A theory of emission of electromagnetic radiation in a plasma with Langmuir turbulence through the plasma-maser interaction owing to a dissipative nonlinear force is presented. The nonlinear force that arises as a result of the resonant interaction between electrons and modulated fields is shown to drive the instability. The growth rate of the electromagnetic emission is obtained, and the results are discussed.

The laser intensity dependence of the inverse bremsstrahlung absorption coefficient in a strongly coupled plasma is investigated, where the electron quiver velocity (${\mathit{v}}_0$=${\mathit{eE}}_0$/m${\mathrm{\omega }}_0$) and excursion length (${\mathit{r}}_0$=${\mathit{eE}}_0$/m${\mathrm{\omega }}_0^2$) in the laser electric field are finite in comparison with the electron thermal velocity and shielding distance, respectively. In plasmas produced by an ultrashort pulse laser, the electron and ion temperatures are not in thermal equilibrium, and the electron temperature is higher than the ion temperature. Since ions are strongly coupled in such plasmas, the ion-ion correlation is described by the hypernetted-chain equation. On the other hand, the electron-ion correlation is described by linear-response theory. By using those correlation functions, the high-frequency conductivity and the laser absorption coefficients are evaluated. The results are applied to a recent experiment on reflectivity [Phys. Rev. Lett. 61, 2364 (1988)]. The analysis discloses the laser intensity dependence of the ultrashort-pulse-laser absorption rate.

A set of measurements of the electron density of plasma jets, generated by a high-pressure discharge capillary operating at quasi-steady-state, is described. The method of measurement is based on the dependence of Stark broadening of the hydrogen ${\mathrm{H}}_{\mathrm{\alpha }}$ and ${\mathrm{H}}_{\mathrm{\beta }}$ spectral lines on the electron density. Spectra were sampled electronically, time integrated over the electrical pulse duration, for various capillary currents and at different axial locations along the emerging plasma jet. The comparison of model predictions [Loeb and Kaplan, IEEE Trans. Magn. 25, 342 (1989)] with electron densities deduced from these spectra, by applying the theory of Stark broadening [Griem, Spectral Line Broadening by Plasma (Academic, New York, 1974)], indicates a good agreement over the tested current (1–8 kA) and density (${10}^{17}$–${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$) ranges. At larger densities, self-absorption might be a problem.

The problem of bound states is studied for an electron-positron plasma in a magnetic field. The case without a magnetic field is also considered. We use the method of quantum-statistical Green’s functions to obtain the relativistic Bethe-Salpeter equations for the bound-state wave function that contains the many-body effects. In the ladder approximation and with neglect of the retardation effects, the nonrelativistic limit of these equations is derived in the form of Schrödinger equations with nonlocal interaction. At T=0 and for small densities, these equations are solved analytically and the spectra are obtained using the perturbation theory. Validity of the approximations and the effect of radiative corrections are also discussed. The results may be of interest for astrophysical applications.

The theory of the anisotropic ferrite wake-field accelerator is solved, wherein the ferrite is driven into saturation by a static magnetic field, resulting in a permeability tensor having off-diagonal elements. We show that it is possible to obtain a maximum accelerating gradient of 1.5 MV/[m (nC driver beam charge)] for a driver beam of 0.7-mm rms bunch length. This compares favorably with wake-field accelerators based upon other types of structures.

The theory of the anisotropic ferrite wake-field accelerator is solved for the case of any general angular mode m. The ferrite is driven into saturation by a static magnetic field, resulting in the permeability tensor having off-diagonal elements. Expressions for the radial and angular transverse forces are obtained. Finally, we give numerical examples showing that the transverse forces in the anisotropic ferrite wake-field accelerator are reduced as the static saturated magnetization is increased.

A spectrum of coherent synchrotron radiation emitted from a bunch train of relativistic electrons accelerated by the Tohoku 300-MeV linear accelerator (linac) has been observed in the wavelength range from 0.16 to 3.5 mm. The energy of the electrons and the longitudinal bunch length are 150 MeV and about 2 mm. The observed spectrum has a broad peak at λ≃1.5 mm, and the intensity decreases sharply towards shorter wavelengths. The peak intensity is enhanced by a factor of 5×${10}^6$ in comparison with ordinary incoherent synchrotron radiation; the enhancement factor is comparable with the average number of electrons in the bunch. The electron distribution in the bunch is derived from the observed spectrum, and the bunch length (full width at half maximum) is obtained to be 0.25 mm. This bunch length is shorter than that estimated from the characteristics of the linac. The relation between the spectrum and the distribution of electrons in the bunch is discussed.

