Table of contents

Describing the hydrodynamics of channels and open seas, the integrable dispersive long wave equations are of current interest. Obtained in this paper, via a symbolic-computation-based method, are soliton-like solutions to the (2 + 1)-dimensional integrable dispersive long wave equations. Solitary waves are found to be only a special case.

In the present paper the evolution criterion used in the first part of this work was extended to chemical reactions that display a chaotic behaviour by using the rate of entropy production. The model given by Willianowski and Rossler was analysed and was shown that the mean value of the rate of entropy production as dependent of the control parameter behaves as a Lyapunov function.

Besides it was found that in the chaotic region the mean value of the rate of entropy production shows continuos jumping even if the resolution was increased. This feature belongs to a thin fractal and is not the result of considering the rate of entropy production as an evolution criterion, the same behaviour should be found if any other Lyapunov function is used. This phenomenon will be considered in a following paper using a stochastic approach.

The use of the FSSR mica spherical crystal spectrograph with CCD detector to study satellite structures of 1s²–1s2p transitions of [He]-like Al ions and fine structure of Kα-lines is presented. It is shown that the FSSR spectrograph is more suitable for study of laser plasma with high spectral and spatial resolution than other types of spectrographs and the use of this spectrograph gives the possibility to measure the sizes of the x-ray sources and the intensity of the dielectronic satellites.

A non-conventional Stark-sweep microwave spectrometer is designed and used to determine the linewidth parameter of a rotational line of the fluoroform molecule. The linewidth parameter for self-broadening of the J = 1–0, M = 0 rotational component of the ground vibrational state is determined over the pressure range of 2.6–6.5 Pa at a temperature of 300 K. An experimental method is presented to correct for modulation broadening, Doppler effect, wall collision, cell length and saturation broadening. The first derivative of the Lorentzian line shape is used to extract the absorption profile information (Δv) from the signals. The second order Stark effect is measured to calibrate the frequency scale. The linewidth parameter for the J = 1–0, M = 0 transition of the CHF₃ molecule in the ground vibrational state is 268.0 ± 6.9 kHz/Pa.

This is a theoretical study of argon plasma under conditions, where Ne- and Na-like ionization stages are dominant. Balance equations are generalized to treat 37 3l states of Ne-like ion and 37 adjacent series of Rydberg states of Na-like ion simultaneously. This allows us to include in the kinetics a diffusion-like motion of the state of the system "Ne-like ion plus one electron" through the multitude of excited levels spread over an energy region of 50 eV. The populations N_i - i (i = (1, ..., 37)) of the Ne-like ion states are introduced explicitly; those of adjacent 37 Rydberg series are accounted for through continuous functions N_i(ε). These functions describe the population distribution within each Rydberg series dependent on the Rydberg electron enegy ε. The elementary processes of the collisionalradiative model connecting all Ne- and Na-like states, as well as processes of redistribution of populations inside each Rydberg series, are accounted for. The rate coefficients for all processes within the Ne-like residue have been calculated previously, using a detailed many-body relativistic theory. The dielectric capture cross sections and autoionization probabilities are presented as analytical continuation of the collisional excitation cross sections. The excited-excited states transitions are included. The rest of the processes are treated in a simple semiclassical approximation. The Lotz formula is generalized by unambiguous analytical continuation to cover the case of bound-bound transitions between Rydberg states of Na-like ions. The radiation reabsorption in a long plasma cylinder is included through Biberman-Holstein coefficients for all transitions. The inclusion of Na-like states, accounting for diffusion-like processes, increases the population inversion for the "lasing candidates" by at least a factor of two for a wide range of plasma conditions. This is important for the ionization equilibrium too. Besides, the functions N_i(ε) bear diagnostic information. Detailed calculations have been done for the homogeneous steady-state Maxwellian plasma. The role of transient processes in the population inversion creation is under discussion.

The spectrum of rhenium was photographed in the 300-2000 Å region on a 3m normal incidence spectrograph using a triggered spark and a sliding spark source. The (5d³ + 5d²6s)–5d²6p transitions of Re V were analysed. All 19 levels of the 5d³ configuration, 15 of 16 levels of the 5d²6s configuration and all 45 levels of the 5d²6p configuration have been established. 381 lines have been classified in Re V. The least-squares-fitted (LSF) and Hartree-Fock (HF) calculations satisfactorily interpret the spectrum.

Absolute excitation rate coefficients for a large number of levels (up to n = 4) of the singlet and triplet system of Si XI have been experimentally determined in a well-diagnosed theta-pinch plasma with the plasma spectroscopic method. The population of the metastable triplet ground state has been derived from the intensity of the intercombination line. A theoretical population model has been developed to investigate whether collisional coupling of the levels and cascading affected the measurements. The model has also been used to calculate line intensity ratios of strongly density or temperature dependent line pairs which can be used for plasma diagnostic purposes. The measured effective excitation rate coefficients are accurate to about ±50%. All of them, apart from the value for the 2s4s ³S₁ level, agreed within the error margins with existing theoretical data.

The Feynman diagram technique was used to calculate the non-relativistic part of the energy of 1s²3l3l' and 1s²3l4l' states. The Hartree-Fock part of the energy was calculated by the Z-expansion method. The correlation part of the energy was obtained as the difference between these two energies represented in form of 1/Z series. The resulting data were compared with theoretical data obtained for the identification of electron spectra (1s²3l3l' - 1s²2l transitions).

