The mode competition in a long-pulse free-electron laser operating in a high-gain Compton regime is analyzed. Due to the strong crossed saturation, a dominant mode is able to suppress competing modes, leading to single-mode operation. This is explicitly shown by a stability analysis of the system of coupled integrodifferential equations describing the evolution of two competing modes, of which only one survives at saturation. In the course of the study the radiation field evolution in the small-signal regime is treated in a unified manner for low and high gain.

Two-level systems are widely used in nonlinear optics; some authors have considered larger systems, but in most of these descriptions the additional levels participate in the dynamics of the two main levels through kinetic rate constants only. Here, we adopt a different point of view. Knowing that two-level models treated in a perturbational approach show peculiar relations between populations and coherences, we analyze the effect of a third perturbating level on these relations. An estimate of the extra contribution to the third-order coherence is made. The role of the dephasing processes on this contribution is analyzed.

In this paper a technique consisting of measuring the Fourier transform $Q_F$ of the time-interval photon statistics distribution is studied when applied to laser Doppler velocimetry. It is supposed that a device that changes the Gaussian intensity profile of the laser beam into a uniform intensity profile is used. A theoretical model for a fluid with a constant velocity is obtained and verified by two ways: experimentally and by a computer-simulation method. Then the experimental conditions for which the signal can be approached to a Lorentzian curve and the error involved in the determination of the fluid velocity are studied from the theoretical model. It is concluded that the measurement of $Q_F$ is a useful technique for very low intensities.

We show that dephasing-induced nonlinear-optical effects whose amplitudes are proportional to trinomials of dephasing rates, ${\Gamma }_{\mathrm{ij}}$+${\Gamma }_{\mathrm{jk}}$-${\Gamma }_{\mathrm{ik}}$, exist in all nonlinear orders of perturbation theory. To do this, we derive a new form for the perturbation expansion of the susceptibility, equivalent to the currently used expansion, but which writes each order as a sum of (1) terms due to single-sided diagrams, and (2) correction terms, all of which are proportional to trinomials of dephasing rates. The proof of this result utilizes a diagrammatic approach involving a new type of double-sided diagram for the latter terms. These diagrams immediately yield the terms proportional to trinomials of dephasing rates in all orders without the need for algebraic manipulation. This approach also reveals some general properties of the Nth-order susceptibility.

It is shown that vacuum fluctuations can be incorporated in the atomic equations of motion as an external multiplicative stochastic process. From the quantum-electrodynamics (QED) vacuum-vacuum transition amplitude it is shown that under the standard Wigner-Weisskopf approximation, this external noise is a Gaussian white noise with an operator-valued diffusion. This property reflects the fundamental difference between QED and a purely stochastic theory in which atomic fluctuations are neglected. It is shown that spontaneous emission results from a stochastic average over this external noise. The role of vacuum and atomic fluctuations in such a process is exhibited.

Expressions of various joint probability distributions of photoelectrons in terms of the photocount distribution P(n,$t_1$,$t_2$) in which n photoelectrons are registered between $t_1$ and $t_2$ are systematically obtained with extensive use of an introduced simple notation. The expressions obtained are used to find two pairs of expressions of the second-order and associated intensity correlation functions in terms of P(n,$t_1$,$t_2$). Some applications to quantum optics are also made to obtain results in agreement with previous work.

Shifts from electron collisions associated with dipole interactions between degenerate levels of a given principal quantum number n are evaluated following D. B. Boercker and C. A. Iglesias [Phys. Rev. A 30, 2771 (1984)]. They are then used to recalculate the plasma shifts of hydrogen and ionized-helium lines from electron collisions, inhomogeneities in the ion-produced quasistatic fields, and some higher-order effects. Because of the partial cancellation of electron collisional shifts by the other effects, inclusion of the Δn=0 collisional shifts leads to an increase of calculated line shifts by a factor ∼1.5, which for Balmer lines of hydrogen and Paschen lines of ionized helium leads to markedly improved agreement with most measurements. Estimates for higher-Z members (Z≥4) of the one-electron isoelectronic sequence yield Δn=0, dipole contributions to the electron-collisional shifts which are much smaller than the effects of Λ=0, penetrating monopole interactions.

Minimum dissipation rate states are explored for a current-carrying channel of magnetofluid, supported by a dc magnetic field and driven by an applied electric field. The minimization is carried out subject to the constraints of constant axial (toroidal) magnetic flux and constant time-averaged rate of supply of magnetic helicity. The solutions of the resulting Euler-Lagrange equations are sensitive to boundary conditions on the current density j. One set of boundary conditions on j leads to the same consequences as Taylor’s ‘‘minimum-energy’’ theory. A different set leads to significantly different consequences, including a departure from the ‘‘force-free’’ magnetic profile and a toroidal component of current density that does not reverse at the wall when the toroidal magnetic field reverses.

