropy.