Table of contents

We consider the nonlinear electrohydrodynamic stability of wave packets of capillary-gravity waves in fluids of any depth; they travel predominantly in one direction, however the wave amplitudes are modulated slowly in both horizontal directions. The method of multiple time scales is used to obtain a nonlinear Schrödinger equation describing the behaviour of the perturbed system. The envelope solutions of steady form are obtained in terms of the Jacobian elliptic functions. It follows that various types of envelope solutions of the modulated Stokes waves may exist depending on the relative signs of terms representing dispersive and nonlinear effects; the solitary and periodic envelope solutions for the general case of any liquid depth are described. It is also shown that the evolution of the envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability of solitons with respect to transverse perturbations is investigated. It is found that such wave packets are stable to short waves, and unstable to long disturbances, and the envelope solitons and the waveguides are always unstable, and the stability of the system depends on the values of the dielectric constant ratio, the electric field, the wavenumber, and the depth of the fluid.

It can be shown that for potentials of a general parabolic type classical and quantum theory give identical results if only one assumption is made: that in classical theory the uncertainty principle is one of its basic postulates. The identity is extended to more general potentials in this paper, and on the example of scattering on a step potential this is explicitly shown.

We use atomic supersymmetry approximation of Rubidium Rydberg states wave function. Accordingly, eigenstates are interpreted as the implementation of broken symmetry and depend on two parameters. We determine the parameter values from spectroscopic measurements of energies and lifetimes. These analytical wave functions allowed us the study of thermal energy Rb(nl) and the collisions where nl is ns, np and nd over a wide range of n values. The total cross sections are in fair agreement and closer to measurements than similar approaches based on hydrogenic representation of the wave function.

A condition upon which sporadic bursts (intermittent behaviour) of the relative energy become possible is derived for the motion in the chaotic layer around the separatrix of a non-linear resonance. This is a condition for the existence of a marginal resonance, i.e. a resonance located at the border of the layer. A separatrix map in Chirikov's form [Chirikov, B. V., Phys. Reports 52, 263 (1979)] is used to describe the motion. In order to provide a straightforward comparison with numeric integrations, the separatrix map is synchronized to the surface of the section farthest from the saddle point. The condition of intermittency is applied to clear out the nature of the phenomenon of bursts of the eccentricity of chaotic asteroidal trajectories in the 3/1 mean motion commensurability with Jupiter. On the basis of the condition, a new intermittent regime of resonant asteroidal motion is predicted and then identified in numeric simulations.

We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrödinger equation that contains also an integrable Ablowitz–Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine–Gordon like ordinary nonlinear differential equation.

Two nonlinearly coupled oscillators submitted to an external periodic force are studied. The method of multiple scales is used to find solutions in the resonant and nonresonant cases. The response curves are discussed. A set of bifurcations diagrams are obtained showing period-doubling and torus-breakdown routes to chaos.

The excitation functions of the ⁵¹V[(α,n), (α,3n), (α,p3n), (α,α3n), (α,α2pn), (α,2α) and (α,2αn)] reactions were studied up to 80MeV using stacked foil activation technique and Ge(Li) gamma-ray spectroscopy. Secondly, a comparison with the pre-equilibrium hybrid model and the index model have been made using the initial exciton number n₀ = 4(4p0h). It was observed that the hybrid model gives a better agreement than the index model for (α.xn) type of reactions. However, both the models failed to explain reactions involving the emission of protons and alpha particles.

The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. One of the basic features of this approach is the use of tables of standard quantities, without which the process of obtaining matrix elements of spin-other-orbit interaction operator between any electron configurations is much more complicated. Some special cases are shown for which the tensorial structure of the spin-other-orbit interaction operator reduces to an unusually simple form.

Comments on a previous paper by V G Pal'chikov, Yu L Sokolov and V P Yakovlev (1997 Physica Scripta55 33–40).