We present a few-mode Galerkin model for convection in binary fluid layers subject to impermeable horizontal boundary conditions at positive separation ratios. It describes convection in the form of rolls in x direction, y direction, and squares. To incorporate symmetry-breaking sidewall forces selecting the spatial phase of the patterns relative to the walls we introduce into the model equations a single small inhomogeneity that favors the experimentally realized phase. Then squares are stabilized shortly above onset of convection where the amplitudes are very small. Far above onset, the amplitudes strongly increase, nonlinear mode coupling dominates, and causes rolls to be stable. In an intermediate regime, there are oscillations between the three competing patterns of rolls in x direction, squares, and rolls in y direction. Heat transport, spatial, and temporal behavior of the various convective states are in good agreement with recent experiments.

Spatial distributions of 811-nm emission from the 2$p_9$ and 2$p_7$ (Paschen notation) levels of Ar have been measured for electrical discharges in Ar at very high ratios of electric field to gas density (E/n) and low nd, where d is the electrode separation. Normalization of the lowest-E/n data to published electron excitation coefficients yields absolute excitation coefficients for 270<E/n<43 000 Td (1 Td=${10}^{\mathrm{-}21}$ V ${\mathrm{m}}^2$) and for 6.4×${10}^{19}$<nd<3.5×${10}^{21}$ ${\mathrm{m}}^{\mathrm{-}2}$. Direct and cascade excitation of 811-nm emisison by electrons calculated using a ‘‘single-beam’’ nonequilibrium electron model is an order of magnitude too small to account for the observed emission at the higher E/n.

A model which includes Ar excitation and ionization by ${\mathrm{Ar}}^{+}$ and by fast Ar (10–200 eV) is developed to explain the observations. The fast atoms are produced by charge-transfer collisions of ${\mathrm{Ar}}^{+}$ with Ar. The estimated excitation by ions is negligible and has the wrong spatial dependence. Using the very limited published cross-section data for 811-nm excitation by fast Ar, the model yields spatial dependencies of emission which agree with experiment, but which are too small by factors ranging from 2.5 at 43 kTd to 10 at 6.3 kTd. This variation in the 811-nm emission with E/n is used to obtain energy-dependent excitation cross sections for fast atoms. The good fit of theory to the experimental spatial dependence near the cathode at the higher E/n shows the importance of ionization of Ar by fast Ar atoms. Excitation by backscattered secondary electrons is an important source of 811-nm emission near the anode. Electrical-breakdown and discharge-maintanance voltages from various experiments, including ours, are compared with the predictions of the model. These analyses show that ionization by ions and fast atoms dominates that by electrons from E/n>15 kTd. The estimated ionization by electrons backscattered from the anode provides sufficient feedback to explain much of the electrical-breakdown data and our discharge-maintenance data. Other breakdown data require either a large yield of ionization by backscattered electrons or a very large ion-induced electron yield at the cathode.

Some of the parametric instabilities of an ordinary electromagnetic wave decaying into (i) a high-frequency upper hybrid wave and a low-frequency mixed-mode kinetic Alfvén wave and (ii) an obliquely propagating ordinary scattered electromagnetic wave and a low-frequency electrostatic-ion Bernstein wave (stimulated Brillouin scattering) have been investigated. In channel (i), the partially electrostatic nature of the kinetic Alfvén wave and the component of the low-frequency ponderomotive force along the direction of the external magnetic field lead to the dominant coupling. Explicit expressions for the growth rate and threshold power are given. It is found that, in the case of channel (ii), the homogeneous threshold power is lowest at the first harmonic of the low-frequency electrostatic-ion Bernstein wave. The relevance of the present investigation to fusion, ionospheric modification experiments, and space plasmas has been pointed out. For example, for fusion plasmas the convective threshold power for channel (i) is found to be approximately 20 kW/${\mathrm{cm}}^2$.

The analytic expressions for steady-state electric field intensity and local density scale length in a plasma irradiated by a double-frequency laser are derived. It is shown that the ponderomotive force due to the double-frequency laser field leads to a local density dip near the critical surface and to the anomalous increase and fluctuation of the critical density scale length in some range of field intensity.

