An experimental analysis of the focusing of a continuous electron beam, induced by the mutual interaction with charges produced by electron impact, is presented. The phenomenon has been observed by measuring the beam current on two different detector active areas as a function of the gas pressure in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. The stationary solutions of a three-fluid model, already developed, allow us to measure the maximum beam density. Moreover, we carry out information about the main processes responsible for ionization and their cross sections in the case of a three-component quasiequilibrium plasma.

Results from the standard quasilinear theory of ion-acoustic and Langmuir plasma microturbulence are incorporated into the kinetic theory of the electron distribution function. The theory is then applied to high current discharges and laser-produced plasmas, where either the current flow or the nonlinear laser-light absorption acts, respectively, as the energy source for the microturbulence. More specifically, the theory is applied to a selenium plasma, whose charge state is determined under conditions of collisional-radiative equilibrium, and plasma conditions are found under which microturbulence strongly influences the electron kinetics. In selenium, we show that this influence extends over a wide range of plasma conditions. For ion-acoustic turbulence, a criterion is derived, analogous to one previously obtained for laser heated plasmas, that predicts when Ohmic heating dominates over electron-electron collisions. This dominance leads to the generation of electron distributions with reduced high-energy tails relative to a Maxwellian distribution of the same temperature. Ion-acoustic turbulence lowers the current requirements needed to generate these distributions. When the laser heating criterion is rederived with ion-acoustic turbulence included in the theory, a similar reduction in the laser intensity needed to produce non-Maxwellian distributions is found. Thus we show that ion-acoustic turbulence uniformly (i.e., by the same numerical factor) reduces the electrical and heat conductivities, as well as the current (squared) and laser intensity levels needed to drive the plasma into non-Maxwellian states.

These effects are large over a wide range of plasma temperatures and densities such as found in Z-pinch, laser-produced, or opening switch plasmas. The reduction in laser intensity thresholds for generating non-Maxwellian states is a result of microturbulence enhanced laser absorption, which can be observed at any laser intensity. Thus, if microturbulence is the cause of the heat flux inhibition, then the magnitude of the inhibition might be directly observed through the use of probe-laser beams. Finally, we calculate the laser intensities and the current densities needed to change the electron distributions in the presence of ion-acoustic turbulence. These calculations are carried out by assuming that the electrostatic fluctuations scale as the square root of the electron plasma parameter in a weakly microturbulent selenium plasma. The laser intensities calculated in this example are found to be only slightly in excess of those used in recently conducted experiments.

The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schrödinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations.

Gas-temperature and velocity profiles at the exit plane of a thermal argon plasma torch have been determined directly from a high-resolution Doppler-shifted line-shape analysis of laser light scattered by the plasma. Peak temperature and velocity values observed were 13 350 K±7% and 1100 m ${\mathrm{s}}^{\mathrm{-}1}$±3%. Velocities as low as 45 m ${\mathrm{s}}^{\mathrm{-}1}$±45% were measured in the fringe of the jet. An injection-seeded pulsed neodymium-doped yttrium aluminum garnet laser was used as the laser source and the scattered laser light was analyzed with a scanning tandem Fabry-Pérot interferometer. Temperature data obtained from laser scattering are compared with values obtained from emission spectroscopy and show a severe departure from local thermodynamic equilibrium (LTE) in the outer regions of the jet. Gas temperatures were observed to increase as the torch operating current increased from 300 to 500 A, but remained constant as the operating current increased to 900 A. However, electron temperatures and densities continued to increase with operating current. This suggests that increasing the electrical power drives the plasma away from LTE. Measured temperature and velocity profiles were found to be nearly parabolic.

Profiles of n=7 to n=6 transitions of C vi, C v, and N v and of the Δn=0, n=2 triplet lines of C v have been measured in a plasma, which was diagnosed by Thomson scattering.

A detailed study of a dynamic aperture is given for electron storage rings with noninterleaved sextupole magnets. As a result of a cancellation of major transverse nonlinearities of sextupoles by -I transformers, other tiny terms such as fringe fields of quadrupoles and kinematical terms of drift spaces come to limit the transverse dynamic aperture. Results for transverse aperture in simulations can be explained by a simple one-dimensional model including these terms. In the longitudinal direction, a modulation of linear betatron motion by synchrotron oscillation is investigated as the source of the aperture limit.

The longitudinal Schottky spectrum of an ultracold ion beam in a storage ring is calculated in the frame of harmonic oscillations of a one-dimensional (1D) Coulomb lattice. It is assumed that the extremely high cooling rate required to bring the beam into a one-dimensional ordered chain can be provided by electron or laser cooling. The anharmonic transversal oscillations with temperature much higher than the longitudinal one are taken into account within the self-consistent phonon approximation. The Schottky spectrum measured by the pickup system consists of bands located near the harmonics of the revolution frequency of the beam. The total intensity of each band characterizes the temperature distribution of the phonons in an ionic chain. The amplitude and the width of the peaks in the spectrum are a function of the strength of relaxation processes (cooling and heating) and the Coulomb correlations, respectively. It is suggested that a careful analysis of these spectra could be a signature of the presence of 1D ordering in the beam.