We prove that an axisymmetric stationary dynamo for the Faraday disc in which the B-field is continuous across the disc's boundary is impossible. The proof suggests that the same conclusion should hold for any stationary dynamo, axisymmetric or not, in a conducting medium with a sharp boundary of generic shape. The case of a spherical shell is an important exception due to its extreme symmetry. This note complements an earlier one (1995 Physica Scripta52 60).

In this paper, we look into some aspects of the mechanism of vortex reconnection in a compressible fluid. A generalization of the local vortex pseudo-advection idea dealing with a compressible fluid is considered.

Aluminum wire X-pinch experiments performed at the Cornell University XP pulsed power generator show detailed high resolution spectra for satellite lines of Li-like, Be-like, B-like and C-like ions. These lines, which correspond to transitions originating from autoionizing levels, are observed in the direction of the anode with respect to the hot X-pinch cross point. The intensities of such satellites are much smaller or absent in the direction of the cathode. These transitions are caused by collisions of ions with energetic electrons (5-15 keV) which are created by inductance between the hot spot and the anode. A collisional-radiative model was constructed using a non-Maxwellian electron energy distribution consisting of a thermal Maxwellian part plus a Gaussian part to represent the high energy electron beam. The shapes of the observed satellite structures are consistent with the calculated spectrum for electron temperatures between 30-100 eV, and beam densities of about 10⁻⁷ times the plasma electron density.

The problem of equilibrium and stability of plasma with flow has been investigated in a framework of the Shafranov model of tokamaks. Two regimes of plasma confinement have been found. The analytical criterion of plasma stability relative to small-scaling modes has been obtained for both regimes.

This paper is devoted to clarify the discrepancy between the experimentally found, rather wide and theoretically predicted, very restricted range of validity of the ideal MHD (IMHD) equations. In the first part of the paper, the standard derivation for a collision-dominated plasma is critically reviewed, leading to even stronger limitations, than those known in the literature. In the second part of the paper, the validity range of the IMHD equations on the Alfvén timescale is, based on a multiple timescale approach, analysed for different collisional regimes. It turns out that the IMHD equations are unrestricted valid for a (strongly magnetized) weak-collisional plasma. For an intermediate- and high-collisional plasma, the adiabaticity is violated essentially due to the work done by the friction forces. However, for both collisional regimes the full set of IMHD equations is obtained for the slow-flowing case, i.e., for plasmas with a magnetic Mach number of the relative velocity |u_i − u_e|/v_A << 1.

The dispersion relation for the modes of a weakly collisional magnetized homogeneous plasma is derived from the two-fluid equations, neglecting charge separation effects and electron inertia. The solution for nearly perpendicular propagation shows a weak instability in the frequency range ω ≃ k · v_A for β > k_||²/k². The thermal noise of the modes has been calculated from "fluctuating hydrodynamics" and compared with the results of a Vlasov description. Finally the critical mode number of the thermal noise for break-up of magnetic surfaces has been estimated for a toroidal plasma with large aspect ratio.

The model equations describing nonlinear interaction between the low frequency potential and magnetic plasma perturbations, are analysed by using the renormgroup (RG) methods. The cubic in k-space correction to the linear damping of the short-wave electrostatic excitations (corresponding to the kinematic viscosity in the Navier-Stokes equation) and the linear correction to the long-wave ones is obtained. It is found that the magnetic nonlinearities may give rise to negative dissipation.

The absorption of whistler waves in a magnetized cylindrical plasma due to coupling with oblique Langmuir waves is investigated. Two types of mechanisms exist for whistler absorption. The first one is related to the excitation of Langmuir waves in the volume of the dense plasma and their subsequent absorption due to the electron collisions. The second one is the emission of Langmuir waves outside of the cylindrical plasma when it is surrounded by the rare plasma. The relation between these whistler absorption mechanisms is discussed.

The scattering of radiation by mildly rough surfaces of non-absorbing materials is analysed in the distorted wave Born approximation wherein the roughness is treated as a perturbation. The basic formulae for the scattering cross-section are derived and corresponding expressions for the reflectivity and transmissivity are given. It is shown that off-specular scattering is proportional to the Fourier transform of an autocorrelation function involving phase factors produced when the actual surface deviates from a flat reference surface. In the specular direction the Fourier transform reduces to a simple surface average. The theory is then applied to periodic surfaces where the Fourier transform is reduced to a weighted sum of delta-functions. Numerical reflectivities are given for a piecewise rectangular and a sinusoidal grating. For such surfaces it is shown that plausible results are obtained even when the deviations are large. Random roughness is considered and explicit results are given for a surface with a Gaussian distribution of the height variation. It is demonstrated that the surface roughness for this type of surface must be small for our perturbative technique to be valid. For off-specular scattering numerical reflectivities are given in the limit of small deviations or small wave vector transfers where the scattering is proportional to the Fourier transform of the autocorrelation function of the deviations themselves.

This work is a development of the article "Polymer Ball Lightning Model" (1994 Physica Scripta50 591). The processes of formation of polymer fire balls in gas discharge conditions, when the polymer components are in the discharge volume, have been considered. A comparison of the experimental and theoretical fire ball formation time, lifetime, and energy store has been made. The conducted analysis shows that such objects are analogous to polymer ball lightnings (BL). This analysis is made on the bases of the fractal properties of polymerization of organic particles and of aggregated polymer structures.

The effect of radiative cooling on Jeans instability is investigated. It is shown that under certain conditions, the radiative cooling can overwhelm the gravitational collapse.