Dissociative recombination and excitation of D₃⁺ have been studied in CRYRING, a heavy-ion storage ring at the Manne Siegbahn Laboratory at Stockholm University. The measured cross section for dissociative recombination was used to deduce a 300 K rate constant of 2.7 × 10^-8cm³s^-1. This is a factor of four smaller than the corresponding value for H₃⁺ measured earlier in CRYRING. Dissociative excitation into both the D and 2D channels (D + D or D₂) were studied. The 2D channel occurs at energies below threshold for the ion's dissociative states, which indicates that resonant enhanced dissociative excitation via autoionizing resonances takes place.

A set of intercombination rules has been used to derive ground state potential parameters for the second group metals (Zn, Cd and Hg) interacting with inert gases (Ne, Ar, Kr and Xe). Results obtained with these rules are compared with various experimental results for these molecules. It is found that these rules can be excellently applied when the interacting atoms are only inert gases. The rules can be very well used for the determination of the position of the potential minimum for all molecules. But concerning the well depth of the ground state (X¹0⁺) of these molecules, it is observed that some of these rules give results that are in close agreement with experimental data only for molecules consisting of two heavy atoms.

Stark widths and shifts of five Si I line were measured at 28500 K electron temperature and 1.9 × 10²³m^-3 electron density in a linear, low-pressure, pulsed arc operated in argon-helium mixture. Our data are compared with values calculated on the basis of quasistatic approximation.

First experimental results are presented for a coherent phenomenon in reflection of radiation by a mirror with a concave round surface. It consists of interference fringes which arise owing to the interaction of rays undergoing different numbers of reflections on the mirror. An analytical theory of the phenomenon is given in the frame of a geometrical optics approach in a small angle approximation. The experimentally measured interference fringes for the visual light of a Ne–He laser reflected by the round part of the mirror are qualitative coincidence with the results of accurate computer calculations performed in the frame of a geometrical optics approach.

Using a variational approach, we examine analytically the three-dimensional self-trapping of Gaussian beams in a medium with higher-order nonlinearity. We find exact analytic solutions for the spot width, and the conditions under which the Gaussian beam is stable to perturbation of its spot width. We also make a comparison with a Kerr-law medium.

Based on a 4-level model, scaling laws for lasing in low-Z neon like ions are derived. The optimum electron density is found to follow a form of N_opt ∼ (Z – 8.8)^6.1, and the maximum gain coefficient follows G_opt(Z – 7.0)^2.7; at conditions near the optimum, the gain coefficient is found to be proportional to N_e(1 – 0.5N_e/N_opt).

The linear theory for magneto-acoustic-gravity waves in an anisotropic and stratified magneto-plasma is extended. In particular it is shown how to generalize the results of previous authors to consider anisotropic pressures according to the generalized Chew–Goldberger–Low model. The possibility of instabilities is demonstrated.

A one dimensional system describing the interaction of three Langmuir waves and an ion-sound wave at the exact resonance is considered. This model includes the energy source and the dissipative regions, and can describe both decay instability and four-wave processes such as modified decay. These two kinds of instabilities appear to have quite different dynamics. The decay instability exhibits a phenomenon known as "chaotic synchronization" between the phases, which is associated with a transition from three-wave processes to four-wave process. Conversely, the "modified decay" instability shows an abrupt transition from the regular behavior to the phase stochastization.

The effects of an axial magnetic field on the convective amplification and the threshold intensity of Raman backscattering instability in an underdense, inhomogeneous plasma is investigated. Two cases of incident pump wave were considered. For the R-circularly polarization case it is shown that the amplification factor increases with the magnetic field, it also increases with the plasma density while the threshold intensity decreases. For the L-circularly polarization case, it is shown that the amplification factor decreases as the magnetic field and the plasma density increase, while the threshold intensity increases as the magnetic field increases but it decreases as the plasma density increases.

