Dissipative surface waves in plasma

Debatable aspects of the theory of nonpotential surface waves propagating along the boundary of a dissipative medium with frequency dispersion are discussed. On the basis of the known theoretical results and theoretical analysis carried out in this work, a theory of surface waves that is valid for any dissipation of the perturbation energy in the medium is developed. It is shown that, if dissipation is sufficiently strong, there can be surface waves the physical nature and dispersion law of which differ radically from those of ordinary surface waves. The damping rate of such waves is low even at large dissipation in the medium, and their group and phase velocities exceed the speed of light. In particular, surface waves on the interface between vacuum and cold collisional electron plasma are considered. The existence of such surface waves for different media of laboratory and natural origin is discussed.     

Theory of Electromagnetic Surface Waves in Plasma with Smooth Boundaries

A theory of nonpotential surface waves in plasma with smooth boundaries is developed. The complex frequencies of surface waves for plasma systems of different geometries and different profiles of the plasma density are calculated. Expressions for the rates of collisionless damping of surface waves due to their resonance interaction with local plasma waves of continuous spectrum are obtained. The influence of collisions in plasma is also considered.     

Electron Landau damping in toroidal plasma with Solov’ev equilibrium

The contribution of untrapped and two groups of trapped particles to the longitudinal (with respect to the magnetic field) elements of the dielectric susceptibility is determined by solving the drift-kinetic equations for such particles in axisymmetric tokamaks with Solov’ev equilibrium. The obtained dielectric characteristics are applicable for studying linear wave processes in the frequency range of Alfvén and fast magnetosonic waves in small- and large-aspect-ratio tokamaks with circular, elliptical, and D-shaped cross sections of magnetic surfaces. The high-frequency power absorbed in plasma via electron Landau damping is estimated by summing up terms containing the imaginary parts of both diagonal and non-diagonal elements of the longitudinal susceptibility. The imaginary part of the longitudinal susceptibility is calculated numerically for spherical tokamaks in a wide range of wave frequencies and magnetic surface radii.     

Surface waves and space charge layers in a spatially inhomogeneous plasma

A theory of surface waves in a layer of a spatially inhomogeneous cold electron plasma is presented. Four types of surface waves are revealed, and the conditions under which they can exist are determined. Complex frequency spectra are obtained, and the mechanisms for wave damping by plasma inhomogeneity are discussed.     

Asymmetric long-wavelength surface modes of isotropic plasma waveguides

A theoretical study is made of the dispersion properties of electromagnetic surface waves with arbitrary azimuthal mode numbers and a small axial wavenumber in cylindrical isotropic waveguides partially filled with plasma. The plasma is assumed to be cold and radially inhomogeneous, and the problem is solved in the hydrodynamic approximation. The eigenfrequency of the waves is investigated as a function of the plasma parameters, the width and the permittivity of the dielectric gap between the metal waveguide wall and the plasma column, the axial wavenumber, and the azimuthal mode number. It is shown that the axial phase velocities of asymmetric surface modes are higher than the speed of light in a dielectric and that the surface modes do not propagate in a waveguide with a vanishingly small width of the dielectric gap. The theory developed is employed in practice in the calculation of the electrodynamic model of a gas discharges maintained by asymmetric long-wavelength surface modes. The power absorbed by the gas-discharge plasma in the regimes of Ohmic damping and resonant damping is calculated, and the plasma produced during the discharge is shown to be azimuthally homogeneous.     

Inference of a stable dispersion relation for electrocortical activity controlled by the lateral hypothalamus

A second test is undertaken for a theory of linear wave motion in electrocortical waves, under lateral hypothalamic control via regulation of damping. This test invokes a general property of linear systems, namely that wave motion with characteristic natural frequencies implies fixed phase velocities associated with each wavelength, independent of the changes in hypothalamic input. A means of testing the invariance of this dispersion relation at the point of recording is derived from a simplified biophysical model for waves in a dipole layer. The method avoids some problems implicit in direct spatio-temporal wave analysis. Results confirm that the model under test is internally consistent, and is also consistent with other findings concerning the origin and spatial nature of the EEG.     

