The spontaneous and induced emission from a free-electron laser is treated for the case in which an axial magnetic field is imposed in addition to the helical, axially periodic wiggler magnetic field. The classes of possible single-particle trajectories in this configuration are discussed, and the results are applied to a calculation of the incoherent radiation from a beam of relativistic electrons in the system. The coherent radiation is treated by solving the Vlasov-Maxwell equations for the linear gain in the tenuous-beam limit, where the beam plasma frequency is much less than the radiation frequency and self-field effects can be ignored.

A theory of stimulated Raman scattering (SRS) is presented which treats in a unified manner the buildup of SRS from spontaneous Raman scattering and the spatial propagation which leads to gain. Maxwell-Bloch equations describe the coupling between the Stokes field operator and the collective atomic operators, which are driven by a classical laser field under low-signal-gain conditions, where the atomic ground states and laser field remain undepleted. An analytic expression is derived for the forward-propagating Stokes field operator in a one-dimensional spatial approximation when the Fresnel number of the excited medium is unity. Steady-state and transient Stokes intensities are evaluated under low-gain (spontaneous) and high-gain (stimulated) conditions. The Stokes intensity is found to be exactly independent of a laser bandwidth arising solely from phase fluctuations. The power spectrum of steady-state SRS is evaluated, giving a gain-narrowed spectral profile when the laser is narrow band, and a spectrum identical to the laser spectrum when the laser is broad band. A strong analogy between SRS and two-level superfluorescence is found; in both cases the macroscopic, collective dipole moment is initiated by quantum fluctuations.

A quasi-two-level system is a generalization of a two-level system where each of the single levels is replaced by a nearly degenerate multiplet. We develop the theory of the photon echo, the stimulated echo, and fluorescence emission for such systems when they are subjected to pulses of electromagnetic radiation that are short compared to the reciprocal (in frequency units) of the widths of the multiplets. The observable in each of these experiments is related to equilibrium time-correlation functions of the system in the absence of the radiation field. The correlation functions associated with these experiments involve more than two dynamical operators and more than two times, unlike the correlation functions for such processes as low-power optical absorption and neutron scattering. We introduce an exactly solvable factorization model for the transition moments, which includes as special cases the situation where either of the multiplets is a single state. We also consider the unitary model, which was introduced by Mims, and which leads to considerable simplification of the correlation functions. Several examples of these models are discussed to investigate the features of time-dependent fluorescence experiments and coherent optical transient experiments. In general, there is no simple connection between the time dependence of the decay of a photon echo and the Fourier transform of the low-power homogeneous absorption spectrum.

An optical test of the metric theories of gravitation which employs a ring laser interferometer in an earthbound laboratory is suggested and analyzed. The proposed test would be sensitive to the presence of a preferred frame of the universe and to the geodetic and Lense-Thirring (frame-dragging) rotations of the local inertial frames relative to fixed stars. The frequency difference of the counterpropagating beams in a Sagnac-type experiment is determined within the framework of the parametrized post-Newtonian formalism. The precision with which the various parameters involved in the expression for the frequency difference can be measured is discussed.

We report experimental observations of dispersive- and absorptive-optical bistability due to saturation of the $D_1$ line of atomic sodium in a tight-focused Fabry-Perot cavity. Under the conditions of large optical power broadening and substantial collisional broadening by argon buffer gas used for part of the data, the sodium very nearly behaves as a two-level homogeneously broadened absorber. It thus yields a test of the two-level mean-field optical-bistability model. That model, including homogeneous broadening, fails to account quantitatively for the power levels and power dependencies of the cavity transmission. In particular, this model predicts too rapid an onset of atomic saturation with cavity power. In contrast, predictions of a two-level Gaussian-field optical-bistability model for the dependence of transmitted power as a function of laser power and frequency are confirmed by the experimental data. However, there is a remaining discrepancy in the absolute value of the cavity power.

