A theory of highly charged, polydisperse, ionomeric colloidal or micellar suspensions with arbitrary charge distributions in the ionomeric layers is formulated and solved using a hybrid mean-spherical–hypernetted-chain approximation. The counterion parts of the problem are solved analytically, irrespective of the approximations used for the colloid parts, thereby obtaining a problem with fewer components. Continuum models for coil- and rodlike charge distributions are proposed, and correlation functions, structure factors, and counterion distributions are computed. In addition, some common thermodynamic quantities and the question of conformational equilibria in the ionomeric layers are discussed.

Ice crystals growing vertically upwards in quiescent ultrapure water have been investigated at small subcoolings in the range of 0.035 <ΔT<1.0 K. At subcooling less than 0.35 K, dendritic tips split and the tip radius ${\mathit{R}}_2$ drops because two tips replace one when viewed from the basal plane. The growth velocity and the tip radius of the edge plane of the dendrite, however, are found to remain independent of time and unaffected by the morphological instabilities in the basal plane. In contrast, when the subcooling is greater than 0.35 K, the tips seem to grow with an invariant shape. The shape of drops of water that are in equilibrium with solid ice is observed to be close to a circular disk. From the shape of these drops, the anisotropy of the surface energy in the edge plane, which is an ellipse, is estimated to be about 30%, while the basal plane is found to be indistinguishable from a circle, despite the hexagonal structure of ice. We speculate here that tip splitting in ice dendrites may be a morphological instability caused by the coupling between lack of anisotropy in the basal plane and natural convection, which becomes significant at small ΔT.

A molecular-dynamics model of chemically reacting hard spheres is applied to study the influence of nonequilibrium effects on the rate constant of a thermally activated chemical reaction. It is demonstrated that these effects can be important if the activation energy of a chemical reaction is in the range between 0.5-${\mathit{k}}_{\mathit{B}}$T and 6${\mathit{k}}_{\mathit{B}}$T. The decrease in reaction-rate constant observed in simulations is larger than that predicted by models of a chemical reaction based on Boltzmann or Enskog equations.

Experiments to study the gas kinetic temperature in a dc hollow cathode discharge have been carried out under conditions suitable for diamond growth using ${\mathrm{CH}}_4$-${\mathrm{H}}_2$ mixtures as the feed gas. The gas kinetic temperature is shown to be equal to the rotational temperature for particular emission bands in ${\mathrm{H}}_2$ and in CN in a ${\mathrm{CH}}_4$-${\mathrm{H}}_2$ discharge containing a small ${\mathrm{N}}_2$ impurity for total pressures above 10 Torr. The gas temperature can be obtained by measuring relative line intensities in emission of either the R branch of the ${\mathit{G}}^1$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$→B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$(0-0) band of ${\mathrm{H}}_2$ or the R branch of the ${\mathit{B}}^2$${\mathrm{\Sigma }}^{+}$→X ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0-0) band of CN. The (0-0) symbol represents a band of transitions occurring between the levels with 0 vibrational quantum number in the upper electronic state and the levels with 0 vibrational quantum number in the lower electronic state. These measurements of gas kinetic temperature in a ${\mathrm{CH}}_4$-${\mathrm{H}}_2$ discharge using optical emission spectroscopy have been confirmed by two different experiments using laser-induced fluorescence.

The ion distribution function in a weakly collisional sheath is obtained analytically for arbitrary electric-field configurations, based on kinetic equations with elastic collisions. In the light of application to plasma etching and deposition, the distribution function is integrated to derive the angular and energy distributions of the ion flux incident at the electrodes. Under the assumption of a constant-sheath electric field, the simple analytic expressions ${\mathrm{\Gamma }}_{\mathrm{\theta }}$∝2 sinθ cosθ(-4 ln sinθ+${\sin }^4$θ-1)/(1+${\sin }^2$θ${)}^2$ and ${\mathrm{\Gamma }}_{\mathrm{en}}$∝-ln(1-η) for the angular and energy distributions of the nonballistic ion flux are obtained, where η denotes the normalized ion kinetic energy. For the more realistic case of a self-consistent electric field, integral formulas for ${\mathrm{\Gamma }}_{\mathrm{\theta }}$ and ${\mathrm{\Gamma }}_{\mathrm{en}}$, which are amenable to numerical quadrature, are also obtained from the Boltzmann-Poisson system. These analytic expressions are compared with Monte Carlo sheath simulations under various conditions and are found to be in excellent agreement.