Amplitude and phase relations of electrocortical waves regulated by transhypothalamic dopaminergic neurones: A test for a linear theory

We have previously proposed that electrocortical activity (EEG) arises as a manifestation of linear waves generated by resonance among telencephalic neurones, and that this activity is controlled in part by ascending neurones from the brain-steim, which regulate the damping of each resonance. The presentexperiments focus on a specific class of ascending neurones, the mesotelencephalic dopaminergic cells, because these cells are thought to mediate important psychological effects, and are conveniently subject to selective lesion. A critical test of the theory is undertaken, by performing selective unilateral lesion, assessing the changes in the power spectrum of the EEG attributable to lesion, and determining whether the changes in phase of the EEG correspond to that predicted from the changes in power. Results support the theory, although the model order applicable in these experiments is inadequate. The consequences of these findings for automata theory, linear network theory and their application to mammalian brains are briefly discussed.     

Study of kinetic effects arising in simulations of Farley-Buneman instability

The Farley-Buneman instability, which has been observed in the E region of the Earth’s ionosphere, is studied using fluid equations for electrons, a four-dimensional (in coordinate-velocity space) kinetic equation for ions, and Poisson’s equation. Numerical simulations with allowance for Landau damping show that the Farley-Buneman instability results in anisotropy of the ion velocity distribution function.     

Measurements of the load resistance of a poloidal antenna and the phase velocity of fast magnetosonic waves during ICR plasma heating in the L-2M stellarator

The propagation and damping of waves excited by a poloidal antenna in a hydrogen plasma at the ion cyclotron resonance (ICR) frequency were investigated. The longitudinal wavenumber and damping length of waves excited in the ohmically heated plasma of the L-2M stellarator, the dependence of the damping length of fast magnetosonic waves on the magnetic field strength, and the dependence of the antenna load resistance on the plasma density were measured. It is the first time that such complex measurements were performed in experiments on ICR heating of a hydrogen plasma at the fundamental harmonic of the ion gyrofrequency in toroidal magnetic confinement systems.     

Quantitation of a mass action of dopaminergic neurones regulating temporal damping of linear electrocortical waves

We have previously proposed that electrocortical waves are linear waves, subject to regulation by mesotelencephalic dopaminergic neurones. As a further means to test this theory, selective unilateral lesions of varying extent were made in the nucleii of origin of the dopaminergic mesotelencephalic tract. Changes in the electrocortical power spectrum were assessed by a repeated measure, between hemispheres comparison of ratio changes in power. With increasing unilateral dopamine cell damage, the animals showed increasing contralateral sensorimotor neglect. Curve fitting the ratio changes in power attributable to lesion, showed that estimates of the power of driving signals and the temporal damping moved in reverse directions with increasing extent of lesion, as expected from the theory. A further test was undertaken, to determine whether equal estimates for a transformation of surface signals were obtained from each side. Equality would not be expected if the equation for relative power were invalid. Left and right equality was found for three grades of unilateral lesion.     

Flutter in collapsible tubes: a theoretical model of wheezes

A mathematical analysis of flow through a flexible channel is examined as a model of flow-induced flutter oscillations that pertain to the production of wheezing breath sounds. The model provides predictions for the critical fluid speed that will initiate flutter waves of the wall, as well as their frequency and wavelength. The mathematical results are separated into linear theory (small oscillations) and nonlinear theory (larger oscillations). Linear theory determines the onset of the flutter, whereas nonlinear theory determines the relationships between the fluid speed and both the wave amplitudes and frequencies. The linear theory predictions correlate well with data taken at the onset of flutter and flow limitation during experiments of airflow in thick-walled collapsible tubes. The nonlinear theory predictions correlate well with data taken as these flows are forced to higher velocities while keeping the flow rate constant. Particular ranges of the parameters are selected to investigate and discuss the applications to airway flows. According to this theory, the mechanism of generation of wheezes is based in the interactions of fluid forces and friction and wall elastic-restoring forces and damping. In particular, a phase delay between the fluid pressure and wall motion is necessary. The wave speed theory of flow limitation is discussed with respect to the specific data and the flutter model.     