In many present and planned compact electron sources and linacs, very large rf accelerating fields are present in the linac structures. A charged particle whose trajectory is parallel to the axis receives no net focusing from the periodic transverse forces arising from the axisymmetric rf wave. However, if the lowest-order periodic transverse motion of the particles is included, a net ponderomotive focusing force is obtained when the momentum transfer is averaged over a period of the motion. Since this force is second order in the electric-field amplitude, the resultant focusing can be non-negligible in high gradient structures. In order to produce and preserve high-brightness beams in rf linacs it is necessary to obtain a better understanding of all the forces acting on the beam and the subsequent beam dynamics. To this end we examine the lowest-order ponderomotive rf focusing of electrons in axisymmetric standing- and traveling-wave linac structures. We obtain a generalized paraxial envelope equation which includes the effects of the ponderomotive focusing and longitudinal acceleration to describe the transverse beam envelope evolution. The implications of our results on beam dynamics in electron linacs are examined, and extensions of the results to positron and proton linacs are discussed.

Direct numerical calculation shows that the total electromagnetic-field energy of a one-dimensional uniformly accelerated classical point charge at one instant is the same as that at another instant when the charge is moving at the same speed but in the opposite direction of the first instant. This seems contradictory to the fact that the radiation power calculated by the Larmor formula is constant, but is required by the fact that the radiation reaction vanishes. It is also shown numerically that the electromagetic-field energy changes a finite amount when a charge begins or ends its uniformly accelerated motion. This change of energy is equal to the work done against a δ-function radiation reaction. The implications of these results on the question of whether a uniformly accelerated charge radiates are discussed.

The effect on the electron-ring dynamics when a cyclotron resonance is crossed in a modified betatron accelerator has been studied analytically and numerically. It has been found that, in the presence of small vertical field errors, there is a field-error-amplitude threshold below which the normalized transverse velocity ${\mathrm{\beta }}_{\mathrm{\perp }}$ of the gyrating electrons is bounded (Fresnel regime) and above which it is unbounded (lock-in regime). In the lock-in regime, the average value of the normalized axial (toroidal) momentum γ${\mathrm{\beta }}_{\mathrm{\theta }}$, where γ is the relativistic factor and ${\mathrm{\beta }}_{\mathrm{\theta }}$ is the normalized axial velocity, remains constant, i.e., the resonance is never crossed. In addition, above threshold, ${\mathrm{\beta }}_{\mathrm{\perp }}$ increases proportionally to the square root of the time. The threshold value of the vertical field error amplitude can be made larger either by increasing the acceleration rate or by adding a small oscillatory toroidal field to the main toroidal field. The multiple crossing of the same resonance, in the presence of such a small oscillatory toroidal field, was also studied with some interesting results.

In this paper we discuss the spectroscopic details of the two-frequency undulator, a recently proposed device to suppress the sideband instability in free-electron lasers. We present an analytic and numerical approach to the problem and discuss the intrinsic differences between the brightnesses of one- and two-frequency undulators. We study the dependence of the emission on various physical parameters including the electron-beam qualities.

A procedure is developed for calculating photon bands in materials characterized by tensor dielectric properties. As a specific example, the cholesteric blue phases are considered, and their respective photon bands are calculated for simple and body-centered-cubic structures. These noncentrosymmetric materials interact strongly with only one of the two possible circularly polarized radiation modes; however, no full photon gaps are found even for this mode. The reasons for this are noted. The technique presented is general and can be applied to all materials characterized by tensor dielectric properties.

We consider the Korteweg–de Vries (KdV) and nonlinear Schrödinger (NS) equations with higher-order derivative terms describing dispersive corrections. Conditions of existence of stationary and radiating solitons of the fifth-order KdV equation are obtained. An asymptotic time-dependent solution to the latter equation, describing the soliton radiation, is found. The radiation train may be in front as well as behind the soliton, depending on the sign of dispersion. The change rate of the soliton due to the radiation is calculated. A modification of the WKB method, that permits one to describe in a simple and general way the radiation of KdV and NS, as well as other types of solitons, is developed. From the WKB approach it follows that the soliton radiation is a result of a tunneling transformation of the nonlinearly self-trapped wave into the free-propagating radiation.

In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum-free-energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structure generates a less visualizable nonscalar ‘‘landscape,’’ where a sequence space is mapped into a space of discrete ‘‘shapes.’’ We investigate the statistical features of both types of landscapes by computing autocorrelation functions, as well as distributions of energy and structure distances, as a function of distance in sequence space. RNA folding is characterized by very short structure correlation lengths compared to the diameter of the sequence space. The correlation lengths depend strongly on the size and the pairing rules of the underlying nucleotide alphabet. Our data suggest that almost every minimum-free-energy structure is found within a small neighborhood of any random sequence. The interest in such landscapes results from the fact that they govern natural and artificial processes of optimization by mutation and selection. Simple statistical model landscapes, like Kauffman and Levin’s n-k model [J. Theor. Biol. 128, 11 (1987)], are often used as a proxy for understanding realistic landscapes, like those induced by RNA folding. We make a detailed comparison between the energy landscapes derived from RNA folding and those obtained from the n-k model. We derive autocorrelation functions for several variants of the n-k model, and briefly summarize work on its fine structure. The comparison leads to an estimate for k=7–8, independent of n, where n is the chain length. While the scaling behaviors agree, the fine structure is considerably different in the two cases. The reason is seen to be the extremely high frequency of neutral neighbors, that is, neighbors with identical energy (or structure), in the RNA case.

