Nonlinear ineraction of an annular electron beam with azimuthal surface waves

A nonlinear theory is developed that describes the interaction between an annular electron beam and an electromagnetic surface wave propagating strictly transverse to a constant external axial magnetic field in a cylindrical metal waveguide partially filled with a cold plasma. It is shown theoretically that surface waves with positive azimuthal mode numbers can be efficiently excited by an electron beam moving in the gap between the plasma column and the metal waveguide wall. Numerical simulations prove that, by applying a constant external electric field oriented along the waveguide radius, it is possible to increase the amplitude at which the surface waves saturate during the beam instability. The full set of equations consisting of the waveenvelope equation, the equation for the wave phase, and the equations of motion for the beam electrons is solved numerically in order to construct the phase diagrams of the beam electrons in momentum space and to determine their positions in coordinate space (in the radial variable-azimuthal angle plane).     

Influence of the shape of the cross section of a plasma-dielectric interface on the dispersion properties of high-frequency azimuthal surface modes

Theoretical study of the propagation of a packet of surface electromagnetic surface waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide within the frequency range that is higher than upper hybrid resonance is carried out. The waveguide is partially filled by plasma and immersed into axial magnetic field. The cross section of the plasma column is assumed to differ from circular shape. The effect of this shape on the dispersion properties of azimuthal surface modes is investigated by the method of successive approximations. The fields of the waves and their eigenfrequencies are determined up to terms of the second order in the deviation of the plasma cross section shape from the ring one. The correction to the eigenfrequency of azimuthal surface modes caused by this feature of the plasma column section is proved to increase with decreasing the external magnetic field and increasing the value of the dielectric constant of the dielectric, that separates the plasma from the metal wall of the waveguide. The spectral composition of the wave packet, in the form of which these modes propagate, is studied. The amplitudes of the satellite harmonics of these modes are found to increase with increasing the plasma density and decreasing the external magnetic field.     

Spectral Properties of Plasma Waves in Periodic Plasma-Filled Structures

The dispersion properties and field distribution of plasma waves in a periodic plasma-filled waveguide are correctly analyzed for the first time with allowance for all spatial harmonics. It is shown that the plasma wave spectrum has a zonal structure and a lower cutoff frequency. The widths of the forbidden bands and the lower cutoff frequency are determined by the waveguide corrugation depth. For a planar periodic plasma-filled waveguide, the allowed and forbidden frequency bands are evaluated analytically. The waveguide periodicity substantially influences the field of the plasma waves at frequencies close to the forbidden bands. This leads to the formation of regions in which the energy density of plasma waves exceeds the average level by more than one order of magnitude. This effect is related to the contribution from the higher spatial harmonics.     

Asymmetric long-wavelength surface waves in magnetized plasma waveguides entirely filled with plasma

A theoretical study is made of the dispersion properties of electromagnetic surface waves with arbitrary azimuthal mode numbers and with a small axial wavenumber in cylindrical metal waveguides entirely filled with a radially inhomogeneous, cold, magnetized plasma. The frequency ranges in which the extraordinary polarized waves under analysis can exist are found, and the conditions for their resonant interaction with an ordinary bulk wave are determined. The eigenfrequency of these surface waves is investigated as a function of the plasma parameters, the axial wavenumber, and the azimuthal mode number. Simple analytic expressions are derived for the eigenfrequencies of the surface waves under study propagating in a homogeneous plasma waveguide.     

Surface flute modes in a rippled magnetic field

An analytic study is made of the propagation of an electromagnetic wave packet with a zero axial number of the fundamental harmonic in a cylindrical metal waveguide partially filled with a plasma placed in a rippled magnetic field. The fields of the waves are determined to second order in the small ripple parameter. It is shown that the ripple-induced correction to the eigenfrequency of the waves is a second-order quantity.     

Excitation of azimuthal surface modes by relativistic flows of electrons in the high-frequency range

Excitation of extraordinarily polarized azimuthal surface eigenwaves is shown to be possible in the frequency range above the upper hybrid resonance in waveguides with metal walls which are partially filled by cold magnetoactive plasma. Interaction of these waves with flows of electrons which rotate around the plasma column in the narrow gap separating the plasma from the wall of the waveguide is studied. Conditions of resonant interaction of the beam with the mentioned high-frequency azimuthal surface waves are shown by numerical methods to be reachable ones in the case of enough strong external magnetic fields without passing to the field of ultra-relativistic velocities of the beam.     

