We review and extend the theory of instabilities in absorptive optical bistability for ring cavities containing homogeneously broadened two-level media. The instabilities occur in the high-transmission branch and result in either a precipitation to the low-transmission branch or in pulsed multimode operation. Two numerical approaches are used to predict operation away from the simple mean-field limit. First, an iterative method is used to solve the general field eigenvalue equation for cavity modes with frequencies displaced from the input frequency. This work shows that the instability region decreases in size as the mirror transmission increases. These calculations are confirmed by the second numerical technique, consisting of direct integrations of the coupled Maxwell-Bloch equations. This second approach also provides time histories of the instability evolutions, and divides the instability range into a precipitation regime and a self-pulsing regime. The results are discussed in terms of first- and second-order phase transitions, and agree with the analytical results obtained within the dressed-mode description of optical bistability. They show that when the incident field is adiabatically decreased along the high-transmission branch, the spiking behavior always appears abruptly. By further decreasing the incident intensity, the self-pulsing disappears either continuously if the system remains in the high-transmission branch, or discontinuously if the system precipitates to the low-transmission branch. Connection is made with induced probe gain known in the saturation spectroscopy of absorbers (uninverted media), in which population pulsations transfer energy from a saturating wave to the probe waves. The very close relationship with multimode operation in homogeneously broadened unidirectional ring lasers is also established.

The design and performance of variable-wiggler, free-electron laser (FEL) amplifiers was studied by using a one-dimensional computer model which incorporated separate sections for design and simulation. Resonant-particle equations were used in the design phase. The variation of the wiggler parameters was not predetermined (linear, exponential, etc.) but was carefully tailored to match the electron energy throughout the FEL amplifier. The simulation section of the model self-consistently tracked the phase-space trajectories of 500 particles for the length of the amplifier. In this way the designs were tested not only for overall gain and efficiency but also for resistance to irregularities in laser input power, electron-beam power, electron-beam-energy spread, and wiggler construction. High-current-density electron beams (electron-beam power > laser-beam power) were found to be essential for stable and efficient amplifiers. Some designs demonstrated better performance under conditions of nonresonant input particles.

It is shown that an interesting duality exists for wave packets and localized pulses as their representations in ($\overrightarrow{\mathrm{x}},t$) and ($\overrightarrow{\mathrm{k}},\omega$) spaces are compared. A wave packet in ($\overrightarrow{\mathrm{x}},t$) space has a slowly varying envelope. This corresponds to a narrow spectrum in ($\overrightarrow{\mathrm{k}},\omega$) space. On the other hand, a localized pulse in ($\overrightarrow{\mathrm{x}},t$) space corresponds to a slowly tapering spectrum in ($\overrightarrow{\mathrm{k}},\omega$) space. The analysis of wave-packet propagation is usually carried out by means of ray theory. It is well known that ray tracing, in spite of its limitations, provides a powerful tool for the analysis of wave-packet propagation in dispersive, weakly inhomogeneous media. Similarly, it is shown here that localized pulses in inhomogeneous, weakly dispersive media, can be analyzed, using the concepts of dual-dispersion equation, dual-ray tracing, and group slowness. Hamilton's equations of geometrical optics are the Euler-Lagrange equations of the variational form known as Fermat's principle. In an analogous manner the dual Fermat principle is introduced here, being equivalent to the dual-ray equations. The method proposed here facilitates the analysis of localized pulses in inhomogeneous, weakly dispersive media. The dual-ray tracing provides a clue to the way in which the spectrum of a pulse in ($\overrightarrow{\mathrm{k}},\omega$) space, hence its shape in ($\overrightarrow{\mathrm{x}},t$) space, change in the course of propagation.

In an earlier paper, we considered a Hamiltonian trilinear in boson operators, which described several physical systems of interest such as interaction of $N$ two-level atoms with a single-mode resonant radiation field, parametric amplification, frequency conversion, Raman and Brillouin scattering, etc. We found that the dynamics of the system can almost exactly be determined if either one of the three modes is strong for all times or any two modes are separately strong in two complementary time domains. In the present paper, we determine the statistical behavior of the system in each case. We give explicit results for a number of initial states (e.g., coherent, chaotic, a mixture of coherent and chaotic, number state, etc.) of the modes 1, 2, and 3.

A closed-form approximant is proposed for the crossover function which connects the asymptotic critical behavior of the viscosity of a fluid with the normal behavior of the viscosity away from the critical point. The expression is used to represent the critical viscosity enhancement near the gas-liquid critical point of fluids as a function of temperature and density.

