An alternative, self-consistent formulation of the homogeneous nucleation theory has been proposed. This approach differs from the classical Becker-Döring-Zeldovich theory in two respects: (i) evaporation rates are evaluated by referring to the stable equilibrium of a saturated vapor rather than to the constrained metastable equilibrium of a supersaturated vapor; and (ii) for the reference stable equilibrium state the Fisher theory of condensation is used in order to obtain a self-consistent definition of the free-energy barrier for l-cluster formation, where l is the number of molecules in the cluster. A comparison of the expressions for the nucleation rate and critical cluster size with the corresponding classical expressions has been made for the different parts of the phase diagram (temperature-supersaturation) and the domain where both theories are close has been found. Predictions of the present theory have been compared with the experimental results on nucleation of n-nonane for the three sets of experiments (diffusion cloud chamber, fast-expansion cloud chamber, and two-piston cloud chamber). It has been shown that the present theory has a much better agreement with experimental results for n-nonane than the classical theory.

Absorption spectroscopy is used to map the absolute density of excited Ar atoms and ground-state ${\mathrm{Hg}}^{+}$ ions in the negative glow of a hot cathode Hg-Ar discharge. The experimental map of the density of excited Ar atoms is compared to, and found to agree with, a Monte Carlo simulation of the resonance-atom density from radiation trapping. The primary production rate per unit volume of excited Ar atoms in the simulation is sharply peaked near the cathode hot spot. The experimental map of the density of ground-state ${\mathrm{Hg}}^{+}$ ions is compared to, and found to agree with, a simulation based on an ambipolar-diffusion model. The production rate per unit volume of ${\mathrm{Hg}}^{+}$ in this second simulation is entirely due to Penning ionization of Hg by the excited Ar atoms. Penning ionization is found to be an important, possibly the dominant, ionization mechanism in the negative glow.

The angle and polarization dependence of optical emission and reflection from dense aluminum plasmas produced in the release wave of a strong shock is investigated theoretically. It is shown that with high-speed measurements (few-picosecond resolution), optical probing of the unloading plasma can be used to examine transport properties and ionization balance of thermodynamic states in the vicinity of the liquid-vapor critical point. The calculations were performed using data from two wide-ranging theoretical models of plasma conductivity, a semianalytical model due to Lee and More [Phys. Fluids 27, 1273 (1984)] and a partial-wave analysis due to Rinker [Phys. Rev. B 31, 4207 (1985); 31, 4220 (1985)]. The models predict substantially different values for the conductivity close to the liquid-vapor critical point (more than a factor of 10 for the electron-ion collison time); the different results obtained for the two models suggest that experimental measurements could provide new information for improving the current understanding of dense plasma properties.

Measurements have been made on the electron excitation coefficients of four Ar levels: 2${\mathit{p}}_1$, 2${\mathit{p}}_5$, 2${\mathit{p}}_7$, and 2${\mathit{p}}_9$. Radiative decay of these levels to 1s levels is responsible for the strongest line features in argon spectra, at 750 nm due to radiation from 2${\mathit{p}}_1$ and 2${\mathit{p}}_5$ levels, and at 811 nm due to transitions from 2${\mathit{p}}_7$ and 2${\mathit{p}}_9$ levels. We have measured excitation coefficients of these levels in the range of E/N from 50 Td to 9 kTd (1 Td=${10}^{\mathrm{-}21}$ V ${\mathrm{m}}^2$). Here E is the electric field and N is the gas density. The optical emission intensities normalized to the local current density were placed on the absolute scale after normalizing the data for the 2${\mathit{p}}_{1\mathrm{-}}$1${\mathit{s}}_2$ transition (750.4 nm) to the previous experimental and theoretical results at 50 Td. We have also made measurements of the excitation coefficients of several 4d and 6s vs E/N, in order to estimate the effect of cascading from upper levels to 2p levels. We have found that the excitations of 2${\mathit{p}}_9$ and 2${\mathit{p}}_7$ are influenced by collisional population transfer between 2p levels at low E/N (E/N<100 Td, N>2.7×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$), by cascading from 3d and 4s levels above 100 Td, and by cascading from 4d and 6s levels at E/N>3 kTd.

The analytical and numerical investigations of the slowing-down process of a two-ion system in an electron plasma are developed on the basis of the Vlasov-Poisson equations, with particular emphasis on two-ion correlation effects, and the main results are presented. The analysis is based on the assumption that the velocities of the two ions are the same. The forces acting on the two particles are calculated and their resulting effects are (a) the appearance of an angular momentum aligning or misaligning the interionic vector with respect to the velocity vector and (b) the appearance of a net transverse momentum acting on the ion pair and proportional to the angle between the interionic vector and the beam direction.

