A three-dimensional, time-dependent theory for spontaneous initiation, radiation propagation, and gain buildup in hot-plasma x-ray lasers is presented. The temporal and spatial evolution of the radiation field and atomic polarization is governed by a set of Maxwell-Bloch equations with an additional Langevin-force term which accounts for stochastic processes. The model equations are solved, in the limit of small signal and large Fresnel numbers, by the ray-tracing technique yielding formulas for the field intensity, autocorrelation function, complex degree of coherence, and the power spectrum in terms of the solution of a set of coupled ray equations. A specific two-dimensional (r,z) numerical example, demonstrating the capacity of the method, showing the transition from the spontaneous stage through a transient buildup stage to steady state is presented.

Multiple-scale perturbation theory is used to obtain periodic orbits of relativistic electrons in the external electric and magnetic fields of a planar cross-field free-electron laser (FEL) operating near the fundamental resonance. The condition for this resonance is 2${\gamma }_0$$k_w$$v_0$≊(${\mathrm{eB}}_0$/${\gamma }_0$$m_0$) (1+${\mathrm{a}}_{\mathrm{w}}^2$${)}^{\mathrm{-}1/2}$, where $k_w$ is the wave number of the magnetic wiggler field, $v_0$=$E_0$/$B_0$ is the electron drift speed in the crossed uniform electric and magnetic fields, ${\gamma }_0$ =(1-$v_0^2$/$c^2$${)}^{\mathrm{-}1/2}$ is the relativistic factor associated with the Lorentz transformation between the laboratory frame and the drift frame, $m_0$ is the rest mass of the electron, $a_w$${=2\mathrm{}}^{\mathrm{-}1/2}$(${\mathrm{eB}}_w$/$m_0$${\mathrm{ck}}_w$) is the normalized rms vector potential of the wiggler field, and $B_w$ is the magnitude of the wiggler field. The orbits are expressed in an approximate form suitable for use in linearized Vlasov stability analysis and are used to obtain Vlasov distribution functions which correspond to kinetic equilibria that are uniform and nonuniform (across the anode-cathode gap). Appropriate moments of these distribution functions yield corresponding fluid equilibria. These equilibria are developed as a basis for a linear-stability analysis of the cross-field FEL operating near the fundamental resonance.

With the use of a quantum theory of optical propagation, a set of nonlinear stochastic partial differential equations may be derived which describes the quantum-statistical properties of traveling waves due to self-phase modulation in a nonlinear medium. We calculate exact moments for the field, which exhibit classical self-phase modulation in the short-interaction limit and periodic quantum evolution through field-superposition states in the long-interaction limit. Reversible and irreversible behaviors of the stochastic description are reviewed. The relation of the present work to the corresponding single-mode nonlinear oscillator is discussed.

The light-induced-drift (LID) effect has been experimentally studied in specially coated capillary cells which manifest a negligible atom-wall interaction. This property permits a rapid evolution of LID and makes possible an experimental study of the stationary states as a function of different laser tunings and laser power densities. The light-induced density profile along the major axis of the cell has been analyzed. The experimental features are qualitatively reproduced by a two-level theory.

Dissipation is expected to have detrimental effects on squeezed light. An analytical expression for dissipation in systems governed by the nonlinear Schrödinger equation is presented. As an example, parameters for an optical fiber were used to evaluate the squeezed-state spectrum. In addition, a scheme for detecting high-frequency components of the squeezed parameter is given.

For the model of Drummond and Walls describing dispersive optical bistability, quantum tunneling rates are calculated in the low-cavity-damping limit. Without damping the system can be described by an appropriate Hamilton operator. By expanding the density operator into eigenstates of this Hamilton operator the equation of motion of the density operator is cast into an equation of motion for the density matrix. In this equation we take into account only diagonal elements and those nondiagonal elements for which the corresponding eigenstates of the Hamilton operator are nearly degenerate. The tunneling rates are then determined by the eigenvalues of the truncated density-matrix equation.

A theory for the buildup of stimulated x-ray radiation from spontaneous emission in relativistic channeling beam systems is presented. Explicit expressions for the startup operator for amplification is obtained from a first-principles quantum Hamiltonian including channel fluctuations (phonons or plasmons). Treating the radiation field as classical, an analytic solution for the evolution of the radiation intensity is derived and threshold conditions are obtained. The evolution toward stimulated emission shows a slow buildup followed by a rapid transition. Time scales of these two stages are analyzed.