A theoretical investigation has been made of dust-acoustic solitary waves in an unmagnetized three-component dusty plasma which consists of a negatively charged dust fluid, free electrons and trapped as well as free ions. It is found that owing to the departure from the Boltzmann ion distribution to a trapped ion one, the dynamics of small but finite amplitude dust-acoustic waves is governed by a modified Korteweg-de Vries equation. The latter admits a stationary dust-acoustic solitary wave solution which has larger amplitude, smaller width, and higher propagation velocity, than that involving adiabatic ions. The effects of trapped ions and free electrons on these dust-acoustic solitary waves are discussed. The present investigation should be useful in understanding some nonlinear features of the dust-acoustic waves which have been observed in a recent numerical simulation study.

The linear and nonlinear properties of electrostatic and electromagnetic waves in the presence of high-energy alpha particles in magnetically confined fusion plasmas are examined. It is found that Boltzmannean alphas can introduce new classes of electrostatic and electromagnetic wave spectra. By employing a hybrid approach, in which electrons and ions are treated like fluids whereas hot alphas by means of a kinetic description, a set of nonlinear equations are derived. The stationary solutions of the latter are discussed.

X-ray spectra due to intrinsic titanium are obtained on the FTU tokamak using a crystal spectrometer with spatial resolution. He-like ion spectra are observed for ohmic and lower hybrid (LH) heated high density plasmas. In a single discharge four spectra are recorded with different lines of sight. With a post-process subroutine of an impurity transport code, synthetic spectra are built up and compared with the experimental ones. Line intensity ratios with respect to the resonance w line are studied. For the intercombination lines x and y the agreement between experiment and simulation is satisfactory, whereas for the forbidden line z the simulations give line ratios higher than the experimental values by 25 to 40%. The electron temperatures T_e deduced from the "dielectronic" satellite line ratios agree with the corresponding values from standard T_e diagnostics. For the "collisional" satellite q the line intensity ratios are sensitive to the titanium ion charge distribution in the plasma core and, consequently, to the impurity transport parameters. Diffusion coefficients D equal to 0.7 and to 2.0m²/s are obtained in the plasma core of, respectively, ohmic and LH heated plasmas. The impurity confinement time τ_p is deduced from the diffusion coefficient D and compared with the predictions of a τ_p scaling law.

The transition from a weakly turbulent plasma state to a strongly turbulent one is considered using the concept of entropy. The validity of the H-theorem for modulational processes is shown. It is demonstrated that the strong turbulence state is more ordered than that of weak turbulence. The validity of the principle of minimum entropy production in processes of self-organization for the case of transition from weak to strong turbulence is verified. This transition can be treated as a nonequilibrium phase transition.

Spectra from various target materials from a KrF-laser plasma source have been investigated in the Extreme UV spectral range between 12 and 17nm using an off-Rowland grazing-incidence spectrograph. The electron temperature T_e and mean ionization stages Z have been measured to amount to T_e = 80eV and Z = 10–12, respectively. Additional calibration and measurement of the spatial and temporal characteristics of the plasma has been done using a combination of a multilayer mirror and XUV diode or fiber image carrier system. The maximum yield at 13.5nm (2.4–3 × 10¹⁵ phot/srnm) has been observed for targets with atomic number Z_a = 32, 50, 73–75, of which the radiative transitions have been identified as 3p–3d, 4d–4f and 4f–5d transitions respectively. The corresponding maximum conversion efficiency at 13.5nm was 0.43% in a 1% bandwidth. An option for further optimization of the KrF laser plasma source for application in EUV lithography is discussed.

It is the purpose of the present comment to point out that the results presented in [M. Shoucri et al., Physica Scripta 55, 617 (1997)] are relevant to the problem of the effect of a slowly varying transport of guiding centers on the physics of the suppression of turbulence and transition from a low flow velocity to a high flow velocity at the edge of a plasma.

The Rayleigh–Taylor mode is re-examined by including the equilibrium parallel sheared plasma flows. A two-fluid model is employed to derive a set of nonlinear equations consisting of the electron continuity and the parallel component of the electron momentum equations, as well as the ion vorticity equation. In the linear limit, we obtain and analyze the local nonlocal dispersion relations. The interplay between the interchange and parallel velocity shear instabilities is examined. Furthermore, it is shown that the newly derived nonlinear equations admit various types of vortices as possible stationary solutions. The relevance of our investigation to laboratory plasmas is pointed out.