Simulations of high-amplitude electron plasma waves have been performed by solving the Vlasov equation numerically to clarify the mechanism of wave breaking in smooth density profiles. We show that wave breaking exists as a phenomenon which is distinct from incoherent hot-electron generation and which has a clear meaning in a kinetic theory: By trapping of entire bunches of electrons in the wave potential the latter is heavily disturbed and becomes irregular. In contrast to hot-electron generation these electron bunches are not accelerated to high velocities. An analytic criterion for wave breaking is derived which is consistent with the numerical simulations.

We have measured the temporal evolution of the electron density of plasmas produced in polyacetal capillaries with diameters between 0.5 and 1.5 mm excited by 110-ns full-width-at-half-maximum discharge pulses with currents between 13 and 42 kA. The electron density was determined from Stark-broadened line profiles of the 4f-3d O vi transition taking into account opacity effects. The electron density was found to increase continuously during the rise of the current pulse, and to decrease near the end of the current pulse, when a drop in plasma temperature causes the degree of ionization of the plasma to decrease. The peak plasma density in a 1-mm capillary excited by a 24-kA pulse was measured to be 5×${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$. The plasma density was observed to increase linearly with discharge energy from 7.5×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$ for a 5-J discharge to 5×${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$ for a 30-J discharge in a 1.5-mm-diam. capillary.

Longitudinal and transverse dielectric functions are derived from the Vlasov equation with the Landau ion-electron collision operator. The linear collisional propagator has been computed with the use of continuous fractions [Phys. Fluids 30, 1353 (1987)]. The model gives results which are valid in all the frequency and collisionality range. For Maxwellian plasmas, the dispersion relations of Langmuir and electromagnetic waves are explicitly computed with thermal corrections up to the fourth order. For the transverse waves, the results obtained are in good agreement with those deduced from the collisional Dawson-Oberman model [Phys. Fluids 5, 517 (1962)]. A numerical solution of the longitudinal damping rate is obtained. The dispersion relations for weakly anisotropic plasmas are studied. It is shown in particular that, for the collisional damping rates, the corrections due to the anisotropic effects are of the same order as the thermal corrections.

Concepts from topology are increasingly finding utility in magnetohydrodynamics. This paper gives an example of how the connectivity of the domain and the gauge freedom of the vector potential can play an important role in computing the helicity of twisted magnetic fields used in several areas of astrophysics, particularly solar physics. By computing the relative helicity of a simple magnetic field configuration used to model solar prominences, it is shown that helicity can have a nonlocal character. This necessitates a reexamination of its conventional physical interpretation. The magnetic energy is also discussed.

The properties of electrostatic oscillations and instability phenomena are studied, accounting for the time-dependent variation of the grain electric charge due to wave motions in an unmagnetized dusty plasma. It is found that charge fluctuations on the dust grains give rise to two purely damped modes, in addition to causing a collisionless damping of the existing normal modes. Furthermore, some interesting electrostatic instabilities arise in the presence of an equilibrium drift of charged fluids.

The modulational instability of a wave in media where the nonlinearity has a focusing-in-space and defocusing-in-time character is investigated. An approximate self-similar solution of the nonlinear Schrödinger equation is derived for this nonlinearity and is used as background envelope of the wave. We show that this background wave envelope can initially enhance exponential growth of a transverse spatial modulation. The analysis is extended to the case of a modulation in both time and space, and it is found that such a spatiotemporal modulation can be unstable as well.

The Stark widths of 3s-3p and 3p-3d transitions of Ne ii, Ne iii, Ne iv, Ne v, Ne vi, F iv, and F v have been measured in the plasma of a gas-liner pinch discharge. The plasma parameters were determined from 90° Thomson scattering. Some of the measured Stark widths for Ne ii, Ne iii, and Ne iv lines are in good agreement with other experimental data. The results of three independent theoretical calculations are used for comparison with the measured widths. A growing discrepancy between theoretical and experimental results with increasing ionization is detected.

We studied depolarization mechanisms of polarized-proton acceleration in high-energy accelerators with snakes and found that the perturbed spin tune due to the imperfection resonance plays an important role in beam depolarization at snake resonances. We also found that even-order snake resonances exist in the overlapping intrinsic and imperfection resonances. Due to the perturbed spin tune of imperfection resonances, each snake resonance splits into two. Thus the available betatron tune space becomes smaller. Some constraints on polarized-beam colliders were also examined.