We describe experiments which throw light on the physics of high-Mach-number electrostatic shocks. A planar carbon target is irradiated with an 18-nsec laser pulse at a wavelength of 1.05 μm with an energy of 100–200 J. Carbon plasma ablates supersonically from the solid target at a velocity of 6×${10}^7$ cm ${\sec }^{\mathrm{-}1}$. A spherical carbon obstacle is placed in the ablating plasma at a distance of around 1 mm from the primary target where the density is ${10}^{18}$ electrons ${\mathrm{cm}}^{\mathrm{-}3}$. The density structure of the plasma is probed by interferometry and schlieren photography, and shows a density jump which can be interpreted as a bow shock in a plasma flowing with a Mach number of around 2.2. Measurements of magnetic field imply a plasma β (8πnkT/$B^2$) in excess of 100. The shock thickness is occasionally very thin (about 10 μm), but more usually 50 μm. In either case the shock thickness is much smaller than the electron and ion Coulomb mean free paths.

We provide a theoretical and experimental study of the nature of morphology transitions in diffusion-controlled systems. The interplay of surface tension and kinetic anisotropy is found to determine the selected morphology in an anisotropic Hele-Shaw cell experiment, and in theoretical computations in the boundary-layer model (BLM) for solidification. We employ the Hele-Shaw cell to demonstrate the existence of surface tension and kinetic dendrites. Using the BLM we show that the selected velocities for kinetic and surface-tension dendrites scale differently with the undercooling Δ. A study of the selected velocity as a function of undercooling is presented for both aligned and competing anisotropies, the latter motivated by the Hele-Shaw experiment. The difference in scaling is related to the reentrant tip splitting found for the case of competing anisotropies in the BLM morphology diagram via a time-dependent solution for the interface evolution. We suggest that the nature of the transitions between morphologies should be classified by the behavior of the selected interfacial velocity as a function of driving force. For the case of the BLM, first- and second-order-like morphology transitions, by analogy to phase transitions, are discussed. We further advance the hypothesis that the fastest growing morphology, whether it be tip splitting or dendritic, emerges as the stable interfacial morphology experimentally. We support our hypotheses by drawing analogies to experimental results of growth from supersaturated solutions and by electrochemical deposition.

We continue our investigation of the properties of a model fluid whose molecules have classical translational degrees of freedom and two quantum internal states. The attractive pair interactions are ‘‘turned on’’ when the internal states are hybridized, corresponding to the molecules acquiring a ‘‘dipole’’ moment. The phase diagram of this system in the temperature-density plane as well as the static and imaginary-time correlations at various densities are investigated by Monte Carlo simulations, using the ‘‘polymer’’ representation, for different strengths of the quantum parameter. These are compared with low-density expansions and mean-field-theory predictions. Good agreement is found in appropriate regimes.

In mixtures of methanol and cyclohexane, a layer of the lower methanol-rich phase (a) intrudes between the upper cyclohexane-rich phase (b) and air (c). As water is added, the layer disappears. In the literature, this effect is interpreted as a wetting-nonwetting transition near a critical point. We suggest instead considering the transition as being caused by the effect of water on the surface tensions ${\sigma }_{\mathrm{ac}}$ and ${\sigma }_{\mathrm{bc}}$ of the two liquid phases against air: In the water-free mixture one finds $w_{\sigma }$≡(${\sigma }_{\mathrm{bc}}$-${\sigma }_{\mathrm{ac}}$)/${\sigma }_{\mathrm{ab}}$>1. Consequently, the b/c interface is thermodynamically unstable, and the system minimizes its free energy by placing a layer of phase a between phase b and air. As water is added, both ${\sigma }_{\mathrm{ac}}$ and ${\sigma }_{\mathrm{ab}}$ increase steeply, whereas ${\sigma }_{\mathrm{bc}}$ is less affected, which makes $w_{\sigma }$ decrease. As soon as $w_{\sigma }$<1, the b/c interface becomes stable and the system gradually disposes with the layer of phase a.

The full second-order, cold-fluid theory of the diocotron and magnetron resonances for nonrelativistic, non-neutral electron flow in planar, crossed-field geometry is investigated using the method of multiple-scales perturbation theory. We find that, for both resonances, the zeroth-order density evolves in the slow time and spatial plane according to a diffusion equation. The quasilinear treatment of the diocotron instability [R. C. Davidson, Phys. Fluids 28, 1937 (1985)] is recovered from the full treatment near the wave-particle, or diocotron, resonance. We also conjecture that, under constant-voltage conditions, this diffusion will cause a small dc current to be set up from the anode to the cathode and that this second-order diffusion equation could possess equilibrium solutions as well. Such solutions would have negative density gradients between all unstable resonances (magnetron as well as diocotron), with plateau formation occurring at the spatial position of all these resonances. Although we cannot show stabilization, we can argue that the introduction of negative density gradients, which would occur as the density profile seeks to re-form into an equilibrium profile, should tend to reduce the linear-instability growth rates, thereby causing the system to tend toward stabilization.