A modified moment method is used to predict the effect of absorbing boundaries on a continuous stream of electrons traveling in a gas in a steady, uniform electric field. Theoretical results are shown to be in good qualitative agreement with published Boltzmann and Monte Carlo calculations for the same physical problem.

Electron-impact excitation rates for transitions in heliumlike Mg xi, calculated with the R-matrix code, are used to derive the electron-density-sensitive emission line ratio R (=f/i) and temperature-sensitive ratio G [=(f+i)/r], where f is the forbidden 1${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S–1s2s ${}_{}{}^3{}_{}{}^{}$S transition, i the intercombination 1${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S–1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{1,2}$ lines, and r the resonance 1${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S–1s2p ${}_{}{}^1{}_{}{}^{}$P transition. A comparison of these with R and G ratios determined from x-ray spectra of the divertor-injected tokamak experiment reveals excellent agreement between theory and observation, with discrepancies of typically 3% and 9% in R and G, respectively. These discrepancies correspond to variations in ${\mathit{N}}_{\mathit{e}}$ and ${\mathit{T}}_{\mathit{e}}$ of approximately 0.1 and 0.15 dex, respectively, and hence it should be possible to use the theoretical results to derive plasma parameters to this level of accuracy for remote sources for which no independent electron temperature and density estimates exist, such as solar flares.

The wave equation for laser light incident on a static, steep-gradient plasma has been solved numerically, with the inclusion of an intensity-dependent electron-ion collision rate, and incorporating spatial dispersion and wave-breaking effects. At moderate intensities (∼${10}^{14}$ W/${\mathrm{cm}}^2$), the nonlinearity has little effect on the calculated reflectivity, but at higher intensities the reflectivity is greater than that predicted by a linear model. The discrepancy is small for a steplike plasma (with a density gradient scale length L∼0.01${\lambda }_0$), but increases for longer scale lengths (L∼${\lambda }_0$). In the case of p-polarized light, the angular dependence of reflectivity is sharpened at higher intensities, and resonance effects play an important role even for very short scale lengths.

The ion-acoustic and entropy-fluctuation resonance peaks in the electron-density fluctuation spectrum S(k,ω) of high-density, low-temperature collisional plasmas (Ar, ${\mathit{T}}_{\mathit{e}}$=2 eV, ${\mathit{N}}_{\mathit{e}}$=1×${10}^{17}$ ${\mathrm{cm}}^{\mathrm{-}3}$; He, ${\mathit{T}}_{\mathit{e}}$=2.3 eV, ${\mathit{N}}_{\mathit{e}}$=1×${10}^{17}$ ${\mathrm{cm}}^{\mathrm{-}3}$) are measured by means of ${\mathrm{CO}}_2$ laser scattering. The spectrum consists of three peaks, two due to ion-acoustic waves, and a central entropy-fluctuation peak. The entropy peak (at ω=0) is observed in a plasma. Two theoretical models are introduced, and their predictions compared with the observations. A two-species BGK kinetic model includes the collisional interactions between ions and electrons, which predicts the fluctuation spectrum better than the BGK model, not including the ion-electron collisional interactions. Alternatively, Braginskii’s two-fluid transport equations may be used with the fluctuation-dissipation theorem to derive an analytic expression for the fluctuation spectrum, which gives the relation of the thermal transport coefficients to the spectrum. The prediction of Braginskii’s equations is used to estimate the transport coefficients experimentally by least-squares fitting the theory to the experiment. The effects on the spectrum of the second-stage ionization species in the plasmas are estimated wtih a three-fluid model.