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.     

The Role of Resonance Frequency of the Plasmons in Electromagnetic Wave Scattering Process from a Dielectric Covered Metallic Rod Placed in a Plasma Antenna

The electromagnetic wave scattering due to excitation of surface plasmons from a metallic rod with dielectric layer embedded in the long plasma column is investigated. In the first part, for short-wavelength waves by investigating the variations of surface polarized charge density on the boundaries, the resonance frequencies and the effective factors on it such as the geometrical dimensions, the radius of the metal, the dielectric thickness, and the plasma radius will be analyzed. In the second part, for presenting an exact analysis and categorizing types of resonant frequency to the dominant resonant frequency and subsidiary resonant frequency of the plasmons, the scattering of long-wavelength waves from the mentioned object will be reviewed. In both cases, the backscattering cross section which is a scale of the scattered power in the direction of incident will be presented.     

Effect of the radial plasma profile on the surface wave structure in a plasma waveguide

A study is made of the effect of the radial plasma profile on the spectra and fields of the surface waves in a plasma waveguide. It is shown that the surface wave is localized in the region where the plasma permittivity vanishes. In waveguides with smoother radial plasma profiles, the region where the surface wave can exist is narrower and may even disappear.     

Resonant effect of the noncircular shape of the plasma surface on the dispersion properties of extraordinary azimuthal surface modes in magnetoactive waveguides

A theoretical study is made of the resonant effect of the shape of the cross section of the plasma column on the propagation of a packet of extraordinary electromagnetic waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide in an axial magnetic field. The waveguide is assumed to be partially filled with a plasma. The effect of the noncircular shape of the plasma cross section on the dispersion properties of surface eigenmodes propagating strictly transverse to the external magnetic field is investigated by the method of successive approximations for the case in which the angular period of the wave perturbations is twice the ripple period of the interface between the plasma and the dielectric. In this resonant case, the fields and eigenfrequencies of the eigenmodes are determined to second order in the small parameter describing the rippling of the plasma-dielectric interface.     

Surface waves in plasma waveguides with a smooth transverse inhomogeneity

A theory of cylindrical surface waves in a circular waveguide filled with a smoothly inhomogeneous plasma is presented. For a special radial profile of the plasma density, dispersion relations for the complex frequencies of surface waves are derived analytically. The dispersion relations are solved numerically (in the long-wavelength limit) and numerically. It is shown that there are two types of surface waves. When passing to the case of a sharply bounded plasma, one of the waves becomes an ordinary surface wave, while the other becomes strongly damped.     

Effect of the shape of the cross section of a plasma-dielectric interface on the dispersion properties of azimuthal surface modes

A theoretical study is made of the propagation of a packet of surface electromagnetic waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide partially filled with plasma in an axial magnetic field. The cross section of the plasma column is assumed to be noncircular. The effect of the noncircular shape of the plasma cross section on the dispersion properties of azimuthal surface modes is investigated by the method of successive approximations. The fields of the waves and their eigenfrequencies are determined to second order in a small parameter.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field

Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.     

Excitation of high-frequency azimuthal surface waves by an annular electron beam in a waveguide with a noncircular interface of the plasma column

An initial stage of the interaction of an electron beam ring rotating along Larmor orbits in a gap between the plasma column and a circular metal chamber of a cylindrical waveguide with extraordinarily polarized electromagnetic waves of the surface type is studied. These waves propagate along the azimuthal angle across an axial magnetic field in the range above the upper hybrid frequency. Using numerical analysis of the dispersion relation, it is shown that by the aid of an appropriate choice of the shape of the plasmavacuum interface one can achieve a significant increasing of growth rates of the resonant beam instability of these waves.     

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.     

Surface Plasmon Resonance Intensification by Cavity-Ring Plasma Structure in the Giga-Hertz Regime

In this paper, we propose a novel sub-wavelength plasma structure that can effectively enhance surface plasmon resonance (SPR) to achieve a significant local field. On the basis of a plasma ring structure, we add a slit and two thin plasma layers, working as a metal-insulator-metal (MIM) waveguide at a specific incident wave frequency and generate the Fabry-Perot resonance (FPR). The structure thus couples the incident wave energy to the vicinity of the slit and intensifies the SPR inside the plasma ring. In addition, we also find the coupling and competing between SPR and FPR. For the coupling mode, the average field enhancement in the ring is up to a factor of 9.7. Moreover, the optimized thickness of the plasma layer is much thinner than the skin depth of the plasma to ensure the incident wave easily entering the MIM waveguide. We further calculate the dispersion relationship of surface plasmon polaritons in the waveguide cavity. The simulation results and theoretical dispersion function are in good agreements.