The mechanics of the first adiabatic invariant μ of nonrelativistic charged particles in time-dependent magnetic inductions B(t) are studied by means of computer simulations and analytic theory. Linear-ramp magnetic-induction profiles B=${\mathit{B}}_0$+(ΔB/Δt)t are utilized, as well as hyperbolic-tangent ramps and sine half-wave ramps. The change in μ that results from an induction change ΔB that occurs over a time Δt is quantified for all values of ΔB and Δt, as well as for all values of the particle position. It is found that the cases fall into two categories with very different μ behavior: cases in which the change in the magnetic induction occurs over a time Δt that is exactly equal to an integer number of gyroperiods (textbook case) or cases in which the change in the induction occurs over a time Δt that is not equal to an integer number of gyroperiods (more general case). In both categories μ is an adiabatic invariant, although the conservation of μ is much poorer in the latter category. It is pointed out that, in addition to the well-known constraints on ΔB and Δt, there is a constraint on the particle’s initial position in the magnetic field if the change in the adiabatic invariant is to be kept small.

The extinction of sound waves in a viscous fluid due to scattering from viscous fluid and solid elastic spheres is investigated. Exact expressions for scattered and transmitted fields caused by an incident-plane compressional wave of unit amplitude are calculated analytically with both compressional and shear modes supported in the viscous fluid and solid elastic media. Furthermore, it is shown that by boundary coupling, incident compressional acoustic waves generate compressional and shear waves in the scattered and transmitted fields. The general expressions for scattering and extinction cross sections are given, and for the special cases of vanishing viscosity, agreement with well-known solutions is obtained. In the Rayleigh-wave range for small scatterers, simple expressions for the cross sections are obtained, and for lossy scattering, absorption phenomena are shown to dominate scattering phenomena in this range. Finally, the extinction coefficient for a dilute cloud of scatterers is derived and the extinction effects due to viscosity are discussed.

Nonisochronism of one oscillator in a system of two coupled nonlinear oscillators leads to an overlap of synchronous and asynchronous regimes. In some cases, two-frequency oscillations may completely destroy synchronization. We derive conditions for the emergence of these competitive two-frequency oscillations and for the destruction of the synchronous regime, which occurs due to the merging of stable and unstable fixed points in phase space. Analysis is done by reducing the averaged coupled oscillator equations to the general nonlinear pendulum equation. Boundaries of each regime derived in this way are in good agreement with those obtained numerically.

We extend a method of control, model-based control, to the realm of partial differential equations. The hallmark of model-based control is that a particular goal dynamics is achieved by using a model for the observed dynamics to create the appropriate driving needed to make the goal dynamics an attractor for the system, alleviating the need for constant feedback, as is necessary with traditional control methods. We investigate a model-based control for the Burgers equation, with particular attention to sensitivity of the control to model inaccuracies, boundary errors, and noise.

The coherent light inelastically scattered from an ideal fluorescent cylinder illuminated by an arbitrary electromagnetic wave is analyzed using an extension of Rayleigh’s theory. Scattering coefficients are solved specifically for a plane wave illuminating the cylinder normal to the axis of the cylinder. The resulting inelastically scattered radiation is not entirely unlike that of elastically scattered radiation from a perfect cylinder. These results are illustrated by numerical calculations for several specific, but arbitrary, cases.

The method of exterior differential systems is applied to the problem of finding propagating singular solutions to Maxwell’s equations. Fresnel ray and wave surfaces are computed for systems that are not restricted to the topology imposed by the symmetries of the Lorentz transformations. The methods distinguish the measurable polarization phase differences between global behavior in optically active and Faraday media. In addition, an example is presented for which time-reversal and parity symmetries are broken: the inbound polarization states propagate with speeds different from the outbound polarization states.