In this paper we describe small-amplitude nonlinear plasma wave solutions to the one-dimensional Vlasov-Maxwell equations. The methods used to construct these waves rely on the decomposition of the distribution functions into odd and even parts and on using BGK forms to represent these pairs of functions; further manipulations using dimensional-reduction techniques from nonlinear functional analysis reduce the problem exactly to an algebraic equation that can be analyzed using bifurcation theory. Using these methods, we first develop a sufficient condition for waves of a given phase velocity to exist arbitrarily close to a given spatially uniform Vlasov equilibrium. Along with this condition we derive sufficient analytical information for the construction of approximate expressions for the electric potential and distribution functions, with exact knowlege of the asymptotic behavior of the error terms. These results have a very surprising physical implication: the Landau damping of small-amplitude waves is not inevitable. Instead, there exist plasma waves that trap particles even at arbitrarily small amplitude and do not damp.

The dynamics of guiding centers in a general configuration of three electrostatic plane waves is studied in the plane (x,y) perpendicular to a strong magnetic field. The associated Hamiltonian is nonautonomous with 11/2 degrees of freedom, and the conjugated variables are the coordinates (x,y). This is the simplest system that exhibits the onset of chaotic motion in electrostatic plasma turbulence. An explicit analytical solution is obtained for the unperturbed integrable system consisting of two low-amplitude waves, by solving a generalized Kepler equation. Chaotic diffusion of guiding centers becomes possible due to the existence of a third wave. As the amplitude of the perturbation increases, chaotic motion is first localized, then extended over a network spread over the whole phase space along separatrices, and finally densely covers the full space.

A compact wiggler offers the opportunity to reach high free-electron-laser frequencies with an electron beam of modest energy. We analyze here the properties of a conducting cylinder, slotted periodically on alternate sides, for use as a compact wiggler. In particular, we obtain the current distribution on the cylindrical surface, from which we obtain the magnetic fields inside the cylinder. We then expand this field into its multipole components, as well as into its axial harmonics. The resulting orbit dynamics are explored, leading to preferred choices for some of the design parameters. Finally, we examine the major consequences of possible fabrication errors, which suggest the tolerances and/or necessary compensation mechanisms required for a satisfactory wiggler design.

The experimental results on the trapping of the beam in the Naval Research Laboratory modified betatron accelerator are in good agreement with a revised model of resistive trapping, and thus it may be concluded that the wall resistivity is responsible for the inward spiral motion of the beam after injection.

A method for up-shifting the frequency of a subpicosecond laser pulse that utilizes the interaction of the pulse with a co-propagating relativistic ionization front is examined. The induced frequency shift is found to initially scale linearly with the propagation time τ. Asymptotically, the frequency scales as ${\mathrm{\tau }}^{1/2}$. Phase-slippage limitations may be overcome by appropriately increasing the plasma density as a function of τ, thus allowing for substantially higher-frequency shifts.

A frequency multiplying device is analyzed that provides power at selected cyclotron harmonics in a quasioptical gyrotron. The device utilizes a prebunching cavity and an uptapered magnetic field that impose a double-resonance condition on the radiation generated. This selects among cyclotron harmonics in the output cavity even though the cavity structure may support all harmonics. The prebunching is accomplished by modulation of electron orbital magnetic moments by a low-frequency-input rf field. Two design examples are given for quasioptical gyrotron frequency multiplier operation at the third cyclotron harmonic (four or seven times the input frequency) with a 10–15 % electronic efficiency and greater than 33% overall rf conversion efficiency. The drawback of this method of prebunching is that high-input electric-field intensities are required for efficient operation. However, it is shown that the double-resonance method allows complete harmonic selection in the linear regime for zero detuning between the cyclotron and field frequency. When this detuning is nonzero, the selected harmonic still has a higher linear efficiency than all others.