This paper presents a unified theory of nonequilibrium transitions which occur in radiation interacting via an $n$-photon transition with atomic systems inside optical cavities. Incoherent pumping of the atoms and coherent driving of the cavity are included. Examples of such systems are the $n$-photon laser, the $n$-photon laser with injected signal, and $n$-photon optical bistability. The state equation and stability conditions for these phenomena are derived. Fluctuations are included via a Fokker-Planck equation in the constant-diffusion approximaton for which potential solutions may be obtained in the steady state. When these solutions are used, moments of the photon distribution can be calculated for the above systems in the specific cases of one- and two-photon transitions.

We show that the most commonly used high-intensity approximations as applied to ionization by strong electromagnetic fields are related. We also discuss the applicability of the steepest-descent method in these approximations, and the relation between them and first-order perturbation theory.

The general time-dependent problem associated with a two-mode-laser Fokker-Planck equation has been considered. Analytic expressions for the eigenvalues and the eigenfunctions have been derived for the below- and above-threshold operation of the system. It is shown that depending on the values of the pump parameters $a_1,a_2$ and the coupling constant $\xi$, a wide variety of dynamical behavior may be encountered. Thus for $\xi <1\mathrm{}$ interesting threshold effects may appear in the behavior of correlation times and linewidths as a function of excitation which may change their behavior whenever a mode passes through its threshold of oscillation. For $\xi =1\mathrm{}$ the correlation time of the stronger mode may pass through a maximum before it starts to decrease with increasing excitation. The weaker mode may show particularly interesting behavior for $\xi =1\mathrm{}$. Both the correlation time and the linewidth may approach a constant value independent of the excitation. For $\xi >1\mathrm{}$ the system may show bistability. Our analysis provides a deeper mathematical understanding of the onset of bistability and the analogy to the thermodynamic phase transition. Expressions for the switching time have been derived using several different procedures. We have also been able to derive closed-form expressions for the two-time joint probability densities. It should be possible to test some of these predictions in photon-counting experiments. Finally, we mention that our results and method should also be applicable in other similar problems, e.g., to the classical theory of coupled fields.

We present measurements of the static dielectric constant $\epsilon$ near the liquid-liquid critical point in polystyrene + cyclohexane. The data show an anomalous decrease in $\epsilon$ as a function of temperature as the critical temperature is approached from the one-phase region at the critical composition. The anomaly reaches an amplitude of about $7\times {10}^{-5\mathrm{}}$ in $\epsilon$ at a few millikelvins from the critical temperature. The data are consistent with the theoretical predictions of a critical exponent for ${\rho }^{-1\mathrm{}}\epsilon$ of ($1-\alpha$), where $\rho$ is the density and $\alpha$ is the specific-heat exponent.

Saturation levels of ion-acoustic-wave turbulence driven by a heat-flux and a suprathermal electron current have been calculated on the basis of perturbed-orbit theory. The levels are found to be lower than those commonly estimated from simple trapping arguments and too low to explain the thermal-flux inhibition observed in many laser-plasma experiments.

In order to describe nematics having an oblong or disclike molecular structure, a system of hard cylinders is considered. After proposing an equation of state, the thermodynamic behavior is calculated and compared with a system of spherocylinders and with experiment.

The Yvon-Born-Green (YBG) theory with Kirkwood superposition is used to determine the critical exponent $\alpha$ for a square-well fluid, where $C_v\sim {|T-T_c|}^{-\alpha } \mathrm{and} T>\mathrm{}{T}_c$. The value obtained, $\alpha =0.30\mathrm{}\pm 0.01$, when taken in conjunction with the exponents $\gamma$, $\beta$, and $\delta$ determined previously by the authors, is found to be consistent with the two inequalities that involve all four exponents. Finally, as was reported earlier by investigators using the Percus-Yevick theory, extrema in $C_v$ are found in the stable fluid region using the YBG theory.

It is shown that if one considers the $n\to 0$ limit of a magnetic system consisting of $n$-component classical spins on a lattice, one indeed obtains a correspondence with a system of self-avoiding random walks; that is, polymer chains with excluded volume in a solution, but the correspondence is not isomorphic. It turns out that $K$ and $H$ do not serve as the activities for the polymer system, which, in fact, are given by $\frac{K}{z}$ and $\frac{H}{\sqrt{z}}$, where $z=1+\frac{H^2}{2}$. Moreover, the polymer free energy $\hat{W}$ is also different from the magnetic free energy $W_0$ in the limit $n\to 0$. Various polymer correlation functions are calculated and are found to be different from those proposed by other authors. It is also shown that $\hat{W}$ satisfies the proper convexity properties, even though $W_0$ does not.