The complete asymptotic description of ultrashort Gaussian-pulse propagation in a single-resonance Lorentz medium in the mature-dispersion regime is presented and compared with the results of two independent numerical experiments of the propagated-field evolution. The nonuniform asymptotic method of Olver [Stud. Appl. Math. Rev. 12, 228 (1970)] (an extension of the method of steepest descents) is first applied to obtain the standard asymptotic description of the propagated field that is due to the given input Gaussian-modulated field. The description afforded by this asymptotic method, although nonuniform in certain space-time regions, is found to be in excellent agreement with purely numerical results, especially when exact, numerically determined saddle-point locations, and exact expressions for the derivatives of the phase function are used in the implementation of the theoretical approach. Modern uniform asymptotic techniques, which generalize Olver’s nonuniform description, are then employed to obtain a rigorous description of ultrashort Gaussian-pulse propagation that is uniformly valid for all space-time points in the mature-dispersion regime. This asymptotic description clearly shows that the propagated field can be expressed solely in terms of a generalized Sommerfeld and a generalized Brillouin precursor field, the first of which dominates the total propagated field when the carrier frequency ${\mathrm{\omega }}_{\mathit{c}}$ is well above resonance while the second generalized precursor field dominates when ${\mathrm{\omega }}_{\mathit{c}}$ is below or near resonance. It is further shown that the pulse distortion is due solely to the manner in which the precursor field amplitude is modified by the initial Gaussian-pulse envelope spectrum. Finally, the frequency dependence of the signal velocity of the input ultrashort, Gaussian-modulated harmonic field in a single-resonance Lorentz medium is discussed.

The capacitance of a thin dielectric sheet with a conducting hole is strongly influenced by the fringe effects around the edges of the hole, particularly when the hole size beomes comparable to the size of the sheet. We present here a numerical study of this situation. By a finite-difference scheme, the potential, field, and surface-charge densities in and around the hole are calculated. The sharp edge of the hole represents a singularity, and the asymptotic behavior of the field and surface-charge densities in the vicinity of the singular point are discussed both analytically and numerically. It is found that the scaled difference between a numerical simulation and the simple parallel-plate-capacitor formula changes with the relative size of the hole in a composite power-law relation.

Cooperation of the nonlinearity and of a constant external field below a critical value ${\mathit{f}}_{\mathrm{crit}}$ is shown to generate a traveling radiation in a forced sine-Gordon system.

This paper presents a derivation for a general formula relating the first derivative of the electric-field intensity in any direction to the first derivative of the direction cosines in the orthogonal direction. A restricted form of the formula valid only in the direction of the field lines was first stated by Thomson, and later proved by others. The general form proved here promises to be useful in other attempts to apply techniques of differential geometry to the rapid solution of field problems.

The Lyapunov exponent algorithm of Benettin et al. [C.R. Acad. Sci. Paris 286A, 431 (1978); Meccanica 15, 9 (1980)] and of Shimada and Nagashima [Prog. Theor. Phys. 61, 1605 (1979)] is converted to a continuous time algorithm. The Gram-Schmidt orthonormalization process is incorporated into the differential equations, making orthogonalization continuous. Differential equations for the k-dimensional fiducial volumes are also derived. It is further shown that this algorithm is a factorization of the fundamental matrix Φ in the form Φ(t)=E(t)W(t)${\mathit{E}}^{\mathrm{-}1}$(${\mathit{t}}_0$), where E(t) is orthonormal and W(t) is upper triangular. Numerical stability of the algorithm is considered, and it is shown that the standard Gram-Schmidt process can be used to stabilize the (possibly) unstable equations of motion for the orthonormal basis vectors. A numerical example is presented.

The continuous time form of the ‘‘standard’’ Lyapunov exponent algorithm is extended to include an imaginary part. It is shown that both the familiar constant-coefficient case and the periodic-coefficient case can be solved by this technique. However, while the algorithm is strongly stable in converging on the real parts of the system characteristic exponents, it will produce random imaginary parts. The choice of the original orthonormal matrix is critical: the special initial conditions which lead to the correct imaginary parts for the constant-coefficient and periodic-coefficient cases are found. Without a way to find the special initial orthonormal initial conditions for the general time-dependent case, the imaginary part of a Lyapunov exponent remains difficult to calculate.

In this paper, we generalize the Förster-Dexter theory to treat photoinduced electronic energy transfer for a system in dense media and for an isolated system (i.e., a system in the collision-free condition). Instead of expressing the rate of energy transfer in terms of spectral overlap, we obtain the expression of the energy-transfer rate constant by evaluating a Fourier integral using the saddle-point method. In this way, the energy-gap dependence and the effect of temperature and the isotope effect on the energy transfer can be easily studied. The effect of bridge groups connecting between donor and acceptor on the energy transfer is also studied.