A generalized Zakharov system (describing interaction of dispersive and nondispersive waves in one dimension), with direct self-interaction of the dispersive waves and weak dissipation in the dispersive subsystem, is considered. Evolution of a one-soliton state under the action of weak dissipation is analyzed. It is proved analytically that three different scenarios of evolution are possible: adiabatic (slow) transformation of a moving subsonic soliton into a stable quiescent one, complete adiabatic decay of a transsonic soliton with small amplitude, and the appearance of a transsonic one with a large amplitude into a critical state, from which a further adiabatic evolution is not possible (it corresponds to a local minimum in the dependence of the soliton’s momentum on its velocity). In the latter case, numerical investigation of the further evolution of the soliton is performed. It is demonstrated that, in a general case, it abruptly splits into a stable quiescent soliton, the slowly decaying small-amplitude transsonic one, and a pair of left- and right-traveling acoustic pulses slowly fading under the action of weak dissipation.

The system of the nonlinear Schrödinger and d’Alembert equations with Zakharov coupling is considered. This system admits both subsonic and transsonic solitons. The subjects of the work are symmetric soliton-soliton collisions in this model. First, the collision-induced emission of acoustic waves (in the d’Alembert subsystem) is treated analytically for the case when the velocities of the solitons are much larger than their amplitudes. It is demonstrated that the acoustic losses are exponentially small unless the solitons’ velocities are much larger than the sound velocity. Next, the collision is simulated numerically in a general case. Two basic phenomena are observed. The collision of subsonic solitons always leads to their fusion into a breather, provided the system is sufficiently far from the integrable limit. The collision between the transsonic solitons gives rise to a multiple production of solitons (both subsonic and transsonic ones are produced), and the quasielastic character of the collision is recovered in the limit of large velocities.

A family of exact pulse solutions of the homogenous free-space scalar wave equation is obtained. These solutions describe moving modified Bessel-Gauss pulses. They include the fundamental Gaussian pulse and the Bessel beam solutions as special cases. The zeroth-order Bessel-Gauss pulse is shown to be more highly localized than the fundamental Gaussian solution because of its extra spectral degree of freedom. A superposition of Bessel-Gauss pulses is used to create a splash pulse that is more localized than the Ziolkowski splash pulse.

The consequences of internal reflection of multiply scattered light at the boundaries of disordered media are studied. We show that the effect of internal reflection due to index mismatch can be quantitatively accounted for with a single parameter by incorporating a reflection coefficient into the boundary condition for the diffusive light. We measure the angular correlation functions in transmission and reflection at different thicknesses for both high- and low-index mismatch. By including the effect of internal reflection, we are able to obtain consistent quantitative agreement between experiment and theory. Extensions to other experiments including diffusing-wave spectroscopy, coherent backscattering, frequency correlations, and pulse propagation are discussed.

Issues pertaining to the rate of beam divergence, the beam intensity, and the measured energy efficiency of beams generated by arrays of radiating elements are central to the practical applications of those beams. It will be shown that a localized-wave pulse-driven array can be designed to outperform similar continuous-wave pulse-driven arrays with respect to each of these beam characteristics. This improved performance is quantified by deriving bounds on those beam quantities for the field generated by an arbitrary pulse-driven array. These bounds extend the meaning of near-field distances or diffraction lengths to the situation where the array driving functions can be broad-bandwidth signals. Particular attention is given to transmitting- and receiving-array systems consisting of elements that are not large in comparison to the shortest wavelength of significance contained in the signals driving them. The output signals of such systems are related to the input driving functions by several time derivatives. It is demonstrated that the properties of the resulting beams depend on the higher-order moments of the spectra of the input driving functions and that diffraction degrades the coherence of these higher-order moments more slowly than its lower orders.

A properly designed set of input driving signals having a high degree of correlation in the higher-order moments of their spectra will produce a beam that has extended diffraction lengths and localization properties. The localized-wave solutions provide an immediate access to this situation. An alternative type of array is required to realize these localized-wave effects—one that has independently addressable elements. The enhanced localization effects are then intimately coupled to the proper spatial distribution of broad-bandwidth signals driving the array, i.e., by controlling not only the amplitudes, but also the frequency spectra of the pulse driving the array. Recently reported experimental comparisons between localized-wave and continuous-wave pulse-driven arrays of ultrasonic transducers in water are reexamined in terms of the theoretical developments presented here. It will be shown that the observed performance enhancements of the localized-wave pulse-driven arrays are in agreement with the theoretical predictions.