The Green-function technique is used to study the interbase H-bond stretch of poly(dA)-poly(dT) and poly(dT-dA)-poly(dT-dA) when an effective enzyme is attached to the helices, where A is adenine and T is thymine. Three different two-atom attachment points are studied. The response is an enhanced interbase H-bond stretch amplitude when the effective enzyme is attached to the helix in poly(dT-dA)-poly(dT-dA). Then a 28-atom attachment to the helix is studied. This corresponds to an enzyme in contact with a 70-base-pair stretch of the helix. A large response is again found for the alternating polymer. This may relate to the fact that biological promoter sites often contain alternating TA sequences. The interbase H-bond stretch is studied as this motion is closely related to the helix transition to the open state involved in a number of biological processes.

The trion represents a localized group of neurons with three levels of firing activity. Networks of a small number of trions (with structured interactions and firing dependent on activity at two previous discrete time steps) support a repertoire of hundreds of quasistable, periodic firing patterns (which can be learned). We report striking phenomena with variation in ‘‘temperature’’ T: There exist a series of ‘‘phase transitions’’ at precise values T(n), giving new repertoires of periodic firing patterns, and the average time for any initial firing configuration to project onto a firing pattern shows a quite sharp change at each T(n). Near a phase transition, in a Monte Carlo simulation, the temporal evolution wanders back and forth between sets of these firing patterns in contrast to the more structured sequential evolutions far from a T(n).

We present a generalized learning rule valid for neurons having membrane potentials with a high-order dependence on the firing rates. The stability of the memorized states is investigated by studying the minima of an energy function. Our estimations of the capacity of memory are in qualitative agreement with results already known from the literature.

We derive the expression of the expected particle concentration in the diffusion-limited-reaction model in one dimension in which A+A→A with probability p and A+A→0 with probability q=1-p. Explicit results are given for the cases where the initial distribution of monomers is a Poisson distribution on the real line and a deterministic distribution with each site occupied on the integer lattice.

We show that a chaotic phase characterized by a strange attractor found by Yokoi, Oliveira, and Salinas [C. S. O. Yokoi, M. J. de Oliveira, and S. R. Salinas, Phys. Rev. Lett. 54, 163 (1985)] in a system with competing interactions on a Cayley tree is of spin-glass nature. The transition from the ferromagnetic to the chaotic phase is first order in a parameter of Edwards-Anderson type, which is defined in terms of the invariant probability density on the attractor. The distinguishing feature of this order parameter is its spectacular robustness. We also suggest an order parameter to test the chaotic nature of this phase in the sense of Bray and Moore [A. J. Bray and M. A. Moore, Phys. Rev. Lett. 58, 59 (1987)], but the numerical results are, as yet, inconclusive, for reasons we briefly discuss.

We analyze the spectral rigidity ${\mathrm{\Delta }}_3$ within the framework of Gutzwiller’s periodic-orbit theory and show that, for generic integrable systems with degeneracies in orbit actions, deviations from the L/15 behavior are to be expected in the region L≪${\mathit{L}}_{\max }$. To a first approximation, Δ${\mathrm{¯}}_3$(L)=${\mathit{n}}_{\mathrm{av}}$(L)L/15, where ${\mathit{n}}_{\mathrm{av}}$(L) is the mean degeneracy of those periodic orbits that contribute to the spectral rigidity at a particular value of L. A similar analysis for the number variance leads to the result ${\mathrm{\Sigma }}^2$(L)=${\mathit{g}}_{\mathrm{av}}$(L)L, ${\mathit{g}}_{\mathrm{av}}$(L) being the average degeneracy of those periodic orbits that contribute to ${\mathrm{\Sigma }}^2$(L). We support these claims numerically for billiard systems.

We investigate the diffusion-controlled A+B→0 reaction taking place on Peano curves, which are topologically one-dimensional unbranched chains, forming structures of arbitrary fractal dimension ${\mathit{d}}_{\mathit{f}}$. The spectral dimension ${\mathit{d}}_{\mathit{s}}$ of such structures is always ${\mathit{d}}_{\mathit{s}}$=1. The kinetics of the diffusion-limited reaction in such systems is shown to depend only on the spectral dimension ${\mathit{d}}_{\mathit{s}}$, whereas the spatial structure of the clusters formed in the course of the reaction depends strongly on ${\mathit{d}}_{\mathit{f}}$. We analyze explicitly the cluster structure for Peano curves filling a Sierpinski gasket or the interior of a plane triangle.