In this paper results are presented from an investigation of the growth of ionization in nitrogen, in a uniform electric field, starting from one or more initiatory electrons. The electrons are described by the distribution function f(vrt) while the ions are assumed stationary. The electron distribution function is obtained with use of Monte Carlo methods, taking into account, self-consistently, collective effects due to the space-charge electric field generated by the electrons and ions. From this kinetic investigation, we have gained insight into the avalanche-to-streamer transition and the role that the velocity distribution and photoionization play in the dynamics of streamers.

A collapse classification for upper-hybrid and lower-hybrid waves in a weakly magnetized plasma is presented. It is proved that, in these nonlinear systems, three-dimensional soliton solutions do not exist. Furthermore, it is demonstrated that the basic criterion for the existence of wave collapse is the unboundedness of the Hamiltonian from below due to nonlinear terms. Finally, it is shown that there exists a hierarchy of wave-collapse regimes, starting with a IweakR-collapse case which formally preserves zero energy into the collapse stage, and concluding with strong collapse, where the trapped wave energy remains finite.

A pulsating Langmuir soliton is investigated and shown to radiate ion-sound waves into the surrounding plasma. A perturbation scheme for treating the coupled nonlinear partial differential equations involved is developed. The spatial and temporal structure of the radiation field is calculated, and it is shown that the soliton radiates energy while conserving both momentum and plasmon number. From an estimate of the relative decrease in amplitude per pulsation period, it is concluded that such a soliton is practically stable if its amplitude is sufficiently small. This effect of low-frequency radiation may be reasonably expected to occur for every nonstationary high-frequency-field localization.

The growth rate of perturbations on the shell of a laser fusion target can be estimated as √gk , where g is the shell acceleration and k is the transverse wave number of the perturbation. This formula overestimates the growth rate, and should be modified for the effects of density gradients and/or ablation of the unstable interface. The density-gradient effect is explored here analytically. With the use of variational calculus to explore all possible density profiles, the growth rate is shown to exceed √gk/(1+kL) , where L is a typical density-gradient scale length. Density profiles actually exhibiting this minimum growth rate are found.

Accurate values of transport properties of electrons in water vapor at room temperature are calculated, over a wide range of E/$n_0$ values, from a numerical solution of Boltzmann’s equation via the momentum method introduced earlier [Phys. Rev. A 33, 2068 (1986); 34, 2185 (1986)]. The dominant features of the E/$n_0$ dependence are explained using the approximate momentum-transfer theory. For the electron–water-vapor rotational interactions the Born-approximation cross sections of Y. Itikawa [J. Phys. Soc. Jpn. 32, 217 (1972)] have been used to obtain satisfactory agreement with experiment.

The microscopic features of the particle trajectories in the Monte Carlo (MC) simulations of strongly coupled one-component plasmas are analyzed as functions of the sequential number c of the MC configurations. It is found that the MC particles behave as if they were trapped in the potential dimples of ion spheres in the small-c regime; in the large-c regime they perform diffusive motion in the fluid simulations and remain localized around the lattice sites in the crystalline simulations. These findings enable us to establish a correspondence between c and the ‘‘MC elapsed time.’’ Application of this correspondence in the large-c regime leads to an estimate of the diffusion coefficient in the fluid regime which agrees well with the one evaluated independently through the molecular-dynamics method.

A mercuric iodide (${\mathrm{HgI}}_2$) detector has been used to obtain x-ray spectra in the energy range from 5 to 200 keV from the Alcator-C tokamak. During high-density Ohmic operation of Alcator-C, this detection system provides a reliable electron-temperature diagnostic. Nonthermal x-ray spectra above 20 keV are observed under certain conditions when a substantial amount of lower-hybrid rf (LHRF) power is injected. The magnitude of this nonthermal behavior strongly increases as the electron density is lowered and is more pronounced in deuterium plasmas than in hydrogen. Model electron distribution functions, which can give rise to the observed x-ray spectra, are discussed.

Three-dimensional convection in a binary-fluid mixture is studied near the onset of the steady-state instability using symmetric bifurcation theory. Idealized boundary conditions are assumed in which the temperature and solute concentration are fixed at top and bottom, with stress-free boundary conditions on the velocity field. The effects of sidewalls are neglected. The problem is formulated as a bifurcation problem on a doubly periodic lattice, with two cases considered in detail: the square lattice and the hexagonal lattice. Symmetry considerations determine the form of the ordinary differential equations governing the dynamics of the neutrally stable modes. The relevant coefficients of these equations are calculated from the governing binary-fluid equations. The bifurcation diagrams are given for all physical values of the separation ratio, the Lewis number, and the Prandtl number. It is found that supercritical rolls are stable to all perturbations lying on the square and hexagonal lattices. Squares, hexagons, and triangles are never stable for the physically accessible regions of parameter space.