On the basis of a quantum-statistical formulation of electronic transport in charged-particle systems, the electrical conductivity of a high-density fully ionized plasma is evaluated using a diagram representation of the Matsubara Green functions. Many-particle effects such as the Debye-Onsager relaxation effect are investigated, and a low-density expansion of the inverse conductivity ${\mathrm{\sigma }}^{\mathrm{-}1}$(T,n)=A(T)lnn+B(T)+C(T)${\mathrm{n}}^{1/2}$lnn+⋅⋅⋅ as a function of temperature T and density n is obtained. Approximative expressions are given for the functions A(T), B(T), and C(T) in the quasiclassical limit, and the resulting conductivity is compared with experiments.

A singular-value decomposition leads to a set of statistically independent variables which are used in the Grassberger-Procaccia algorithm to calculate the correlation dimension of an attractor from a scalar time series. This combination alleviates some of the difficulties associated with each technique when used alone, and can significantly reduce the computational cost of estimating correlation dimensions from a time series.

The static distortions in a homogeneously aligned nematic liquid-crystal film in crossed electric and magnetic fields are theoretically analyzed. Both fields are orthogonal to the undistorted molecular alignment and destabilizing. In the limit of small distortions, a first-order transition between two distorted configurations, with bistability and hysteresis, is obtained if the dielectric anisotropy parameter 1-${\mathrm{\epsilon }}_{\mathrm{\parallel }}$/${\mathrm{\epsilon }}_{\mathrm{\perp }}$ is lower than the elastic anisotropy parameter ($k_3$-$k_2$${)}^2$/(4$k_1$$k_2$), where $k_1$, $k_2$, and $k_3$ are the Frank elastic constants. This condition is satisfied by many commonly used nematic materials. At higher distortions an inversion point is found, above which the transition becomes of the second order. At this point a phenomenon similar to the critical opalescence of fluids is expected.

We study the spatial interparticle distribution function in diffusion-limited reactions and its effect on the macroscopic reaction rate. For an exactly soluble model we find that a universal scaling interparticle distribution function is achieved regardless of initial conditions, and that the macroscopic kinetics is described by an autonomous polynomial rate equation only when the initial distribution of particles is of the functional form of the scaling distribution. Monte Carlo simulations are used to verify the analysis, as well as to investigate interparticle distribution functions for some other reactions.

The growth of ${\mathrm{NH}}_4$Br dendrites from supersaturated aqueous solution is investigated to test recent theories of dendritic growth. A key prediction of these theories is that the tip radius ρ and steady-state growth speed v depend strongly on the surface tension anisotropy ɛ. We measure the capillary length d${¯}_0$ and the crystalline anisotropy of ${\mathrm{NH}}_4$Br, along with the radius and speed of steady-state dendritic tips, in order to make a quantitative test of the theory. The stability constant ${\sigma }^{\mathrm{*}}$ (defined to be 2d${¯}_0$D/v${\rho }^2$, where D is the diffusion constant) is found to be 0.081±0.02 for this material, in approximate agreement with the theoretical prediction of 0.065±0.02. The initial side-branch wavelength is found to be slightly larger than predicted. These measurements are consistent with the hypothesis that ‘‘microscopic solvability’’ determines the steady state of a dendrite.

A one-dimensional model of diatomic molecules with harmonic intramolecular forces and highly anharmonic (hard-rod) intermolecular forces is studied numerically. This interaction allows a numerical integration of the equations of motion with only rounding errors, but no truncation errors. The goal was to investigate the transition from dynamics to classical statistical mechanics for this model; in particular, to check deviations from equipartition and ergodicity which have been reported in the literature for similar models. For a given number of molecules and small vibrational frequencies (much lower than those which occur in nature), no equipartition is found. However, with increasing frequency, equipartition is established, first between the two vibrational degrees of freedom and then also with the translational motion of the molecules. While for a small number of molecules and small frequencies Kol’ogorov-Arnol’d-Moser–like motion dominates, this behavior changes with increasing frequency to chaotic motion. The decay time of the vibrational-energy–time correlation function does not show any increase with frequency, in contrast to what G. Benettin, L. Galgani, and A. Giorgilli [Phys. Lett. A 120, 23 (1987)] found for a model, similar to ours but with a soft repulsive interaction. Thus, the present model behaves in accordance with classical statistical mechanics.

A linear term linked to molecular chirality occurs in the bending energy of membranes with $C_2$ or $D_2$ symmetry. We find it to alternate in sign, depending on the direction of a cylindrical curvature, and discuss consequences for anisotropic solid membranes, tilted fluid bilayers, and ferroelectric smectic liquid crystals.

A generalization is given of the method introduced by Nosé for simulating isothermal behavior by molecular dynamics. An infinity of physically inequivalent choices for dynamics can be made to evaluate average properties of an equilibrated canonical ensemble. The availability of different choices may, we suggest, open the principal possibility of searching for a dynamics which will adequately mimic not only the equilibrium but also the time-dependent properties of a particular physical system.