On the propagation of a wave front in viscoelastic arteries

In formulating a mathematical model of the arterial system, the one-dimensional flow approximation yields realistic pressure and flow pulses in the proximal as well as in the distal regions of a simulated arterial conduit, provided that the viscoelastic damping induced by the vessel wall is properly taken into account. Models which are based on a purely elastic formulation of the arterial wall properties are known to produce shocklike transitions in the propagating pulses which are not observed in man under physiological conditions. The viscoelastic damping characteristics are such that they are expected to reduce the tendency of shock formation in the model. In order to analyze this phenomenon, the propagation of first and second-order pressure waves is calculated with the aid of a wave front expansion, and criteria for the formation of shocks are derived. The application of the results to the human arterial system show that shock waves are not to be expected under normal conditions, while in case of a pathologically increased pressure rise at the root of the aorta, shocklike transitions may develop in the periphery. In particular, it is shown that second-order waves never lead to shock formation in finite time for the class of initial conditions and mechanical wave guides which are of interest in the mammalian circulation.     

High-Frequency Quasi-Potential Waves in the Plasma Formed under Tunnel Ionization of Atoms

The dispersion law and collisionless damping rate of quasi-potential waves in the plasma formed upon tunnel ionization of gas atoms in the field of a short pulse of circularly or linearly polarized radiation are found. It is shown how the frequency and damping rate of quasi-potential waves depend on the wave propagation direction relative to the symmetry axis of the photoelectron distribution. It is established that, in plasma with a toroidal photoelectron velocity distribution, weakly damped waves with a linear dispersion law and frequency above the electron plasma frequency can propagate in a wide range of angles. In the case of a bi-Maxwellian photoelectron distribution, the frequency of weakly damped waves is comparable with the electron plasma frequency and the anisotropy of electron motion manifests itself in relatively small corrections to the dispersion law.     

Viscous damping of Alfvén surface waves in the solar atmosphere

The dispersion relation for the propagation of viscous Alfvén surface waves along viscous plasmaplasma interface has been derived. Two modes of Alfvén surface waves are found to propagate with their characteristics depend on the interface parameters like magnetic field, density ratio, viscosity, etc. The viscous damping of Alfvén surface waves has been studied in the astrophysical point of view. The damping length of Alfvén surface waves due to viscosity in the solar atmosphere has been estimated.     

Transmission characteristics of axial waves in blood vessels

The elastic behavior of blood vessels can be quantitatively examined by measuring the propagation characteristics of waves transmitted by them. In addition, specific information regarding the viscoelastic properties of the vessel wall can be deduced by comparing the observed wave transmission data with theoretical predictions. The relevance of these deductions is directly dependent on the validity of the mathematical model for the mechanical behavior of blood vessels used in the theoretical analysis. Previous experimental investigations of waves in blood vessels have been restricted to pressure waves even though theoretical studies predict three types of waves with distinctly different transmission characteristics. These waves can be distinguished by the dominant displacement component of the vessel wall and are accordingly referred to as radial, axial and circumferential waves. The radial waves are also referred to as pressure waves since they exhibit pronounced pressure fluctuations. For a thorough evaluation of the mathematical models used in the analysis it is necessary to measure also the dispersion and attenuation of the axial and circumferential (torsion) waves.