In this paper we study the effect of hydrostatic pressure on the thermal stability of DNA base pairs. The thermal stability of a base pair is predominantly determined by the fluctuational motion of the interbase hydrogen bonds in the base pair. We postulate that the pressure exerted on the surface of DNA creates a compressive stress in the interbase hydrogen bonds. This stress in turn induces a strain in these hydrogen bonds. The effect of this compressive stress on the thermal fluctuational motion of the strained interbase hydrogen bonds in DNA can be analyzed by the modified self-consistent phonon approximation theory. We calculate individual hydrogen bond disruption probabilities and base pair opening probabilities of two B-conformation DNA polymers, an adenine-thymine copolymer and a guanine-cytosine homopolymer, at various pressures and at temperatures both in the premelting region and in the helix-coil transition region. Our calculated pressure dependence of the melting temperature for both polymers is in fair agreement with experimental observations. Our values for the melting temperatures are also in agreement with observation and our theory is successful as a theory of cooperative melting.

An alternative nuclear-magnetic-resonance (NMR) method for the measurement of the lateral diffusion coefficient D of phospholipids along the plane of a spherical bilayer on a solid support is presented. D values are determined at various temperatures for palmitoyl-oleoyl-phosphatidylcholine (POPC) bilayer on a spherical silica support of 640 nm diameter. The method is based upon the measurement of the quadrupolar transverse relaxation times obtained by the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence for a series of different pulse spacing times. It takes advantage of the fact that the CPMG sequence can progressively filter out contributions to the transverse relaxation arising from motions like lateral diffusion, which are slow on the NMR time scale. The combination of this sequence with a new membrane model system, single bilayers on a spherical support of well-defined diameter, enables the determination of D. The D values which we obtain for POPC supported bilayers [D=(2.1±0.7)×${10}^{\mathrm{-}12}$ ${\mathrm{m}}^2$/s at 10 °C, D=(4.0±0.8)×${10}^{\mathrm{-}12}$ ${\mathrm{m}}^2$/s at 30 °C, and D=(7.0±1.0)×${10}^{\mathrm{-}12}$ ${\mathrm{m}}^2$/s at 50 °C] are in good agreement with those obtained by other methods like fluorescence recovery after photobleaching (FRAP) and pulsed-field-gradient NMR (PFG-NMR).

The discrepancies between the obtained D values and those reported recently from quasielastic neutron-scattering studies are discussed in terms of the different characteristic lengths and time scales over which the methods are sensitive. This NMR method is superior to FRAP and electron spin resonance methods since it requires no bulky labels attached to the phospholipids and it measures the average diffusion of all molecules (and not only that of the probes) in the bilayer. Moreover, the characteristic length scale of the CPMG method is significantly shorter than for FRAP or PFG-NMR. These advantages give the present method potential for the study of demixing and domain formation processes near phase transitions in model membrane systems.

We present photoemission spectromicroscopy results on biological specimens. The data, obtained with x-ray secondary (photoelectron) emission microscopy, study individual elements in micrometer-size portions of neuron networks.

The eigenstates of the Wu-Austin Hamiltonian without coupling to the pumping system are considered. We are able to show that for a high quantum number N the energy of the system is proportional to -${\mathit{N}}^2$. This has dramatic effects for the entire system at any temperature. We have Bose condensation even without pumping. The rate equations defined by Fröhlich do not describe this behavior.

We show that differential adhesion with fluctuations is sufficient to explain a wide variety of cell re- arrangement, by using the extended large-Q Potts model with differential adhesivity to simulate different biological phenomena. Different values of relative surface energies correspond to different biological cases, including complete and partial cell sorting, checkerboard, position reversal, and dispersal. We examine the convergence and temperature dependence of the simulation and distinguish spontaneous, neutral, and activated processes by performing simulations at different temperatures. We discuss the biological and physical implications of our quantitative results.

We analyze the dynamics and statistical mechanics of attractor neural networks with ‘‘distributed’’ updating rules in which groups of one or more neurons are updated simultaneously. Such partially parallel updating schemes are a central feature of neural-network architectures that use many processors, implemented either on special multiprocessor hardware, or among many computers linked over a network. Several updating rules are classified and discussed; these rules generalize the parallel dynamics of the Little model and the one-at-a-time dynamics of the Hopfield model. Analytic results presented herein include a stability criterion that specifies sufficient conditions under which distributed dynamics lead to fixed-point attractors. For binary neurons with block-sequential updating and a Hebbian learning rule, the storage capacity is found as a function of the number of update groups. Several open problems are also discussed.