A statistical theory of Langmuir turbulence is developed for the equations of Zakharov in the approximation formally equivalent to the direct-interaction approximation (DIA). At this level the theory is realizable, conserves the mean values of the three invariants of the Zakharov equations, contains the modulational instability, and goes over continuously to weak-turbulence theory in the proper limit. This paper concentrates on the properties of the electrostatic and ion-density response functions which arise in the theory; a new continued-fraction representation is given which is numerically more efficient than direct integration of the DIA equations. These response functions contain a new nonlinear dispersion relation for the modulational instability of a fluctuating Langmuir spectrum. Comparison is made between the continued-fraction representation, direct integration of the DIA, and a Monte Carlo simulation. The noninvariance of the DIA to random gauge transformation is discussed as well as the saturation of the modulational instability by spectral broadening.

The effect of electron temperature and ion density gradients on x-ray diagnostics for dense plasmas is studied. Time-independent calculations of the $K$-shell radiation spectrum from imploding wire arrays and laser-foil interaction experiments are performed using a one-dimensional collisional-radiative equilibrium ionization model with probability-of-escape radiation transport. The resulting spectra are analyzed using diagnostic techniques based on the assumption that the plasma is an isodense, isothermal emitter. It is shown that temperature determinations via line ratios and bound-free continuum slopes are affected by plasma opacity, the temperature dependence of line and continuum emission power, and the spatial ion density distribution in the plasma. Significant differences between actual and predicted values of plasma parameters are found, and the physical reasons for the discrepancies are discussed in detail.

The dielectric tensor is calculated for critical classical fluids in the presence of acoustic waves by the linear-response theory. Two effects are examined and proposed as new experimental methods. They are diffraction of light by acoustic waves (Debye-Sears effect) and acoustically induced birefringence. These two effects are found to grow near the critical point.

A method is presented for treating ionization equilibrium in the presence of plasma coupling, which allows for the fact that heavy ions may be strongly coupled (liquidlike) while electrons are only moderately coupled (gaslike). The theory utilizes a many-body perturbation expansion of the grand canonical partition function. Three distinct renormalizations are required to handle the general problem. They account for (1) formation of electron-nucleus composites, (2) coupling of the composite particles to the plasma, and (3) strong coupling of multiply charged heavy ions. Five dimensionless parameters, which are the ratios of two lengths, are required to define the limits of applicability of the theory. Equation-of-state calculations for Ar have been carried out. Corrections to the Saha equation are found to be significantly smaller than predicted by the Debye-Hückel theory. At moderate density this is due to decreased net Coulomb attraction. At high density core repulsion tends to offset (or exceed) the Coulomb attraction term.

The autocorrelation functions of the microscopic electric current $J\left(t\right)\mathrm{}$ and the electron velocity $Z_2\mathrm{}\left(t\right)\mathrm{}$ are calculated for strongly coupled, semiclassical two-component plasmas. The corresponding memory functions are expressed in terms of mode-coupling integrals involving density- and energy-correlation function in the framework of a microscopic kinetic theory which preserves the exact statics. Through a sequence of well-defined approximations, the expressions for the memory functions are made self-consistent, the resulting equations are solved iteratively with the interaction potentials, and the static-partial-structure factors as the only input. The theory is then applied to weakly degenerate hydrogen and carbon plasmas for values of the plasma parameter of order 1. The resulting correlational functions $J\left(t\right)\mathrm{}$ and $Z_2\mathrm{}\left(t\right)\mathrm{}$ and their integrals, the electrical conductivity, and the electron self-diffusion constant, agree reasonably well with the "molecular-dynamics" data of Hansen and McDonald and with additional simulation results presented here. The "long-time tail" in $J\left(t\right)\mathrm{}$ observed in the simulations is interpreted in terms of mode-coupling effects. The damping and frequency shift of the plasmon peak in the dynamical charge-fluctuation spectrum are explicity evaluated in the long-wavelength limit; the frequency shift above the plasma frequency is shown to be nonnegligible for strong coupling.

Plasma waves propagating within a relativistic quantum plasma embedded in a strong magnetic field (from which follows the anisotropy of the equation of state) are investigated from hydrodynamical equations. It is shown (i) that, owing to relativistic effects, the plasma and the Larmor frequencies become density and temperature dependent and (ii) that these frequencies "split" into longitudinal and transverse frequencies, owing to the anisotropy brought by the strong magnetic field.