A low energy plasma focus nuclear fusion device with central electrode and insulator of different materials was investigated. Maximum neutron yield was observed with electrodes having low spark erosion. The enhancement of neutron yield is expected to be more pronounced at higher energy. This may extend the maximum neutron yield obtainable from a plasma focus.

The influence of Coulomb collisions on the wave propagation in plasmas is considered. It is demonstrated that the nonlinear coupling of the nonresonant wave with electric field fluctuations resonant with the plasma particles as well as contribution of the system nonstationarity induced by the collisions is crucial to obtain the correct conservation equation for the wave occupation number. In contrast to the occupation number, the canonical wave energy changes because of the nonstationarity of the system. Since the definition of the wave energy is not necessarily unique and depends on separation into background and wave subsystems, the result for the change of the canonical wave energy is not universal. An alternative way of separation into background and wave subsystems is discussed.

The force density acting on a non-stationary and inhomogeneous dispersive medium in the presence of a high-frequency electromagnetic field is calculated in a covariant formalism. It is demonstrated that the average Lorentz force density due to a wave in the medium can be written using only the Maxwell electromagnetic tensor.

Essential parameters for the application of crystals to quantitative X-ray spectroscopy are the upper wavelength limit and the quantitative reflection properties (intrinsic resolving power, luminosity) of the crystal. Due to the large lattice constant, muscovite, a mica group mineral, can be used in the wavelength range up to about 2nm. Muscovite crystals can be bent to small radii of curvature due to their favourable cleavage and elastic properties. Characteristic reflection properties at reflections 002 – 00 24 were investigated theoretically and experimentally. The integrated reflectivity was calculated for various reflections of perfect flat as well as spherically bent muscovite crystals with curvature radii R = 100 and R = 186mm. It was measured for flat crystals in the reflections 00 10 – 00 26 using CuKα- and MoKα-radiation from X-ray tubes and compared with calculations for both perfect and mosaic crystals. Available high-quality muscovite crystals have a mosaic structure with a mosaic spread of about 1 arcmin. This mosaic spread limits the spectral resolving power for high reflection orders.

We report on magnetoresistance measurements of the misfit layer compound (SnS)_1.17(NbS₂) in the superconducting state down to 50mK. Its anisotropy was found to be in the range of 10 and remains constant down to the lowest temperature of measurement. On the other hand, the coherence length in the direction perpendicular to the superconducting planes at zero temperature is higher than the distance separating the centers of two successive superconducting layers, so this compound behaves as a 3D-superconductor.

A new type of atom is considered. The nucleus of such an atom (positive ion) is located on a depth l under the surface of a solid cryodielectric with negative electron affinity (for example solid hydrogen or neon), with an orbiting electon outside the cryodielectric. It is shown that such atoms can be treated like specific Rydberg atoms with very large lifetime, and their energy spectrum is defined mainly by the shape of the solid cryodielectric–hydrogen interface and depth l, i.e. they can be "constructed" by varying these parameters.

Cadmium oxide thin films were prepared onto glass substrates by a DC magnetron reactive sputtering method from a metallic cadmium target in an argon and oxygen atmosphere. A systematic study has been made on the influence of oxygen partial pressure, ranging from 2 × 10^-4mbar to 5 × 10^-3mbar, on the film structure and optical properties. The films were polycrystalline in nature with cubic structure. The grain size of the films was in the range 40–80nm. The optical transmittance of the films was in the range 65–85% in the wavelength region 600–1600nm. The optical band gap and refractive index of the films increased from 2.46eV to 2.54eV and 2.33 to 2.42 with increase in the partial pressure of oxygen ranging from 5 × 10^-4mbar to 5 × 10^-3mbar respectively.