     

A multiscale approach for modelling wave propagation in an arterial segment

A mathematical model of blood flow through an arterial vessel is presented and the wave propagation in it is studied numerically. Based on the assumption of long wavelength and small amplitude of the pressure waves, a quasi-one-dimensional (1D) differential model is adopted. It describes the non-linear fluid-wall interaction and includes wall deformation in both radial and axial directions. The 1D model is coupled with a six compartment lumped parameter model, which accounts for the global circulatory features and provides boundary conditions. The differential equations are first linearized to investigate the nature of the propagation phenomena. The full non-linear equations are then approximated with a numerical finite difference method on a staggered grid. Some numerical simulations show the characteristics of the wave propagation. The dependence of the flow, of the wall deformation and of the wave velocity on the elasticity parameter has been highlighted. The importance of the axial deformation is evidenced by its variation in correspondence of the pressure peaks. The wave disturbances consequent to a local stiffening of the vessel and to a compliance jump due to prosthetic implantations are finally studied.     

Propagation of MHD waves in a plasma in a sheared magnetic field with straight field lines

The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is solved using a simplified model: a cold plasma is inhomogeneous in one direction, and the magnetic field lines are straight. The waves are assumed to travel in the plane perpendicular to the radial coordinate (i.e., the coordinate along which the plasma and magnetic field are inhomogeneous). It is shown that the character of the singularity at the resonance surface is the same as that in a homogeneous magnetic field. It is found that the shear gives rise to the transverse dispersion of Alfvén waves, i.e., the dependence of the radial component of the wave vector on the wave frequency. In the presence of shear, Alfvén waves are found to propagate across magnetic surfaces. In this case, the transparent region is bounded by two turning points, at one of which, the radial component of the wave vector approaches infinity and, at the other one, it vanishes. At the turning point for magnetosonic waves, the electric and magnetic fields are finite; however, the radial component of the wave vector approaches infinity, rather than vanishes as in the case with a homogeneous field.     

Influence of the outer-magnetospheric magnetohydrodynamic waveguide on the reflection of hydromagnetic waves from a shear flow at the magnetopause

The coefficient of reflection of a fast magnetosonic wave incident on the magnetosphere from the solar wind is studied analytically in the framework of a plane-stratified model of the medium with allowance for the transverse inhomogeneity of the magnetosphere and a jump of the plasma parameters at the magnetopause. Three factors decisively affecting the properties of reflection are taken into account: the shear flow of the solar wind plasma relative to the magnetosphere; the presence of a magnetospheric magnetohydrodynamic waveguide caused by the transverse plasma inhomogeneity; and the presence of an Alfvén resonance deep in the magnetosphere, where the oscillation energy dissipates. If the solar wind velocity exceeds the wave phase velocity along the magnetopause, then the wave energy in the solar wind is negative and such a wave experiences overreflection. In the opposite case, the wave energy is positive and the wave is reflected only partially. The wave reflection has a pronounced resonant character: the reflection coefficient has deep narrow minima or high narrow maxima at the eigenfrequencies of the magnetospheric waveguide. For other frequencies, the reflection coefficient only slightly differs from unity. The wave energy influx into the magnetosphere is positive for waves with both positive and negative energies. For waves with a negative energy, this is a consequence of their overreflection, because the flux of negative energy carried away by the reflected wave exceeds the incident flux of negative energy.     

Molecular dynamics simulations of polyampholytes inside a slit

Alternating and diblock polyampholytes confined in a slit with and without an electric field have been simulated by the molecular dynamics method with a Langevin thermostat. It is shown that the slit has a strong effect on the properties of the polyampholyte. The effect is stronger when the electric field is weak, or the temperature is not too high. When a polyampholyte chain moves close to the slit wall, its radius of gyration perpendicular to the wall becomes smaller but that parallel to the wall becomes larger. Owing to the confinement of the slit, the polyampholyte chain closer to the slit wall tends to lie on the wall and becomes more flat. The width of the slit has only a little influence on the properties of solutions near the slit wall, values of several physical statistics are very close with different widths. However, when the electric field strength is strong enough in a narrow slit, the obtained properties obviously differ.