A time-dependent direct correlation function (TDDCF) is defined and discussed. The definition (which differs from that proposed by Percus and Yevick) is motivated by linear response theory. The TDDCF consequently has a functional-derivative or stimulus-response interpretation closely analogous to that of the static direct correlation function. Mean-field considerations suggest that the TDDCF separates into a term which is simply related to the pair potential and a spatially shorter-ranged remainder. This behavior is confirmed in the Vlasov-Zwanzig approximation.

The collisionless cyclotron damping of a transverse wave near electron-cyclotron resonance is measured in well-defined experimental conditions. The observed wave dispersion and damping are in good agreement with a hotplasma theory. It has been revealed that spatial damping rates are determined by only one parameter, i.e., the ratio of resonance velocity to the thermal velocity.

Measurements of the Rayleigh-Brillouin spectra of light scattered by two classes of gaseous mixture; helium-xenon, and helium-hydrogen and helium-deuterium, have been performed over a range of density, concentration, and wave vectors. For He-Xe mixtures, under certain experimental conditions the data are accurately accounted for by a complete two-component hydrodynamic theory and light scattering has been shown to be a good method to deduce the thermal diffusion coefficient. We have thus determined in a quantitative way the range of applicability of the hydrodynamic theory. On the other hand, when the partial desnity of helium is not too small, systematic deviations between experimental and the calculated spectra are observed. These deviations can be understood in terms of kinetic effects to be discussed in a subsequent paper. For He-${\mathrm{H}}_2$ and He-${\mathrm{D}}_2$ mixtures, the hydrodynamic theory is in good agreement with our experimental data in the full range of densities and concentrations. We discuss the reason for this different behavior for the two classes of mixtures.

A theory is presented to analyze the Raman scattering from liquids formed by diatomic molecules. This theory is based on the fact that the Hamiltonian of a liquid sample is invariant under the operations of the full $N$-symmetric group. This symmetry entirely determines the structure of the theory; it is applicable for all vibrational-modulation speeds. Moreover, the notion of coherence and incoherence of a light scattering process is examined. One finds that the isotropic Raman process is partially coherent, and the anisotropic Raman scattering is basically an incoherent process.

In this paper we analyze the basic characteristics of experimentally observed second-harmonic light spectra generated during long-duration high-intensity laser-plasma interactions. It is shown that the observed spectrum characteristics of threshold, red-shift, and target material dependence can be explained by a two-step mechanism of parametric coupling affected by a strong "imposed" ponderomotive force. The imposed ponderomotive force, generated by the laser light's standing-wave pattern, affects the parametric coupling through increased linear wave dispersion. Experimental results agree with the theoretical prediction and suggest the existence of additional parametric instabilities in the ponderomotive-force-dominated regime.

The friction coefficient for a smooth hard sphere (Brownian particle) moving through a fluid composed of finite-sized particles with internal rotational degrees of freedom is computed. Inertial effects are included. The long-time limit of the velocity-autocorrelation function is obtained. We find that the velocity-autocorrelation function decays as $t^{-\frac{3}{2}}$ but with a coefficient that is altered from the usual Navier-Stokes results to include contributions from transport processes involving internal rotational degrees of freedom of the fluid.

The coefficient of frictional torque acting on a rough hard sphere (Brownian particle) which rotates about a fixed axis in a fluid composed of finite-sized particles with internal rotational degrees of freedom is computed. Inertial effects are included. The long-time limit of the angular-velocity-autocorrelation function is obtained. We find that angular-velocity-autocorrelation function decays as $t^{\frac{-5\mathrm{}}{2}}$, but with a coefficient that is altered from the usual Navier-Stokes result to include contributions from transport processes involving internal rotational degrees of freedom of the fluid.

Although the method of dual coordinates has been employed in the literature to quantize the damped harmonic oscillator, one cannot reproduce the proper classical limit by this method. This is shown by constructing operators which have the correct damped behavior and obtaining coherent states as their eigenstates. These states turn out to be nonnormalizable; this is shown to be due to the unphysical nature of the Hamiltonian employed in the method of dual coordinates.

Collisional dissociation of 750-2000-eV $\mathrm{H}_3^{}{}_{}{}^{+}$ ions has been studied by translational spectroscopy. From the energy spectra of the $\mathrm{H}_2^{}{}_{}{}^{+}$ ions arising from electronic excitation to the ${}_{}{}^1{}_{}{}^{}E_1^{\prime }{}_{}{}^{}$ repulsive state, the energy of the lowest ${}_{}{}^1{}_{}{}^{}A_1^{\prime }{}_{}{}^{}$ state of $\mathrm{H}_3^{}{}_{}{}^{+}$ was found to be - 1.33±0.01 hartree.