Nonequilibrium molecular dynamics is used to study the conduction of heat due to a radial temperature gradient in a rotating two-dimensional disk of dense fluid. These calculations show that Coriolis's force contributes to the heat flux.

The kinetic theory for time-correlation functions at low density is studied for potentials with bound states and finite collision times. The contribution to the binary-collision operator from bound pairs of atoms with arbitrarily large interaction times is shown to exist and to vanish for times large compared to the characteristic scattering time, justifying the Boltzmann limit for potentials with attractive parts. The effects of such bound states and finite collision times on the short-time behavior of correlation functions are illustrated by a detailed calculation of the velocity-autocorrelation function for a square-well potential. Good agreement with the corresponding results from molecular dynamics is obtained.

We extend the theory of isotropic tensors, developed by Robertson, Batchelor, and Chandrasekhar, to cover the general case of turbulence with a pseudovector-preferred direction, without assuming mirror-reflection invariance. Attention is focused on two-point-correlation functions, and it is shown that the form of the decomposition into proper and pseudotensor contributions is restricted by the homogeneity requirement. We present the somewhat unexpected result that the vector- and pseudovector-preferred-direction cases yield different results: A pseudovector-preferred direction allows the correlation matrix one more functional degree of freedom than does the "proper" vector case. We present an explicit form of the two-point-correlation tensor in the presence of a uniform mean magnetic field which may be appropriate for use in analysis of magnetic fluctuations in plasma containment devices or the interplanetary medium. A procedure for determining the magnetic helicity from experimental data is presented.

We have calculated the Helmholtz free energy of liquid Na and Al using a variational principle based on the Gibbs-Bogolyubov inequality in conjunction with hard-sphere and one-component-plasma reference systems. For liquid Na, the one-component plasma gives a lower variational bound to the free energy and fits the experimental structure factor better than does the hard-sphere fluid, in agreement with the findings of Ross et al. for liquid Li. Liquid Al, however, is better described by the hard-sphere reference system when exchange-correlation corrections to the pair potential are properly included. We ascribe the difference to the fact that the pair potentials of Al are relatively stiff, and those of the alkali metals relatively soft at small separations.

The surface layers of tokamak plasmas are strongly unstable to low-frequency oscillations. The limiter, by imposing a nonaxisymmetric state in the plasma scrape-off layer, may increase the free energy driving the instabilities. An active, two-faced sandwich limiter is proposed to symmetrize the scrape-off layer, thereby minimizing the mismatch between the inner and outer tokamak states.

The solutions of the Lorenz system are investigated by examination of their complex-time singularities. It is found that the location and type of singularity that occurs for complex time is critical in determining the behavior of the real-time solution. By direct expansion of the solution at a singularity its structure is determined. In general, the solutions are multiple valued in the neighborhood of a singularity; a property that is intimately related to the nonintegrability of the system. A numerical investigation is made of the analytic structure of solutions exhibiting turbulent bursts and undergoing period-doubling bifurcations.

Intense nonrelativistic light-ion beams generated in magnetically insulated diodes can reach total beam currents large enough to confine charged fusion products within pinch channels which are formed by these beams if they are projected onto thermonuclear material. Furthermore, since the required beam currents are still below the critical Alfvén current, these pinch channels are magnetohydrodynamically stable. However, because the time these beams last is very short and of the order of 10 nsec, the thermonuclear target must have a density at least as large as solid-state density to satisfy the Lawson criterion. This large target density makes it necessary that the beam be focused down to a radius less than ∼ ${10}^{-2\mathrm{}}$ cm, to balance the plasma pressure against the magnetic pressure. To make this focusing possible a new kind of a low-emittance intense ion source is proposed. It consists of pointlike pulsed dense plasma positioned in the field-free space behind a meshlike anode. The focusing itself can be done in three steps, first by sufficiently good ion optics, second by wall focusing, and third by radiation cooling. This inertial-confinement fusion concept avoids the problems of reaching this goal through highdensity target compression by ablative implosion.