To this end a method has been developed to determine the phase velocities and damping of sinusoidal axial waves in the carotid artery of anesthetized dogs with the aid of an electro-optical tracking system. For frequencies between 25 and 150 Hz the speed of the axial waves was between 20 and 40 m/sec and generally increased with frequency, while the natural pressure wave travelled at a speed of about 10 m/sec. On the basis of an isotropic wall model the axial wave speed should however be approximately 5 times higher than the pressure wave speed. This discrepancy can be interpreted as an indication for an anisotropic behavior of the carotid wall. The carotid artery appears to be more elastic in the axial than in the circumferential direction.     

Contributions of noradrenergic neurones of the locus coeruleus to the temporal damping of linear electrocortical waves

The preceeding paper (Wright et al. 1985a) gives evidence that mesotelencephalic dopaminergic neurones regulate gross electrocortical waves with linear properties, by influencing the strength of their driving signals and temporal damping. The present study further generalises the findings to ascending noradrenergic neurones, which have different fields of termination to dopaminergic fibres. It is shown that: Estimates of the major groups of natural frequencies for the telencephalic system obtained from curve-fitting the ratio changes in the power spectrum attributable to unilateral noradrenergic neurone lesion, are again centered about the frequencies of the major cerebral rhythms. Estimates of electrode transfer characteristics, using parameters obtained from curve fitting ratio changes in power, in conjunction with the raw left and right power spectra, are again found to be equal left and right, as required by the theoretical derivation. Changes in relative amplitude of electrocortical waves and their relative phase are significantly in accord with the relationship expected from theory.     

Quantitation of mitral annular oscillations and longitudinal "ringing" of the left ventricle: a new window into longitudinal diastolic function.

For diastolic function (DF) quantification, transmitral flow velocity has been characterized in terms of the geometric features of a triangle (heights, widths, areas, durations) approximating the E-wave contour, whereas mitral annular velocity has only been characterized by E'-wave peak amplitude. The fact that E-waves convey global DF information, whereas annular E'-waves provide longitudinal DF information, has not been fully characterized, nor has the physiological legitimacy of combining fluid motion (E)- and tissue motion (E')-derived measurements into routinely used indexes (E/E') been fully elucidated. To place these Doppler echo measurements on a firmer causal, physiological, and clinical basis, we examined features of the E'-wave (and annular motion in general), including timing, amplitude, duration, and contour (shape), in kinematic terms. We derive longitudinal rather than global indexes of stiffness and relaxation of the left ventricle and explain the observed difference between E- and E'-wave durations. On the basis of the close agreement between model prediction and E'-wave contour for subjects having normal physiology, we propose damped harmonic oscillation as the proper paradigm in which to view and analyze the motion of the mitral annulus during early filling. Novel, longitudinal indexes of left ventricular stiffness, relaxation, viscosity, and stored (end-systolic) elastic strain can be determined from the E'-wave (and any subsequent waves) by modeling annular motion during early filling as damped harmonic oscillation. A subgroup exploratory analysis conducted in diabetic subjects (n = 9) and nondiabetic controls (n = 12) indicates that longitudinal DF indexes differentiate between these groups on the basis of longitudinal damping (P < 0.025) and longitudinal stored elastic strain (P < 0.005).     

The Dissipation and Dispersion of Small Waves in Arteries and Veins with Viscoelastic Wall Properties

Theoretical and experimental evidence suggests that the dissipation of high frequency pressure waves in blood vessels is caused primarily by the viscoelastic behavior of the vessel wall. In this theoretical analysis the vessels are considered as fluid-filled circular cylindrical shells whose walls have isotropic and homogeneous viscoelastic properties and are subjected to an initial axial stretch and a transmural pressure. If the wall material is incompressible and behaves as a Voigt solid in shear, the results predict a decrease in wave amplitude per wavelength which is essentially independent of frequency over a wide range. This finding is in qualitative agreement with recent experiments on anesthetized dogs. A parametric study also shows a great sensitivity of the dissipation to changes in transmural pressure and axial stretch. Axisymmetric waves are only mildly dispersive, while all nonaxisymmetric waves are highly dispersive and exhibit much stronger damping per wavelength at low frequencies than do axisymmetric waves.